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

Size: px
Start display at page:

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

Transcription

1 AEROSPACE ENGINEERING DEPARTMENT Second Year - Second Term ( ) Fluid Mechanics & Gas Dynamics Similitude,Dimensional Analysis &Modeling (1) [7.2R*] Some common variables in fluid mechanics include: volume flowrate, Q, acceleration of gravity, g, viscosity, μ, density, ρ, and length, L. Which of the following combinations of these variables are dimensionless? (a) Q 2 /gl 2 (b) ρq/μl (c) gl 5 /Q 2 (d) ρql/μ (2) [7.3R*] A fluid flows at a velocity V through a horizontal pipe of diameter D. An orifice plate containing a hole of diameter d is placed in the pipe. It is desired to investigate the pressure drop, Δp, across the plate. Assume that Δp = f (D, d, ρ, V) Where ρ is the fluid density. Determine a suitable set of pi terms. (3) [7.6R*] The thrust T, developed by a propeller of a given shape depends on its diameter, D, the fluid density, ρ, and the viscosity, μ, the angular speed of rotation, ω, and the advance velocity, V. Develop a suitable set of pi terms, one of which should be ρd 2 ω / μ.. (4) [7.5*] At a sudden contraction in a pipe the diameter changes from D 1 to D 2. The pressure drop Δp, which develops across the contraction, is a function of D 1 and D 2, as well as the velocity, V, in the larger pipe, and the fluid density, ρ, and the viscosity μ. Use D 1, V, and μ as repeating variables to determine a suitable set of dimensionless parameters. Why would it be incorrect to include the velocity in the smaller pipe as an additional variable? (5) [7.6*] Assume that the power, P, required to drive a fan is a function of the fan diameter, D, the fluid density ρ, the rotational speed, ω, and the flowrate, Q. Use D, ω and ρ as repeating variables to determine a suitable set of pi terms. (6) [7.9*] The pressure rise, Δp, across a pump can be expressed as Δp = f (D, ρ, ω, Q) where D is the impeller diameter, ρ the fluid density, ω the rotational speed, and Q the flow-rate. Determine a suitable set of dimensionless parameters. 1

2 (7) [7.10*] The drag, D, on a washer-shaped plate placed normal to a stream of fluid can be expressed as: D = f (d 1, d 2, V, μ, ρ) where d1 is the outer diameter, d2 is the inner diameter, V the fluid velocity, μ the fluid viscosity, and ρ the fluid density. Some experiments are to be performed in a wind tunnel to determine the drag. What dimensionless parameters would you use to organize these date? (8) [7.18*] The pressure drop Δp, along a straight pipe of diameter D has been experimentally studied, and it is observed that for laminar flow of a given fluid and pipe, the pressure drop varies directly with the distance, L, between pressure taps. Assume that Δp is a function of D and L, the velocity, V, and the fluid viscosity, μ. Use dimensional analysis to deduce how the pressure drop varies with pipe diameter. (9) [7.8R*] The pressure drop per unit length in a 0.25-in diameter gasoline fuel line is to be determined from a laboratory test using the same tubing but with water as the fluid. The pressure drop at a gasoline velocity of 1.0 ft/s is of interest. (a) What water velocity is required? (b) At the properly scaled velocity from part (a), the pressure drop per unit length (using water) was found to be 0.45 psf/ft. What is the predicted pressure drop per unit length for the gasoline line? (10) [7.34*] The drag characteristics of a torpedo are to be studied in a water tunnel using a 1 : 5 scale model. The tunnel operates with freshwater at 20 o C, whereas the prototype torpedo is to be used in seawater at 15.6 o C. To correctly simulate the behavior of the prototype moving with a velocity of 30 m/s, what velocity is required in the water tunnel? (11) [7.40*] The lift and drag developed on the hydrofoil are to be determined through wind tunnel test using standard air. If full-scale tests are to be run, what is the required wind tunnel velocity corresponding to a hydrofoil velocity in seawater at 15 mph? Assuming Reynolds number similarity is required. (12) [7.44*] The drag on a 2-m-diameter satellite dish due to an 80 km/hr wind is to be determined through a wind tunnel test using a geometrically similar 0.4-m-diameter model dish. Assume standard air for both model and prototype. (a) At what air speed should the model test be run? 2

