# 4 Finite Control Volume Analysis Introduction Reynolds Transport Theorem Conservation of Mass

Size: px
Start display at page:

Download "4 Finite Control Volume Analysis Introduction Reynolds Transport Theorem Conservation of Mass"

Transcription

1 iv Bourdon Gage Pressure Transducer Manometer Piezometer U-tube and inclined-tube manometers Forces on Plane Surfaces Forces on Curved Surfaces Buoyancy Fully Submerged Bodies Partially Submerged Bodies Buoyancy effects within fluids Rigid-Body Motion of Fluids Liquid with Constant Acceleration Liquid in a Rotating Container Problems Kinematics and Streamline Dynamics Introduction Kinematics Tracking the Movement of Fluid Elements The Material Derivative Flow Rates Dynamics of Flow Along a Streamline Applications of the Bernoulli Equation Flow through Orifices Flow Measurement Pitot-static tube Venturi meter Trajectory of a Liquid Jet Compressibility Effects Viscous Effects Branching Conduits Curved Flows and Vortices Forced Vortices Cylindrical forced vortex Spiral forced vortex Free Vortices Cylindrical free vortex Spiral free vortex Problems Finite Control Volume Analysis Introduction Reynolds Transport Theorem Conservation of Mass

3 vi Velocity Potential Two-Dimensional Potential Flows Fundamental and Composite Potential Flows Principle of Superposition Uniform Flow Line Source/Sink Flow Line Vortex Flow Spiral Flow Towards a Sink Doublet Flow Flow Around a Half-Body Rankine Oval Flow Around a Circular Cylinder Turbulent Flow Occurrence of Turbulence Turbulent Shear Stress Mean Steady Turbulent Flow Conservation of Energy Problems Dimensional Analysis and Similitude Introduction Dimensions in Equations Dimensional Analysis Conventional Method of Repeating Variables Alternative Method of Repeating Variables Method of Inspection Dimensionless Groups as Force Ratios Dimensionless Groups in Other Applications Modeling and Similitude Problems Flow in Closed Conduits Introduction Steady Incompressible Flow Friction Effects in Laminar Flow Friction Effects in Turbulent Flow Practical Applications Estimation of Pressure Changes Estimation of Flow Rate for a Given Head Loss Estimation of Diameter for a Given Flow Rate and Head Loss Head Losses in Noncircular Conduits Empirical Friction-Loss Formulae Local Head Losses Pipelines with Pumps or Turbines Water Hammer

4 vii 7.7 Pipe Networks Nodal Method Loop Method Building Water-Supply Systems Specification of Design Flows Specification of Minimum Pressures Determination of Pipe Diameters Problems Turbomachines Introduction Mechanics of Turbomachines Hydraulic Pumps and Pumped Systems Flow Through Centrifugal Pumps Efficiency Dimensional Analysis Specific Speed Performance Curves System Characteristics Limits on Pump Location Multiple-Pump Systems Variable-Speed Pumps Fans Performance Characteristics of Fans Affinity Laws of Fans Specific Speed Hydraulic Turbines and Hydropower Impulse Turbines Reaction Turbines Practical Considerations Problems Flow in Open Channels Introduction Basic Principles Steady-State Continuity Equation Steady-State Momentum Equation Darcy Weisbach equation Manning equation Velocity distribution Surface-Wave propagation Steady-State Energy Equation Energy grade line Specific energy Water-Surface Profiles

5 viii Profile Equation Classification of Water-Surface Profiles Hydraulic Jump Computation of Water-Surface Profiles Direct-integration method Direct-step method Standard-step method Practical considerations Problems Drag and Lift Introduction Fundamentals Friction and Pressure Drag Drag and Lift Coefficients Flow Over Flat Surfaces Flow over Curved Surfaces Estimation of Drag Coefficients Drag on Flat Surfaces Drag coefficient on hydrodynamically smooth surfaces Drag coefficient on hydrodynamically rough surfaces Drag coefficient on intermediate surfaces Drag coefficient with flow normal to a flat plate Drag on Spheres and Cylinders General characteristics Analytic expressions for drag coefficients of spheres Terminal velocities of spheres and other bodies Drag on Vehicles Drag on Ships Drag on Two-Dimensional Bodies Drag on Three-Dimensional Bodies Drag on Composite Bodies Drag on Miscellaneous Objects Added Mass Estimation of Lift Coefficients Lift on Airfoils Lift on Airplanes Lift on Hydrofoils Lift on a Spinning Sphere in Uniform Flow Problems Boundary-Layer Flow Introduction Laminar Boundary Layers Blasius Solution for Plane Surfaces

6 ix Blasius Equations for Curved surfaces Turbulent Boundary Layers Analytic Formulation Turbulent Boundary Layer on a Flat Surface Flow in the viscous sublayer Flow in the transition layer Flow in the turbulent layer One-seventh-power law velocity distribution Boundary Layer Thickness and Shear Stress Applications Displacement Thickness Momentum Thickness Momentum Integral Equation General Formulations for Self-Similar Velocity Profiles Mixing-Length Theory of Turbulent Boundary Layers Smooth Flow Rough Flow Velocity-Defect Law One-Seventh-Power-Law Distribution Boundary Layers in Closed Conduits Smooth Flow in Pipes Rough Flow in Pipes Notable Contributors to Understanding Flow in Pipes Problems Compressible Flow Introduction Principles of Thermodynamics The Speed of Sound Thermodynamic Reference Conditions Isentropic Stagnation Condition Isentropic Critical Condition Basic Equations of One-Dimensional Compressible Flow Steady One-Dimensional Isentropic Flow Effect of Area Variation Choked Condition Flow in Nozzles and Diffusers Converging nozzle Converging-diverging nozzle Normal Shocks Steady One-Dimensional Non-Isentropic Flow Adiabatic Flow with Friction Isothermal Flow with Friction Diabatic Frictionless Flow Application of Fanno and Rayleigh Relations to Normal Shocks

7 x 12.9 Oblique Shocks, Bow Shocks, and Expansion Waves Oblique Shocks Bow Shocks and Detached Shocks Isentropic Expansion Waves Problems A Units and Conversion Factors 1015 A.1 Units A.2 Conversion Factors B Fluid Properties 1019 B.1 Water B.2 Air B.3 The Standard Atmosphere B.4 Common Liquids B.5 Common Gasses B.6 Nitrogen C Properties of Areas and Volumes 1027 C.1 Areas C.2 Properties of Circles and Spheres C.2.1 Circles C.2.2 Spheres C.3 Volumes D Pipe Specifications 1031 D.1 PVC Pipe D.2 Ductile-Iron Pipe D.3 Concrete Pipe D.4 Physical Properties of Common Pipe Materials

8 Chapter 4 Finite Control Volume Analysis 4.1 Introduction The motion and properties of a fluid can be described using a variety of reference frames, with different reference frames giving different perspectives of the flow. The two reference frames that are most commonly used in fluid mechanics are: (1) a reference frame moving with a specified fluid element that contains a defined mass of fluid, and (2) a reference frame fixed in space. A reference frame moving with a fluid element containing a defined mass of fluid can be regarded as the fundamental reference frame, since the laws of motion and thermodynamics are directly applicable to a defined fluid mass as it moves within a fluid continuum. In contrast, a fixed reference frame describes the motion of (different) fluid elements as they pass by a fixed point in space, which is the usual perspective from which fluid motions are observed and measured. The equations governing the behavior of fluids are typically formulated by first applying the fundamental laws to a specified fluid element or a defined fluid mass, and then transforming the defined-fluid-mass equations into equivalent fixed-reference-frame equations to facilitate practical applications. Lagrangian and Eulerian reference frames. A Lagrangian reference frame moves with a fluid element that contains a fixed mass of fluid, and fluid properties within the fluid element are only observed to change with time. For example, the velocity, v, of a fluid element in a Lagrangian reference frame is described in the form, v(t), where t is the time. An Eulerian reference frame is fixed in space, and changes in fluid properties are described at fixed locations. For example, the velocity field of a fluid in an Eulerian reference frame is described in the form v(x,t), where x is the location and t is the time. From a practical viewpoint, we are usually interested in the behavior of fluids at particular locations in space, in which case an Eulerian reference frame is preferable. The complicating factor in working with Eulerian reference frames is that the fundamental equations of fluid motion and thermodynamics are all stated for fluid elements in Lagrangian reference frames. For example, Newton s second law states that the sum of the forces on any fluid element (as it moves within the fluid continuum) is equal to the mass of fluid within the fluid element multiplied by the acceleration of the fluid element. To transform the fundamental equations of fluid motion and thermodynamics into useful equations in Eulerian reference frames, it is necessary to understand the relationship between Lagrangian equations and Eulerian equations, and the transformation of Lagrangian equations into Eulerian equations is generally done using Reynolds transport theorem. 253