3 (b) With all similarly conditions satisfied, the measured drag on the model was determined to be 170 N. What is the predicted drag on the prototype dish? (13) [7.50*] The drag, F D, on a sphere located in a pipe through which a fluid is flowing is to be determined experimentally (see the figure). Assume that the drag is a function of the sphere diameter, d, the pipe diameter, D, the fluid velocity, V, and the fluid density, ρ. (a) What dimensionless parameters would you use for this problem? (b) Some experiments using water indicate that for d = 0.2 in., D = 0.5 in., and V = 2 ft/s, the drag is 1.5x10-3 lb. If possible, estimate the drag on a sphere located in a 2-ft-diameter pipe through which water is flowing with a velocity of 6 ft/s. The sphere diameter is such that geometric similarity is maintained. If it is not possible, explain why not. (14) [7.10R*] The drag on a 30-ft long, vertical, 1.25-ft diameter pole subjected to a 30 mph wind is to be determined with a model study. It is expected that the drag is a function of the pole length and diameter, the fluid density and viscosity, and the fluid velocity. Laboratory model tests were performed in a high-speed water tunnel using a model pole having a length of 2 ft and a diameter of 1 in. Some model drag data are shown in figure. Based on these data, predict the drag on the full-sized pole. 3

4 (15) [7.24*] The pressure rise, Δp = p 2 p 1, across the abrupt expansion shown in figure, through which a liquid is flowing can be expressed as: Δp = f (A 1, A 2, ρ, V 1 ) where A 1 and A 2 are the upstream and downstream cross-sectional areas, respectively, ρ is the fluid density, and V 1 is the upstream velocity. Some experimental data obtained with A 2 = 1.25 ft 2, V 1 = 5.00 ft/s. and using water with density ρ = 1.94 slugs/ft 2 are given in the following table. A 1 (ft 2 ) Δp (lb/ft 2 ) Plot the result of these tests using suitable dimensionless parameters. With the aid of a standard curve fitting program determine a general equation for Δp and use this equation to predict Δp for water flowing through an abrupt expansion with an area ratio A 1 /A 2 = 0.35 at a velocity V 1 = 3.75 ft/s. 4

5 (16) [7.65*] The pressure rise, Δp, across a centrifugal pump of a given shape (see the figure) can be expressed as: Δp = f (D, ω, ρ, Q) where D is the impeller diameter, ω the angular velocity of the impeller, ρ the fluid density, and Q the volume rate of flow through the pump. A model pump having a diameter of 8 in. is tested in the laboratory using water. When operated at an angular velocity of 40 π rad/s the model pressure rise as a function of Q is shown in figure. Use this curve to predict the pressure rise across a geometrically similar pump (prototype) for a prototype flowrate of 6 ft 3 /s. The prototype has a diameter of 12 in. and operates at an angular velocity of 60π rad/s. The prototype fluid is also water. *Selected problems from the text book: Fundamentals of Fluid Mechanics, 3 rd Edition, by: Munson, Young and Okiishi,