9 322 Intake Discharge Q Pump? Figure 4.41: Flow through a pump 4.2. In the United States, flow rates through shower heads are regulated to be no greater than 9.5 L/min (2.5 gpm) under any water-pressure condition likely to be encountered in a home. Water pressures in homes are typically less than 550 kpa (80 psi). A practical shower head will deliver water at a velocity of at least 5 m/s. If nozzles in a shower head can be manufactured with diameters of 0.75 mm, what is the maximum number nozzles that would be required to make a practical shower head? 4.3. An air conditioner delivers air into a 200-m 3 room at a rate of 3.5 m 3 /min. Air from the room is removed by a 0.6 m 0.8 m duct. Assuming steady-state conditions and incompressible flow, what is the average velocity of air in the exhaust duct? 4.4. At a particular section in a 100-mm diameter pipe, the velocity is measured as 1200 m/s. Downstream of this section, the flow is expanded to a 300-mm pipe in which the velocity and density of the air flow is measured as 700 m/s and 1.1 kg/m 3, respectively. If flow conditions are steady, estimate the density of the air at the upstream (100-mm diameter) section Air enters a heat exchanger at a rate of 200 kg/h and exits at a rate of 195 kg/h, as illustrated in Figure The purpose of the heat exchanger is to dehumidify the air. Estimate the rate at which liquid water drains from the system. 200 kg/h air Heat Exchanger 195 kg/h air Liquid water Figure 4.42: Flow through a heat exchanger 4.6. A piston moving at 10 mm/s displaces air from a 100-mm diameter cylinder into a 25-mm discharge line as shown in Figure Assuming that compressibility effects can be neglected, what is the volumetric flow rate and velocity in the discharge line? 100 mm 10 mm/s Piston Air Cylinder 25 mm Discharge line Figure 4.43: Air flow driven by a piston

10 Air enters a 1.2-m 3 storage tank at a rate of 0.5 m 3 /s, and at a temperature of 20 C and pressure of 101 kpa as shown in Figure When air is released from the tank at a rate of 0.3 m 3 /s, the pressure of the released air is measured as 150 kpa, and a weight scale indicates that the weight of the air in the tank is increasing at a rate of 0.1 kg/s. Estimate the temperature and the density of the air that is being released from the tank. 0.5 m 3 /s Air 20 o C Air storage tank 0.3 m 3 /s 101 kpa Weight scale Figure 4.44: Air storage in a tank 150 kpa 4.8. Pipelines containing gasoline, water, and methanol merge to create a mixture as shown in Figure All fluids are at 20 C, and the known diameters and fluid velocities in the merging pipes are also shown in Figure (a) What is the volumetric flow rate of the mixture? (b) What is the density of the mixture? Gasoline Water Methanol Mixture Diameter Velocity Pipe (mm) (m/s) Fluid Gasoline Water Methanol 4 50? Mixture Figure 4.45: Mixing in pipes 4.9. Water flows from a garden hose into a sprinkler at a volume flow rate, Q, of 20 L/min. The flow exits the sprinkler via four rotating arms as shown Figure The radius, R, of the sprinkler is 0.2 m, and the diameter of each discharge port is 10 mm. At what rate, ω, would the sprinkler have to rotate such that the absolute velocity of the discharged water is equal to zero. Can you visualize how this would look to a stationary observer? D R Q ω Figure 4.46: Rotating sprinkler The flow in a pipeline is divided as shown in Figure The diameter of the pipe at Sections

11 324 1, 2, and 3 are 100 mm, 75 mm, and 50 mm, respectively, and the flow rate at Section 1 is 10 L/s. Calculate the volumetric flow rate and velocity at Section mm 10 L/s 100 mm 50 mm 3 V = 1 m/s Figure 4.47: Divided flow Water at 20 C is flowing in a 100-mm diameter pipe at an average velocity of 2 m/s. If the diameter of the pipe is suddenly expanded to 150 mm, what is the new velocity in the pipe? What are the volumetric and mass flow rates in the pipe? A 200-mm diameter pipe divides into two smaller pipes, each of diameter 100 mm. If the flow divides equally between the two smaller pipes and the velocity in the 200-mm pipe is 1 m/s, calculate the velocity and flow rate in each of the smaller pipes Water flows steadily through the round pipe shown in Figure The entrance velocity is constant, u = U 0, and the exit velocity approximates turbulent flow with a velocity distribution ( u(r) =u max 1 r ) 1 7 (4.170) R (a) Use the velocity distribution given by Equation to determine the volume flow rate in the pipe in terms of u max and R. (b) Determine the ratio U 0 /u max. U 0 u(r) Inflow r R Ou low x = 0 x = L Figure 4.48: Flow through a pipe Consider the 1-m 3 storage tank shown in Figure Initially, the density of the liquid in the tank is 1000 kg/m 3. At a particular instant, the inlet valve is opened and a fluid of density 900 kg/m 3 flows into the tank at a rate of 100 L/min. At this same instant, the outlet valve is opened and adjusted such that the liquid level in the tank is maintained at a constant elevation, a mixer is also turned on to ensure that the liquid in the tank is well mixed. How long will it take after the valves are open and the mixer turned on for the density of the liquid

12 325 in the tank to decline from 1000 kg/m 3 to 950 kg/m 3? If the system is left operating long enough, what will be the ultimate density of the liquid in the tank? 100 L/min 900 kg/m 3 1 m 3 Mixer Storage tank Figure 4.49: Flow through a tank Water drains from a funnel that has a top diameter of 20 cm, a bottom (outlet) diameter of 0.5 cm, and a height of 25 cm. The exit velocity is related to the depth of water, h, inthe funnel by the relation V = 2gh Determine the relationship between the rate of change of depth (dh/dt) and the depth (h). What is the rate of change of depth when the funnel is half full? Water enters the cylindrical reservoir shown in Figure 4.50 through a pipe at point A at a rate of 2.80 L/s, and exits through a 5-cm diameter orifice at B. The diameter of the cylindrical reservoir is 60 cm, and the velocity, v, of water leaving the orifice is given by v = 2gh where h is the height of the water surface (in the reservoir) above the orifice. How long will it take for the water surface in the reservoir to drop from h =2mtoh =1m? [Hint: You might need to use integral tables.] 60 cm h 2.80 L/s A B v = 2gh Figure 4.50: Water exiting a cylindrical reservoir Water leaks out of a 5-mm diameter hole in the side of a large cup as shown in Figure Estimate how long it takes for the cup to go from being full to being half-full. [You can assume that the velocity at the outlet is 2gh where h is the height of the water above the outlet. Also, you might need to know that the volume of a cone is πr 2 h/3.]

13 cm 50 cm 10 cm 20 cm Figure 4.51: Leaking cup A 2-m high cone with a 1-m diameter base is turned upside down to form a reservoir and is filled with water. A drain hole in the side of the reservoir is opened to release water, and the release rate, Q, is given by Q =7.8 h 0.02 where Q is in L/s and h is the height of the water surface above the bottom of the reservoir in meters. Estimate how long it will take for the reservoir to empty half of its volume. [The volume of a cone is πr 2 h/3] A storage tank with a volume of 0.1 m 3 contains compressed air. Air is released from the tank by opening a valve connected to a 10-mm diameter tube. At the instant that the valve is opened, air exits at a velocity of 200 m/s. Find the density and the rate of change of density of the air in the tank instant of valve opening under the following conditions: (a) the density of the air exiting the tank is 5 kg/m 3, and (b) the air exiting the tank has a temperature of 15 C and an absolute pressure of 350 kpa. Section 4.4: Conservation of Linear Momentum Calculate the momentum correction coefficient, β, for the following velocity distribution ( ] r 2 v(r) =V 0 [1 R) where v(r) is the velocity at a distance r from the centerline of a pipe of radius R Water flows over a 0.2-m high step in a 5-m wide channel, as illustrated in Figure If the flow rate in the channel is 15 m 3 /s and the upstream and downstream depths are 3.00 m and 2.79 m, respectively, calculate the force on the step.

14 m 3 /s 3 m 2.79 m 0.2 m Figure 4.52: Flow over a step Water at 20 C flows at 30 m 3 /s in a rectangular channel that is 10 m wide. The flowing water encounters 3 piers as shown in Figure 4.53, and the flow depths upstream and downstream of the piers are 3 m and 2.5 m, respectively. Estimate the force on each pier. 30 m 3 /s Side of channel Pier Pier Water surface 10 m 0.7 m (a) Plan view 3 m (b) Eleva on view 2.5 m Bo om of channel Figure 4.53: Piers in stream The 3-m high and 7-m wide spillway shown in Figure 4.54 is designed to accommodate a flow of 35 m 3 /s. 6 m 35 m 3 /s Spillway Soil 3 m Piles 10 m 1.5 m Figure 4.54: Flow over a spillway

15 328 Under design conditions the upstream and downstream flow depths are 6 m and 1.5 m respectively. The base length of the spillway is 10 m. (a) Estimate the force exerted by the water on the spillway and the shear force exerted by the spillway on the underlying soil. (2) If the shear force is resisted by piles, and each pile can resist a shear force of 100 kn, how may piles are necessary Air at standard atmospheric conditions flows past a structure as shown in Figure The flow conditions do not change in the direction perpendicular to the plane shown in Figure Upstream of the structure, the air velocity is uniform at 25 m/s, and downstream of the structure the air velocity is reduced linearly behind the structure as shown in Figure A bounding streamline expands by an amount δ between locations upstream and downstream of the structure, and within the bounding streamline the volumetric flow rate remains constant. (a) Estimate the value of δ. (b) Estimate the force of the air on the structure per unit length perpendicular to the plane of the air flow. 25 m/s 25 m/s δ 4 m y Structure Bounding streamline δ Figure 4.55: Air flow past a structure A jet pump such as that illustrated in Figure 4.56 is used in a variety of practical applications, such as in extracting water from ground-water wells. Consider a particular case in which a jet of diameter 150 mm with a velocity of 40 m/s is used to drive the flow of water in a 350-mm diameter pipe where the velocity of flow in the pipe at the location of the jet is 4 m/s. At the location of the jet, Section 1, the pressure is approximately the same across the entire cross section, and at the downstream location, Section 2, the jet momentum is dissipated and the velocity is the same across the entire cross section. Estimate the increase in the water pressure between Section 1 and Section 2. Assume water at 20 C. Jet Flow 150 mm m/s 40 m/s 350 mm Figure 4.56: Jet pump

16 A reducer is to be used to attach a 400-mm diameter pipe to a 300-mm diameter pipe. For any flow rate, the pressures in the pipes upstream and downstream of the reducer are expected to be related by p 1 γ + V 1 2 2g = p 2 γ + V 2 2 2g where p 1 and p 2 are the upstream and downstream pressures and V 1 and V 2 are the upstream and downstream velocities. Estimate the force on the reducer when water flows through the reducer at 200 L/s and the upstream pressure is 400 kpa The vertical nozzle shown in Figure 4.57 is attached to a pipe via a thread connection. The diameter of the source pipe is 25 mm, the diameter of the nozzle exit is 10 mm, the length of the nozzle is 100 mm, and the mass of the nozzle is 0.2 kg. The nozzle is oriented vertically downward and discharges water at 20 C. What force will be exerted on the thread connection when the flow through the nozzle is 20 L/min? Thread connec on Nozzle 25 mm Flow 10 mm 100 mm Figure 4.57: Flow through a vertical nozzle Air flows in a 150-mm diameter duct, and at a particular section the velocity, pressure, and temperature are measured as 70 m/s, 600 kpa, and 23 C, respectively. At a downstream section, the pressure and temperature are measured as 150 kpa and 73 C. Estimate: (a) the average velocity at the downstream section, and (b) the wall friction between the upstream and downstream sections Water under a pressure of 350 kpa flows with a velocity of 3 m/s through a 90 bend in the horizontal plane. If the bend has a uniform diameter of 300 mm, and assuming no drop in pressure, calculate the force required to keep the bend in place Water flows at 100 L/s through a 200-mm diameter vertical bend, as shown in Figure If the pressure at Section 1 is 500 kpa and the pressure at Section 2 is 450 kpa, then determine the horizontal and vertical thrust on the support structure. The volume of the bend is 0.16 m 3.

17 L/s 1 g 500 kpa Ver cal bend kpa 200 mm Support Figure 4.58: Flow through a vertical bend The bend shown in Figure 4.59 discharges water into the atmosphere. Determine the force components at the flange required to hold the bend in place. The bend lies in the horizontal plane, the interior volume of the bend is 0.25 m 3, and the mass of the bend material is 250 kg. Flange Bend Flow 60 cm 60 o Atmosphere 30 cm 10 m/s Figure 4.59: Bend The fire-hose nozzle shown in Figure 4.60 is to be held by two firemen who (working together) can support a force of 1 kn. (a) Determine the maximum flow rate in the fire hose that can be supported by the firemen. Give your answer in liters per minute. If the firemen were to let go of the nozzle, in what direction would it move? (b) If the nozzle is pointed vertically upward, how high will the water jet rise? Flow Fire hose 25 cm Nozzle 5 cm Jet Figure 4.60: Nozzle on fire hose

18 Water at 20 C flows through a 300-mm diameter pipe that discharges into the atmosphere as shown in Figure When a partially open valve extends 200 mm from the top of the pipe, the flow rate in the pipe is 0.2 m 3 /s and the (gage) pressure just upstream of the valve is 600 kpa. Estimate the force exerted by the water on the partially open valve. 600 kpa Valve 0.2 m 3 /s 300 mm Atmosphere 100 mm Figure 4.61: Flow past a partially open valve A 30 bend connects a 250-mm diameter pipe (inflow) to a 400-mm pipe (outflow). The volume of the bend is 0.2 m 3, the weight of the bend is 400 N, and the pressures on the inflow outflow sections are related by p 1 γ + V 1 2 2g = p 2 γ + V 2 2 2g The pressure at the inflow section is 500 kpa, the bend is in the vertical plane, and the bendsupport structure has a maximum allowable load of 18 kn in the horizontal direction and 40 kn in the vertical direction. Determine the maximum allowable flowrate in the bend Determine the force required to restrain the pipe junction illustrated in Figure Assume that the junction is in the horizontal plane and explain how your answer would differ if the junction were in the vertical plane. 40 L/s p = 350 kpa 150 mm Pipe junc on 30 o 40 o Flow 60 L/s 200 mm p = 400 kpa 250 mm p = 420 kpa Figure 4.62: Pipe junction The pipe connection shown in Figure 4.63 is to be used to split the flow from one pipe into two pipes.