6 Viscous Flow in Pipes (1) [8.2R*] A fluid flows through two horizontal pipes of equal length, which are connected together to form a pipe of length 2L.The flow is laminar and fully developed. The pressure drop of the first pipe is 1.44 times grater than it is for the second pipe. If the diameter of the first pipe is D, determine the diameter of the second pipe. (2) [8.4*] Air at 100 o F flows at standard atmospheric pressure in a pipe at a rate of 0.08 lb/s. Determine the minimum diameter allowed if the flow is to be laminar. (3) [8.5*] Carbon dioxide at 20 o C and a pressure of 550 kpa (abs) flows in a pipe at a rate of 0.04 N/s. Determine the maximum diameter allowed if the flow is to be turbulent. (4) [8.11*] Water flows in a constant diameter pipe with the following conditions measured: At section (a) P a = 32.4 psi and z a = 56.8 ft, at section (b) P b = 29.7 psi and z b = 68.2 ft. Is the flow from (a) to (b) or from (b) to (a)? Explain. (5) [8.5 R*] Water flows in a smooth plastic pipe of 200-mm diameter at a rate of 0.10 m 3 /s. Determine the friction factor for this flow. (6) [8.17 *] Glycerin at 20 o C flows upward in a vertical 75-mm-diameter pipe with a centerline velocity of 1.0 m/s. Determine the head loss and pressure drop in a 10-m length of the pipe. (7) [8.18*] A fluid flows through a horizontal 0.1-in. diameter pipe. When the Reynolds number is 1500, the head loss over a 20- ft length of the pipe is 6.4 ft. Determine the fluid velocity. (8) [8.6 R*] After a number of years of use, it is noted that to obtain a given flowrate, the head loss is increased to 1.6 times its value for the originally smooth pipe. If the Reynolds number is 10 6, determine the relative roughness of the old pipe. (9) [8.9 R*] Determine the pressure drop per 300-m length of new 0.20-mdiameter horizontal cast iron water pipe when the average velocity is 1.7 m/s. (10) [8.21*] A fluid flows in a smooth pipe with a Reynolds number of By what percent would the head loss be reduced if the flow could be maintained as laminar flow rather than the expected turbulent flow? 6

7 (11) [8.29*] Carbon dioxide at a temperature of 0ºC and a pressure of 600 kpa (abs) flows through a horizontal 40-mm-diameter pipe with an average velocity of 2 m/s. Determine the friction factor if the pressure drop is 235 N/m 2 per 10- m length of pipe. (12) [8.11 R*] An above ground swimming pool of 30 ft diameter and 5 ft depth is to be filled from a ground hose (smooth interior) of length 100 ft and diameter 5/8 in. If the pressure at the faucet to which the hose is attached remains at 55 psi gauge, how long will it take to fill the pool? The water exits the hose as a free jet 6 ft above the faucet. (13) [8.12 R*] Water is to flow at a rate of 1.0 m 3 /s. through a rough concrete pipe (ε = 3 mm ) that connects two ponds. Determine the pipe diameter if the elevation difference between the two ponds is 10 m and the pipe length is 1000 m. Neglect minor losses. (14) [8.13 R*] Without the pump shown in figure it is determined that the flow rate is two small. Determine the horsepower added to the fluid if the pump causes the flowrate to be doubled. Assume the friction factor remains at in either case. (15) [8.52*] Gasoline flows in a smooth pipe of 40-mm diameter at a rate of m 3 /s. If it were possible to prevent turbulence from occurring. What would be the ratio of the head loss for the actual turbulent flow compared to that if it were laminar flow? (16) [8.53*] A 3-ft-diameter duct is used to carry ventilating air into a vehicular tunnel at a rate of 9000 ft 3 /min. Tests show that the pressure drop is 1.5 in. of water per 1500 ft of duct, what is the value of the friction factor for this duct and the approximate size of the equivalent roughness of the surface of the duct? (17) [8.54*] Natural gas ( ρ = slugs/ft 3 and υ = 5.2 x 10-5 ft 2 /s) is pumped through a horizontal 6-in.-diameter cast-iron pipe at a rate of 800 lb/hr. 7

8 If the pressure at section (1) is 50 psi (abs), determine the pressure at section (2) 8 mi downstream if the flow is assumed incompressible. Is the incompressible assumption reasonable? Explain. (18) [8.82*] A water flowrate of 3.5 ft 3 /s is to be maintained in a horizontal aluminum pipe ( ε = 5 x 10-6 ft). The inlet and outlet pressures are 65 psi and 30 psi, respectively, and the pipe length is 500 ft. Determine the diameter of this pipe. (19) [8.89*] The pump shown in figure adds 25 kw to the water and causes a flowrate of 0.04 m 3 /s. Determine the flowrate expected if the pump is removed from the system. Assume f = for either case and neglect minor losses. (20) [8.97*] Air, assumed incompressible, flows through the two pipes shown in figure. Determine the flowrate if the minor losses are neglected and the friction factor in each pipe is Determine the flowrate if the 0.5-in.- diameter pipe were replaced by a 1-in.-diameter pipe. Comment on the assumption of incompressibility. *Selected problems from the text book: Fundamentals of Fluid Mechanics, 3 rd Edition, by: Munson, Young and Okiishi,