19 g 2 m 160 mm 0.04 m 3 /s 200 mm p = 400 kpa 2 m 40 o 30 o 120 mm 3 Figure 4.63: Pipe connection The pipe connection weighs 200 lb, the pressure at the incoming section (Section 1) is 400 kpa, the flow at Section 1 is 0.04 m 3 /s, the flow divides such that 60% goes to Section 2 and 40% goes to Section 3, and the temperature of the water is 20 C. Determine the force required to support the connection Find the x- and y-force components on the horizontal T-section shown in Figure Neglect viscous effects. 12 m/s 500 kpa 60 mm 60 mm y x 8 m/s 40 mm Figure 4.64: T-section of pipe Water is flowing into and discharging from a pipe U-section as shown in Figure At Flange 1, the total absolute pressure is 200 kpa, and 30 kg/s flows into the pipe. At Flange 2, the total pressure is 150 kpa. At Location 3, 8 kg/s of water discharges to the atmosphere, which is at 100 kpa. The center of the pipe at Flange 2 is located 4.0 m above the center of the pipe at Flange 1. The weight of the water in the bend is 280 N, and the weight of the bend is 200 N. Determine the total x- and z- forces (including their directions) to be supported by the two flanges connecting the pipe. Take the momentum-flux correction factor to be 1.03.

20 mm 8 kg/s mm Atmosphere (p = 100 kpa) 22 kg/s 4.0 m p = 150 kpa z 1 50 mm Flange x g 30 kg/s p = 200 kpa Figure 4.65: Pipe U-section Water flowing at 20 L/s in a 150-mm diameter pipeline is delivered to two separate pipelines via the connection shown in Figure At the connection, one outflow pipeline has a diameter of 100 mm, makes an angle of 45 with the inflow pipeline, and carries 8 L/s, while the other outflow pipeline has a diameter of 120 mm, makes an angle of 60 with the inflow pipeline, and carries 12 L/s. The pressure in the inflow pipe is 500 Pa and the connection is in the horizontal plane. (a) Estimate the pressures in the outflow pipelines, and (b) determine the force on the connection. 8 L/s 100 mm 20 L/s 500 Pa 150 mm 45 o 60 o Flange 120 mm Figure 4.66: Pipe junction 12 L/s The thin-plate orifice shown in Figure 4.67 causes a large pressure drop. For 20 C water flow at 500 gal/min, with a pipe D = 100 mm and orifice d = 60 mm, p 1 p kpa. If the wall friction is negligible, estimate the force of the water on the orifice plate.

21 gpm 60 mm 100 mm Orifice plate Figure 4.67: Thin-plate orifice A nozzle with a quarter-circle shape discharges water at 4 m/s as shown in Figure The radius of the quarter-circle is 300 mm and the height of the nozzle is 25 mm. Estimate the force required to hold the nozzle in a fixed position. 300 mm Nozzle 4 m/s Inflow 25 mm Ou low (a) Plan view (b) Eleva on view Figure 4.68: Quarter-circular nozzle An jet of water at 20 C exits a nozzle into air and and strikes a stagnation tube as shown in Figure If head losses are neglected, estimate the mass flow in kg/s and the height h of the fluid in the stagnation tube. Flow 12 cm 110 kpa 4 cm Stagna on tube h Jet Figure 4.69: Water striking stagnation tube A jet of water at 10 m 3 /s is impinging on a stationary deflector that changes the flow direction of the jet by 45. The velocity of the impinging jet is 10 m/s and the velocity of the deflected jet is 9 m/s. What force is required to keep the deflector in place?

22 The concrete structure shown in Figure 4.70 is to be overturned by a jet of water striking at the center, P, of the vertical panel. The structure is expected to overturn along the side QR. The diameter of the jet is 200 mm, and it can be assumed that the density of concrete is 2300 kg/m 3. Estimate the velocity of the jet that will be required to overturn the structure. The panel is made of concrete. 1.2 m 0.9 m Q R 1.4 m P 0.3 m 0.2 m Water jet Concrete structure 1.4 m Figure 4.70: Jet impinging on concrete structure Water at 20 C is contained in a pressurized tank that is supported by a cable as shown in Figure The (gage) air pressure above the water in the tank is 600 kpa, the depth of water in the tank is 1 m, the diameter of the tank is 1 m, the weight of the tank is 1 kn, and there is a 50-mm diameter orifice in the bottom of the tank. The discharge coefficient of the orifice is 0.8. Estimate the tension is the cable supporting the tank. Cable Air 600 kpa Tank 1 m 50 mm Orifice 1 m Figure 4.71: Tank supported by cable A 100-mm diameter water jet strikes a flat plate as shown in Figure 4.72(a). Prior to striking the plate, the jet has a velocity of 20 m/s and is oriented normal to the plate. What support force must be provided to keep the plate from moving? Assume water at 20 C.

23 m/s Water jet 100 mm Flat plate 20 m/s Water jet 100 mm Flat plate 50 mm Orifice (a) Without orifice (b) With orifice Figure 4.72: Water jet striking flat plate A 100-mm diameter water jet strikes a flat plate with a 50-mm diameter orifice whose center is aligned with the water jet as shown in Figure 4.72(b). Prior to striking the plate, the jet has a velocity of 20 m/s and is oriented normal to the plate. What support force must be provided to keep the plate from moving? Assume water at 20 C Water-jet cutters are used to cut a wide variety of materials using a very high-pressure water jet. A particular water-jet cutter uses water at 20 C at a flow rate of 4 L/min and a jet diameter of 0.25 mm. If this jet is used to cut a flat plate where the plate is oriented normal to the jet, what is the force per unit area exerted by the jet on the plate? Air at 20 C and 1 atm flows in a 25-cm diameter duct at 15 m/s as shown in Figure 4.73; the exit is choked by a 90 cone. Estimate the force of the air flow on the cone. 25 cm 1 cm Air flow 90 o 40 cm Cone Figure 4.73: Air flow onto a cone An air tank is hovers above a solid surface supported only by the air being released through a 15-mm diameter orifice that is located immediately below the center of gravity of the tank, as shown in Figure It is known that the temperature of the air in the tank is 23 C, and the weight of the tank plus air in the tank is 100 N. The flow of air through the orifice can be assumed to be incompressible and frictionless, and atmospheric pressure can be taken as 101 kpa. Estimate the air pressure in the tank.

24 337 Tank Air T = 23 o C p =? 15 mm Orifice Solid surface Figure 4.74: Tank supported by air jet A blade attached to a turbine rotor is driven by a stream of water that has a velocity of 18 m/s. The blade moves with a velocity of 8 m/s and deflects the stream of water through an angle of 85 ; the entrance and exit flow areas are each equal to 1.5 m 2. Estimate the force on the moving blade and the power transferred to the turbine rotor A circular jet of water at 20 C impinges on the vane shown in Figure The incident jet has a velocity of 30 m/s and a diameter of 150 mm. The vane divides the incident jet equally, and the jet exits the vane as two jets that each make an angle of 15 with the incoming jet. (a) Determine the force on the vane when the vane is moving at a speed of 10 m/s in the same direction as that of the incident jet. (b) Determine the force on the vane when the vane is moving at a speed of 10 m/s in the opposite direction to that of the incident jet. Assume water at 20 C. 30 m/s 150 mm Incident jet V v 15 o Moving vane Figure 4.75: Force on moving vane Water flows out the 6-mm slots as shown in Figure Calculate the angular velocity (ω) if 20 kg/s is delivered by the two arms. [Note: The velocities of the exit jets might not be uniform as shown in the figure.] Exit jet ω Sprinkler rotor 2 cm 5 cm 15 cm Figure 4.76: Sprinkler The rocket shown in Figure 4.77 is launched vertically from high in the atmosphere where aerodynamic drag on the rocket is negligible. The rocket has an initial mass of 600 kg,

25 338 burns fuel at a rate of 7 kg/s, and the velocity of the exhaust gasses relative to the rocket is 2800 m/s. (a) Determine the velocity and acceleration of the rocket 10 seconds after launch. (b) Compare the acceleration of the rocket at 10 seconds with the acceleration at launch. Rocket g v e Exhaust gas Figure 4.77: Rocket with vertical trajectory A 60-mm diameter jet of water impacts a vane at a velocity of 30 m/s as shown in Figure The vane has a mass of 100 kg and deflects the jet through a 50 angle. The vane is constrained to move in the x direction, and there is no force opposing the motion of the vane. Determine the acceleration of the vane when it is first released. Assume water at 20 C. 30 m/s 60 mm 50 o Moving vane Figure 4.78: Motion of a vane caused by a water jet A wind turbine is being proposed for commercial development in Miami, Florida. The proposed turbine will have a hub height of 50 m and rotor diameter of 70 m. Miami is approximately at sea level. Estimate the wind power density and assess the feasibility of using wind as a source of energy in Miami Estimate the maximum wind power density available at any location within the land area of the 48 contiguous United States. For such a location, provide a rough layout of a 1 mi 2 wind farm, where each wind turbine would have a 90-m diameter rotor. What is the peak power that could be produced from this wind farm? Assume standard temperature and pressure A 3-cm diameter orifice is 1 m below the surface of a 1.5 m diameter barrel containing water at 20 C. Estimate the force on the barrel when water is flowing freely out of the orifice A vertical jet discharges water onto a reservoir, and water discharged from the same reservoir via an opening that is inclined at 45 to the horizontal as shown in Figure The inflow

26 339 jet has a diameter of 25 mm, the outflow jet has a diameter of 35 mm, and conditions are at steady state. (a) What is the net force on the reservoir? (b) How high will the discharge jet rise above its discharge elevation? Inflow jet 25 mm Reservoir 45 o 1.2 m Ou low jet 35mm Figure 4.79: Inflow and outflow jets in a reservoir A jet engine is mounted on an aircraft that is operating at an elevation of 8 km in a standard atmosphere, and the speed of the aircraft is 250 m/s. The intake area of the engine is 1.5 m 2, the fuel consumption rate is 25 kg/s, and the exhaust gas exits at a speed of 200 m/s relative to the moving aircraft. The pressure of the exhaust gas is approximately equal to the ambient atmospheric pressure. Under these conditions, what thrust is expected from the engine? The specifications of a jet engine indicate that it has an intake diameter of 2.57 m, consumes fuel at a rate of 1.5 L/s, and produces an exhaust jet with a velocity of 800 m/s. If the jet engine is mounted on an airplane that is cruising at 845 km/h (525 mph) where the air density is kg/m 3, estimate the thrust produced by the engine. Assume that the jet fuel has a density of 820 kg/m Jet engines are usually tested on a static thrust stand as shown in Figure In such tests, the pressures of the inflow and outflow gasses are usually expressed as gage pressures. In a particular test of an engine with an inflow area of 1.2 m 2, the inflow air has a velocity of 250 m/s, a (gage) pressure of 50 kpa, and a temperature of 50 C. The exhaust gas has a velocity of 550 m/s and is at atmospheric pressure, which is 101 kpa (absolute). (a) Estimate the thrust on the test stand assuming that the mass flow rate of the exhaust gasses is equal to the mass flow rate of the inflow air. (a) Estimate the thrust on the test stand taking into account that fuel is supplied to the engine at a mass flow rate equal to 2% of the air mass flow rate. Which estimated thrust is likely to be more accurate?

27 m/s 50 kpa -50 o C Jet engine Open atmosphere 550 m/s 0 kpa Sta c thrust stand Thrust Figure 4.80: Jet engine on test stand The performance of a rocket with a 200-mm diameter nozzle exit is tested on a stand as shown in Figure Under the conditions of a particular test, atmospheric pressure is 101 kpa, the exhaust gas has an exit velocity of 1500 m/s, a pressure of 150 kpa absolute, and a mass flow rate of 10 kg/s. (a) Estimate the thrust generated by the rocket. (b) How is the mass flow rate of the exhaust gas related to the fuel consumption rate of the rocket? Rocket Exhaust gas 1500 m/s 150 kpa 10 kg/s 200 mm Test stand Figure 4.81: Rocket on a test stand A rocket weighs 6000-kg, burns fuel at a rate of 40 kg/s, and has an exhaust velocity of 3000 m/s. Estimate the initial acceleration of the rocket and the velocity after 10 seconds. Neglect the drag force of the surrounding air and assume that the pressure of the exhaust gasses is equal to the pressure of the surrounding atmosphere. Section 4.5: Angular-Momentum Principle Water flows through a 12-cm diameter pipe that consists 3-m long riser and a 2-m long horizontal section with a 90 elbow to force the water to be discharged downward. Water discharges to the atmosphere at a velocity of 4 m/s, and the mass of the pipe section when filled with water is 15 kg per meter length. (a) Determine the moment acting at the intersection of the vertical (riser) and horizontal pipe sections (i.e. point A in Figure 4.82). (b) What would be the moment if the flow were discharged upward instead of downward? (c) Which discharge orientation creates the greatest stress on the elbow at A?

28 341 A 2 m Elbow 3 m Riser (pipe) 4 m/s 12 cm Figure 4.82: Pipe system Water flows through the pipe bend and nozzle arrangement shown in Figure 4.83 which lies with its axis in the horizontal plane. The water issues from the nozzle into the atmosphere as a parallel jet and friction may be neglected. Find the moment of the resultant force due to the water on this arrangement about a vertical axis through the point X. Flow 8 cm 128 kpa Pipe Flexible joint 10 cm X 20 cm Nozzle 1 cm 16 m/s Figure 4.83: Force on nozzle Water at 20 C flows through the pipe bend in Figure 4.84 at 4000 gallons per minute, where the bend is in the horizontal plane. (a) Compute the torque required at point B to hold the bend stationary, and (b) determine the location of the line of action of the resultant force.

### Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015

Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 I. Introduction (Chapters 1 and 2) A. What is Fluid Mechanics? 1. What is a fluid? 2. What is mechanics? B. Classification of Fluid Flows 1. Viscous

### 4 Mechanics of Fluids (I)

1. The x and y components of velocity for a two-dimensional flow are u = 3.0 ft/s and v = 9.0x ft/s where x is in feet. Determine the equation for the streamlines and graph representative streamlines in

### AEROSPACE ENGINEERING DEPARTMENT. Second Year - Second Term ( ) Fluid Mechanics & Gas Dynamics

AEROSPACE ENGINEERING DEPARTMENT Second Year - Second Term (2008-2009) Fluid Mechanics & Gas Dynamics Similitude,Dimensional Analysis &Modeling (1) [7.2R*] Some common variables in fluid mechanics include:

### Fundamentals of Fluid Mechanics

Sixth Edition Fundamentals of Fluid Mechanics International Student Version BRUCE R. MUNSON DONALD F. YOUNG Department of Aerospace Engineering and Engineering Mechanics THEODORE H. OKIISHI Department

### ENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids

CHAPTER 1 Properties of Fluids ENGINEERING FLUID MECHANICS 1.1 Introduction 1.2 Development of Fluid Mechanics 1.3 Units of Measurement (SI units) 1.4 Mass, Density, Specific Weight, Specific Volume, Specific

### Lesson 6 Review of fundamentals: Fluid flow

Lesson 6 Review of fundamentals: Fluid flow The specific objective of this lesson is to conduct a brief review of the fundamentals of fluid flow and present: A general equation for conservation of mass

### FE Fluids Review March 23, 2012 Steve Burian (Civil & Environmental Engineering)

Topic: Fluid Properties 1. If 6 m 3 of oil weighs 47 kn, calculate its specific weight, density, and specific gravity. 2. 10.0 L of an incompressible liquid exert a force of 20 N at the earth s surface.