9 9

10 One-Dimensional Isentropic Flow 1. Air flows through a variable area duct. Measurements indicate that the pressure is 80 kpa, the temperature is 5 o C, and the velocity is 150 m/s at a certain section of the duct. Estimate, assuming incompressible flow, the velocity and pressure at a second section of the duct at which the duct area is half that of the section where the measurements were made. Comment on the validity of the incompressible flow assumption in this situation. 2. Air is assumed to be perfect gas, flowing with a velocity of 200 m/s. If the static temperature and pressure are 25 o C and 1 atm respectively, calculate the total properties, the critical properties, and the non-dimensional velocity M*. 3. An airplane flies at an altitude of 15 km with a velocity of 800 km/h. Calculate the maximum possible temperature on the airplane, the maximum possible pressure intensity on the airplane, the critical velocity of the air relative to the airplane, and the maximum possible velocity of the air relative to the airplane. 4. The exhaust gases from a rocket engine can be assumed to behave as a perfect gas with a specific heat ratio of 1.3 and a molecular weight of 32. The gas is expanded from the combustion chamber through the nozzle. At a point in the nozzle where the cross-sectional area is 0.2 m 2 the pressure, temperature, and Mach number are 1500 kpa, 800 o C, and 0.2 respectively. At some other point in the nozzle, the pressure is found to be 80 kpa.find the Mach number, temperature, and cross-sectional are at this point. Assume one-dimensional, isentropic flow. 5. A convergent nozzle has an exit area of 6.5 cm 2 and total inlet conditions of 680 kpa and 370 o K. Assume isentropic flow calculate the mass flow rate if the ambient pressure is 359 kpa, 540 kpa, and 200 kpa. 6. An aircraft is flying at a Mach number of 0.95 at an altitude where the pressure is 30 kpa and the temperature is 50 o C. The diffuser at the intake to the engine decreases the Mach number to 0.3 at the inlet to the compressor. Find the pressure and temperature at the inlet to the compressor. 7. Consider a rocket engine that burns hydrogen and oxygen. The combustion chamber temperature and pressure are 3800 K and 1.5 MPa respectively, the velocity in the combustion chamber being very low. The pressure on the nozzle exit plane is 1.5 kpa. Assuming that the flow is isentropic, find the Mach 10

11 number and the velocity on the exit plane. Assume that the products of combustion behave as a perfect gas with γ = 1.22 and R = J/kg/K. Normal Shock Waves 1. A blast wave created by an explosion moves with a velocity of 1384 km/s into still atmospheric air having a pressure of 1 atm and temperature of 25 o C calculate; the Mach number of the shock wave relative to the stationary air, and the static and stagnation values of the pressure and temperature behind the shock wave relative to a stationary observer. 2. A normal shock wave is propagated into still air with a velocity of 700 m/s. The still air pressure is 1 atm and its temperature is 300 o K, calculate the Mach number, the pressure, temperature, and the velocity in back of the normal shock wave, relative to a stationary observer. 3. Air at a static pressure of 150 kpa and a static temperature of 300 o K flows at 150 m/s in a pipe. The valve at the end of the pipe is suddenly closed, propagating a normal shock wave back into the pipe. Calculate the velocity of the shock wave relative to the pipe. 4. A pitot tube is mounted on a nose of an airplane. The stagnation and the free stream pressure readings, for three different flight conditions are: (0.816 atm, atm), (1.570 atm, atm), (3.580 atm, atm). Calculate the free stream Mach number at which the airplane is flying for each flight. 5. A blunt-nosed missile is flying at Mach 2 at standard sea level. Calculate the temperature and pressure at the nose of the missile. One-Dimensional Flow with Heat Addition 1. Air enters a constant area duct at M 1 = 0.2, p 1 =1atm, and T 1 =273 K. Inside the duct, the heat added per unit mass is q = 1.0 x 106 J/kg. Calculate the flow properties M 2, p 2, T 2, ρ 2, T o2, and P o2 at the exit of the duct. 2. Air enters a constant area duct at M 1 = 3, p 1 =1atm, and T 1 =300 K. Inside the duct, the heat added per unit mass is q = 3 x 105 J/kg. Calculate the flow properties M 2, p 2, T 2, ρ 2, T o2, and P o2 at the exit of the duct. 3. Air enters the combustor of a jet engine at P 1 =10 atm, T 1 = 1000 R, and M 1 = 0.2. Fuel is injected and burned, with a fuel to air ratio (by mass) of Calculate the Mach number, the static pressure, and the static temperature at the exit of the combustor. Assume one-dimensional frictionless flow with γ = 11