### Part A: 1 pts each, 10 pts total, no partial credit.

Part A: 1 pts each, 10 pts total, no partial credit. 1) (Correct: 1 pt/ Wrong: -3 pts). The sum of static, dynamic, and hydrostatic pressures is constant when flow is steady, irrotational, incompressible,

### Chapter Four fluid flow mass, energy, Bernoulli and momentum

4-1Conservation of Mass Principle Consider a control volume of arbitrary shape, as shown in Fig (4-1). Figure (4-1): the differential control volume and differential control volume (Total mass entering

### CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS NOOR ALIZA AHMAD

CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS 1 INTRODUCTION Flow often referred as an ideal fluid. We presume that such a fluid has no viscosity. However, this is an idealized situation that does not exist.

### ME3560 Tentative Schedule Spring 2019

ME3560 Tentative Schedule Spring 2019 Week Number Date Lecture Topics Covered Prior to Lecture Read Section Assignment Prep Problems for Prep Probs. Must be Solved by 1 Monday 1/7/2019 1 Introduction to

### ME3560 Tentative Schedule Fall 2018

ME3560 Tentative Schedule Fall 2018 Week Number 1 Wednesday 8/29/2018 1 Date Lecture Topics Covered Introduction to course, syllabus and class policies. Math Review. Differentiation. Prior to Lecture Read

### 2 Navier-Stokes Equations

1 Integral analysis 1. Water enters a pipe bend horizontally with a uniform velocity, u 1 = 5 m/s. The pipe is bended at 90 so that the water leaves it vertically downwards. The input diameter d 1 = 0.1

### Therefore, the control volume in this case can be treated as a solid body, with a net force or thrust of. bm # V

When the mass m of the control volume remains nearly constant, the first term of the Eq. 6 8 simply becomes mass times acceleration since 39 CHAPTER 6 d(mv ) CV m dv CV CV (ma ) CV Therefore, the control

### William В. Brower, Jr. A PRIMER IN FLUID MECHANICS. Dynamics of Flows in One Space Dimension. CRC Press Boca Raton London New York Washington, D.C.

William В. Brower, Jr. A PRIMER IN FLUID MECHANICS Dynamics of Flows in One Space Dimension CRC Press Boca Raton London New York Washington, D.C. Table of Contents Chapter 1 Fluid Properties Kinetic Theory

### Objectives. Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation

Objectives Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation Conservation of Mass Conservation of Mass Mass, like energy, is a conserved

### 5 ENERGY EQUATION OF FLUID MOTION

5 ENERGY EQUATION OF FLUID MOTION 5.1 Introduction In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics. The pertinent laws

CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK 3 0 0 3 UNIT I FLUID PROPERTIES AND FLUID STATICS PART - A 1. Define fluid and fluid mechanics. 2. Define real and ideal fluids. 3. Define mass density

### Chapter 3 Bernoulli Equation

1 Bernoulli Equation 3.1 Flow Patterns: Streamlines, Pathlines, Streaklines 1) A streamline, is a line that is everywhere tangent to the velocity vector at a given instant. Examples of streamlines around

### Fluid Mechanics. du dy

FLUID MECHANICS Technical English - I 1 th week Fluid Mechanics FLUID STATICS FLUID DYNAMICS Fluid Statics or Hydrostatics is the study of fluids at rest. The main equation required for this is Newton's

### COURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour. Basic Equations in fluid Dynamics

COURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour Basic Equations in fluid Dynamics Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 Description of Fluid

### INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad AERONAUTICAL ENGINEERING QUESTION BANK : AERONAUTICAL ENGINEERING.

Course Name Course Code Class Branch INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 00 0 AERONAUTICAL ENGINEERING : Mechanics of Fluids : A00 : II-I- B. Tech Year : 0 0 Course Coordinator

### FE Exam Fluids Review October 23, Important Concepts

FE Exam Fluids Review October 3, 013 mportant Concepts Density, specific volume, specific weight, specific gravity (Water 1000 kg/m^3, Air 1. kg/m^3) Meaning & Symbols? Stress, Pressure, Viscosity; Meaning

### Mass of fluid leaving per unit time

5 ENERGY EQUATION OF FLUID MOTION 5.1 Eulerian Approach & Control Volume In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics.

### 2 Internal Fluid Flow

Internal Fluid Flow.1 Definitions Fluid Dynamics The study of fluids in motion. Static Pressure The pressure at a given point exerted by the static head of the fluid present directly above that point.

### vector H. If O is the point about which moments are desired, the angular moment about O is given:

The angular momentum A control volume analysis can be applied to the angular momentum, by letting B equal to angularmomentum vector H. If O is the point about which moments are desired, the angular moment

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### APPLIED FLUID DYNAMICS HANDBOOK

APPLIED FLUID DYNAMICS HANDBOOK ROBERT D. BLEVINS H imhnisdia ttodisdiule Darmstadt Fachbereich Mechanik 'rw.-nr.. [VNR1 VAN NOSTRAND REINHOLD COMPANY ' ' New York Contents Preface / v 1. Definitions /

### R09. d water surface. Prove that the depth of pressure is equal to p +.

Code No:A109210105 R09 SET-1 B.Tech II Year - I Semester Examinations, December 2011 FLUID MECHANICS (CIVIL ENGINEERING) Time: 3 hours Max. Marks: 75 Answer any five questions All questions carry equal

### Final 1. (25) 2. (10) 3. (10) 4. (10) 5. (10) 6. (10) TOTAL = HW = % MIDTERM = % FINAL = % COURSE GRADE =

MAE101B: Advanced Fluid Mechanics Winter Quarter 2017 http://web.eng.ucsd.edu/~sgls/mae101b_2017/ Name: Final This is a three hour open-book exam. Please put your name on the top sheet of the exam. Answer

### Approximate physical properties of selected fluids All properties are given at pressure kn/m 2 and temperature 15 C.

Appendix FLUID MECHANICS Approximate physical properties of selected fluids All properties are given at pressure 101. kn/m and temperature 15 C. Liquids Density (kg/m ) Dynamic viscosity (N s/m ) Surface

### Chapter 4 DYNAMICS OF FLUID FLOW

Faculty Of Engineering at Shobra nd Year Civil - 016 Chapter 4 DYNAMICS OF FLUID FLOW 4-1 Types of Energy 4- Euler s Equation 4-3 Bernoulli s Equation 4-4 Total Energy Line (TEL) and Hydraulic Grade Line

### Q1 Give answers to all of the following questions (5 marks each):

FLUID MECHANICS First Year Exam Solutions 03 Q Give answers to all of the following questions (5 marks each): (a) A cylinder of m in diameter is made with material of relative density 0.5. It is moored

### EXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER

EXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER 1.1 AIM: To determine the co-efficient of discharge of the orifice meter 1.2 EQUIPMENTS REQUIRED: Orifice meter test rig, Stopwatch 1.3 PREPARATION 1.3.1

### CALIFORNIA POLYTECHNIC STATE UNIVERSITY Mechanical Engineering Department ME 347, Fluid Mechanics II, Winter 2018

CALIFORNIA POLYTECHNIC STATE UNIVERSITY Mechanical Engineering Department ME 347, Fluid Mechanics II, Winter 2018 Date Day Subject Read HW Sept. 21 F Introduction 1, 2 24 M Finite control volume analysis

### CLASS SCHEDULE 2013 FALL

CLASS SCHEDULE 2013 FALL Class # or Lab # 1 Date Aug 26 2 28 Important Concepts (Section # in Text Reading, Lecture note) Examples/Lab Activities Definition fluid; continuum hypothesis; fluid properties

### Fluid Dynamics Exercises and questions for the course

Fluid Dynamics Exercises and questions for the course January 15, 2014 A two dimensional flow field characterised by the following velocity components in polar coordinates is called a free vortex: u r

### MOMENTUM PRINCIPLE. Review: Last time, we derived the Reynolds Transport Theorem: Chapter 6. where B is any extensive property (proportional to mass),

Chapter 6 MOMENTUM PRINCIPLE Review: Last time, we derived the Reynolds Transport Theorem: where B is any extensive property (proportional to mass), and b is the corresponding intensive property (B / m

### 10.52 Mechanics of Fluids Spring 2006 Problem Set 3

10.52 Mechanics of Fluids Spring 2006 Problem Set 3 Problem 1 Mass transfer studies involving the transport of a solute from a gas to a liquid often involve the use of a laminar jet of liquid. The situation

### V/ t = 0 p/ t = 0 ρ/ t = 0. V/ s = 0 p/ s = 0 ρ/ s = 0

UNIT III FLOW THROUGH PIPES 1. List the types of fluid flow. Steady and unsteady flow Uniform and non-uniform flow Laminar and Turbulent flow Compressible and incompressible flow Rotational and ir-rotational

### Fluid Mechanics c) Orificemeter a) Viscous force, Turbulence force, Compressible force a) Turbulence force c) Integration d) The flow is rotational

Fluid Mechanics 1. Which is the cheapest device for measuring flow / discharge rate. a) Venturimeter b) Pitot tube c) Orificemeter d) None of the mentioned 2. Which forces are neglected to obtain Euler

### UNIT I FLUID PROPERTIES AND STATICS

SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : Fluid Mechanics (16CE106) Year & Sem: II-B.Tech & I-Sem Course & Branch:

### Piping Systems and Flow Analysis (Chapter 3)

Piping Systems and Flow Analysis (Chapter 3) 2 Learning Outcomes (Chapter 3) Losses in Piping Systems Major losses Minor losses Pipe Networks Pipes in series Pipes in parallel Manifolds and Distribution

### equation 4.1 INTRODUCTION

4 The momentum equation 4.1 INTRODUCTION It is often important to determine the force produced on a solid body by fluid flowing steadily over or through it. For example, there is the force exerted on a

### Higher Education. Mc Grauu FUNDAMENTALS AND APPLICATIONS SECOND EDITION

FLUID MECHANICS FUNDAMENTALS AND APPLICATIONS SECOND EDITION Mc Grauu Higher Education Boston Burr Ridge, IL Dubuque, IA Madison, Wl New York San Francisco St. Louis Bangkok Bogota Caracas Kuala Lumpur

### Signature: (Note that unsigned exams will be given a score of zero.)

Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (-1 point if not circled, or circled incorrectly): Prof. Dabiri Prof. Wassgren Prof.

### MASS, MOMENTUM, AND ENERGY EQUATIONS

MASS, MOMENTUM, AND ENERGY EQUATIONS This chapter deals with four equations commonly used in fluid mechanics: the mass, Bernoulli, Momentum and energy equations. The mass equation is an expression of the

### Experiment (4): Flow measurement

Experiment (4): Flow measurement Introduction: The flow measuring apparatus is used to familiarize the students with typical methods of flow measurement of an incompressible fluid and, at the same time

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### Basic Fluid Mechanics

Basic Fluid Mechanics Chapter 5: Application of Bernoulli Equation 4/16/2018 C5: Application of Bernoulli Equation 1 5.1 Introduction In this chapter we will show that the equation of motion of a particle

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### CLASS Fourth Units (Second part)

CLASS Fourth Units (Second part) Energy analysis of closed systems Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. MOVING BOUNDARY WORK Moving boundary work (P

### 2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False A. True B.

CHAPTER 03 1. Write Newton's second law of motion. YOUR ANSWER: F = ma 2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False 3.Streamwise

### Conservation of Momentum using Control Volumes

Conservation of Momentum using Control Volumes Conservation of Linear Momentum Recall the conservation of linear momentum law for a system: In order to convert this for use in a control volume, use RTT

### SPC Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30

SPC 307 - Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30 1. The maximum velocity at which an aircraft can cruise occurs when the thrust available with the engines operating with the

### MULTIPLE-CHOICE PROBLEMS:(Two marks per answer) (Circle the Letter Beside the Most Correct Answer in the Questions Below.)

MULTIPLE-CHOICE PROLEMS:(Two marks per answer) (Circle the Letter eside the Most Correct Answer in the Questions elow.) 1. The absolute viscosity µ of a fluid is primarily a function of: a. Density. b.

### ME332 FLUID MECHANICS LABORATORY (PART II)

ME332 FLUID MECHANICS LABORATORY (PART II) Mihir Sen Department of Aerospace and Mechanical Engineering University of Notre Dame Notre Dame, IN 46556 Version: April 2, 2002 Contents Unit 5: Momentum transfer

### The online of midterm-tests of Fluid Mechanics 1

The online of midterm-tests of Fluid Mechanics 1 1) The information on a can of pop indicates that the can contains 460 ml. The mass of a full can of pop is 3.75 lbm while an empty can weights 80.5 lbf.

### Consider a control volume in the form of a straight section of a streamtube ABCD.

6 MOMENTUM EQUATION 6.1 Momentum and Fluid Flow In mechanics, the momentum of a particle or object is defined as the product of its mass m and its velocity v: Momentum = mv The particles of a fluid stream

### UNIT II CONVECTION HEAT TRANSFER

UNIT II CONVECTION HEAT TRANSFER Convection is the mode of heat transfer between a surface and a fluid moving over it. The energy transfer in convection is predominately due to the bulk motion of the fluid

### Contents. I Introduction 1. Preface. xiii

Contents Preface xiii I Introduction 1 1 Continuous matter 3 1.1 Molecules................................ 4 1.2 The continuum approximation.................... 6 1.3 Newtonian mechanics.........................

### For example an empty bucket weighs 2.0kg. After 7 seconds of collecting water the bucket weighs 8.0kg, then:

Hydraulic Coefficient & Flow Measurements ELEMENTARY HYDRAULICS National Certificate in Technology (Civil Engineering) Chapter 3 1. Mass flow rate If we want to measure the rate at which water is flowing

### Please welcome for any correction or misprint in the entire manuscript and your valuable suggestions kindly mail us

Problems of Practices Of Fluid Mechanics Compressible Fluid Flow Prepared By Brij Bhooshan Asst. Professor B. S. A. College of Engg. And Technology Mathura, Uttar Pradesh, (India) Supported By: Purvi Bhooshan

### AER210 VECTOR CALCULUS and FLUID MECHANICS. Quiz 4 Duration: 70 minutes

AER210 VECTOR CALCULUS and FLUID MECHANICS Quiz 4 Duration: 70 minutes 26 November 2012 Closed Book, no aid sheets Non-programmable calculators allowed Instructor: Alis Ekmekci Family Name: Given Name:

### Lecture 3 The energy equation

Lecture 3 The energy equation Dr Tim Gough: t.gough@bradford.ac.uk General information Lab groups now assigned Timetable up to week 6 published Is there anyone not yet on the list? Week 3 Week 4 Week 5

### NPTEL Quiz Hydraulics

Introduction NPTEL Quiz Hydraulics 1. An ideal fluid is a. One which obeys Newton s law of viscosity b. Frictionless and incompressible c. Very viscous d. Frictionless and compressible 2. The unit of kinematic

### Mechanical Engineering Programme of Study

Mechanical Engineering Programme of Study Fluid Mechanics Instructor: Marios M. Fyrillas Email: eng.fm@fit.ac.cy SOLVED EXAMPLES ON VISCOUS FLOW 1. Consider steady, laminar flow between two fixed parallel

### 11.1 Mass Density. Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an

Chapter 11 Fluids 11.1 Mass Density Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an important factor that determines its behavior

### In which of the following scenarios is applying the following form of Bernoulli s equation: steady, inviscid, uniform stream of water. Ma = 0.

bernoulli_11 In which of the following scenarios is applying the following form of Bernoulli s equation: p V z constant! g + g + = from point 1 to point valid? a. 1 stagnant column of water steady, inviscid,

### Fluid Mechanics Testbank By David Admiraal

Fluid Mechanics Testbank By David Admiraal This testbank was created for an introductory fluid mechanics class. The primary intentions of the testbank are to help students improve their performance on

### Exam #2: Fluid Kinematics and Conservation Laws April 13, 2016, 7:00 p.m. 8:40 p.m. in CE 118

CVEN 311-501 (Socolofsky) Fluid Dynamics Exam #2: Fluid Kinematics and Conservation Laws April 13, 2016, 7:00 p.m. 8:40 p.m. in CE 118 Name: : UIN: : Instructions: Fill in your name and UIN in the space

### S.E. (Mech.) (First Sem.) EXAMINATION, (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum Marks : 100

Total No. of Questions 12] [Total No. of Printed Pages 8 Seat No. [4262]-113 S.E. (Mech.) (First Sem.) EXAMINATION, 2012 (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum

### B.E/B.Tech/M.E/M.Tech : Chemical Engineering Regulation: 2016 PG Specialisation : NA Sub. Code / Sub. Name : CH16304 FLUID MECHANICS Unit : I

Department of Chemical Engineering B.E/B.Tech/M.E/M.Tech : Chemical Engineering Regulation: 2016 PG Specialisation : NA Sub. Code / Sub. Name : CH16304 FLUID MECHANICS Unit : I LP: CH 16304 Rev. No: 00

### Figure 3: Problem 7. (a) 0.9 m (b) 1.8 m (c) 2.7 m (d) 3.6 m

1. For the manometer shown in figure 1, if the absolute pressure at point A is 1.013 10 5 Pa, the absolute pressure at point B is (ρ water =10 3 kg/m 3, ρ Hg =13.56 10 3 kg/m 3, ρ oil = 800kg/m 3 ): (a)

### Engineering Fluid Mechanics

Engineering Fluid Mechanics Eighth Edition Clayton T. Crowe WASHINGTON STATE UNIVERSITY, PULLMAN Donald F. Elger UNIVERSITY OF IDAHO, MOSCOW John A. Roberson WASHINGTON STATE UNIVERSITY, PULLMAN WILEY

### Chapter 5 Control Volume Approach and Continuity Equation

Chapter 5 Control Volume Approach and Continuity Equation Lagrangian and Eulerian Approach To evaluate the pressure and velocities at arbitrary locations in a flow field. The flow into a sudden contraction,

### Chapter 1 INTRODUCTION

Chapter 1 INTRODUCTION 1-1 The Fluid. 1-2 Dimensions. 1-3 Units. 1-4 Fluid Properties. 1 1-1 The Fluid: It is the substance that deforms continuously when subjected to a shear stress. Matter Solid Fluid

### Page 1. Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.)

Page 1 Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (-1 point if not circled, or circled incorrectly): Prof. Vlachos Prof. Ardekani

### Experiment- To determine the coefficient of impact for vanes. Experiment To determine the coefficient of discharge of an orifice meter.

SUBJECT: FLUID MECHANICS VIVA QUESTIONS (M.E 4 th SEM) Experiment- To determine the coefficient of impact for vanes. Q1. Explain impulse momentum principal. Ans1. Momentum equation is based on Newton s

### IX. COMPRESSIBLE FLOW. ρ = P

IX. COMPRESSIBLE FLOW Compressible flow is the study of fluids flowing at speeds comparable to the local speed of sound. This occurs when fluid speeds are about 30% or more of the local acoustic velocity.

### Reynolds, an engineering professor in early 1880 demonstrated two different types of flow through an experiment:

7 STEADY FLOW IN PIPES 7.1 Reynolds Number Reynolds, an engineering professor in early 1880 demonstrated two different types of flow through an experiment: Laminar flow Turbulent flow Reynolds apparatus

### Iran University of Science & Technology School of Mechanical Engineering Advance Fluid Mechanics

1. Consider a sphere of radius R immersed in a uniform stream U0, as shown in 3 R Fig.1. The fluid velocity along streamline AB is given by V ui U i x 1. 0 3 Find (a) the position of maximum fluid acceleration

### Visualization of flow pattern over or around immersed objects in open channel flow.

EXPERIMENT SEVEN: FLOW VISUALIZATION AND ANALYSIS I OBJECTIVE OF THE EXPERIMENT: Visualization of flow pattern over or around immersed objects in open channel flow. II THEORY AND EQUATION: Open channel:

### The Bernoulli Equation

The Bernoulli Equation The most used and the most abused equation in fluid mechanics. Newton s Second Law: F = ma In general, most real flows are 3-D, unsteady (x, y, z, t; r,θ, z, t; etc) Let consider

### Atmospheric pressure. 9 ft. 6 ft

Name CEE 4 Final Exam, Aut 00; Answer all questions; 145 points total. Some information that might be helpful is provided below. A Moody diagram is printed on the last page. For water at 0 o C (68 o F):

### 6.1 Momentum Equation for Frictionless Flow: Euler s Equation The equations of motion for frictionless flow, called Euler s

Chapter 6 INCOMPRESSIBLE INVISCID FLOW All real fluids possess viscosity. However in many flow cases it is reasonable to neglect the effects of viscosity. It is useful to investigate the dynamics of an

### MULTIPLE-CHOICE PROBLEMS :(Two marks per answer) (Circle the Letter Beside the Most Correct Answer in the Questions Below.)

Test Midterm 1 F2013 MULTIPLE-CHOICE PROBLEMS :(Two marks per answer) (Circle the Letter Beside the Most Correct nswer in the Questions Below.) 1. The absolute viscosity µ of a fluid is primarily a function

### Hydraulics for Urban Storm Drainage

Urban Hydraulics Hydraulics for Urban Storm Drainage Learning objectives: understanding of basic concepts of fluid flow and how to analyze conduit flows, free surface flows. to analyze, hydrostatic pressure

### 150A Review Session 2/13/2014 Fluid Statics. Pressure acts in all directions, normal to the surrounding surfaces

Fluid Statics Pressure acts in all directions, normal to the surrounding surfaces or Whenever a pressure difference is the driving force, use gauge pressure o Bernoulli equation o Momentum balance with

### Outlines. simple relations of fluid dynamics Boundary layer analysis. Important for basic understanding of convection heat transfer

Forced Convection Outlines To examine the methods of calculating convection heat transfer (particularly, the ways of predicting the value of convection heat transfer coefficient, h) Convection heat transfer

### Answers to questions in each section should be tied together and handed in separately.

EGT0 ENGINEERING TRIPOS PART IA Wednesday 4 June 014 9 to 1 Paper 1 MECHANICAL ENGINEERING Answer all questions. The approximate number of marks allocated to each part of a question is indicated in the

### BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING)

No. of Printed Pages : 6 BME-028 BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING) Term-End Examination December, 2011 00792 BME-028 : FLUID MECHANICS Time : 3 hours

### CVE 372 HYDROMECHANICS EXERCISE PROBLEMS

VE 37 HYDROMEHNIS EXERISE PROLEMS 1. pump that has the characteristic curve shown in the accompanying graph is to be installed in the system shown. What will be the discharge of water in the system? Take

### Flow Measurement in Pipes and Ducts COURSE CONTENT

Flow Measurement in Pipes and Ducts Dr. Harlan H. Bengtson, P.E. COURSE CONTENT 1. Introduction This course is about measurement of the flow rate of a fluid flowing under pressure in a closed conduit.

### Principles of Convection

Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid

### TOPICS. Density. Pressure. Variation of Pressure with Depth. Pressure Measurements. Buoyant Forces-Archimedes Principle

Lecture 6 Fluids TOPICS Density Pressure Variation of Pressure with Depth Pressure Measurements Buoyant Forces-Archimedes Principle Surface Tension ( External source ) Viscosity ( External source ) Equation

### s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum equations E. Pipe and other internal flow 7% of FE Morning Session I

Fundamentals of Engineering (FE) Exam General Section Steven Burian Civil & Environmental Engineering October 26, 2010 s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum

### Hydraulics and hydrology

Hydraulics and hydrology - project exercises - Class 4 and 5 Pipe flow Discharge (Q) (called also as the volume flow rate) is the volume of fluid that passes through an area per unit time. The discharge