12 1.4 for the fuel air mixture. The heat released during the combustion per slug of fuel is equal to 4.5x10 8 lb.ft. One-Dimensional Flow with Friction 1. Consider the flow of air through a pipe of inside diameter = 0.15 m and length = 30 m. The inlet flow conditions are M 1 = 0.3, p 1 = 1 atm, and T 1 = 273 K. Assuming f = constant =.005, calculate the flow conditions at the exit M 2, p 2, T 2, ρ 2, T o2, and P o2. 2. Consider the flow of air through a pipe of inside diameter = 0.4 ft and length = 5 ft. The inlet flow conditions are M 1 = 3, p 1 = 1 atm, and T 1 = 300 K. Assuming f = constant = 0.005, calculate the flow conditions at the exit M 2, p 2, T 2, ρ 2, T o2, and P o2. 3. Air is flowing through a pipe of 0.02 m inside diameter and 40 m length. The exit flow conditions of the pipe are M 2 = 0.5, p 2 = 1 atm, and T 2 = 270 K. Assuming adiabatic, one-dimensional flow, with a local friction coefficient of 0.005, calculate the flow conditions at the entrance of the pipe (M 1, p 1, T 1, ρ 1, T o1, and P o1 ). Variable Area Flow 1. A convergent divergent nozzle has total conditions of 700 kpa and 330 o K. The mass flow rate is 1 kg/s. the total exit pressure is 550 kpa and the static exit pressure is 500 kpa. If the flow is isentropic except for the occurrence of a shock, calculate the throat area, the Mach number before and after the shock, the area where the shock occurs, the exit area and exit velocity and density. 2. A nozzle is to be designed to expand air isentropically from the total conditions 300 o K and atm to the atmosphere, at 15 km altitude, with a rate of 25 kg/s. Assume that the air is a perfect gas with γ =1.4, R=287 J/kg/K and the flow is one dimensional. Calculate the throat and exit diameters of the nozzle and find the flow velocity at the exit section. What is the exit velocity and the mass flow rate when the nozzle is operated at sea level. (At sea level the ambient pressure is kpa and at 15 km altitude the ambient pressure is kpa) 3. A convergent divergent nozzle is designed to operate with an exit Mach number of The nozzle is supplied from an air reservoir at 1000 psia. Assuming one dimensional flow, calculate: The maximum back pressure to choke the nozzle, 12

13 The range of back pressures over which a normal shock will appear in the nozzle, The back pressure for the nozzle to be perfectly expanded to the design Mach number, The range of back pressures for supersonic flow at the nozzle exit plane. 4. A convergent divergent nozzle is designed to expand air from a chamber in which the pressure is 700 kpa and the temperature is 35 o C to give a Mach number of 1.6. The mass flow rate through the nozzle under design conditions is kg/s. Find: the throat and exit areas of the nozzle, the design back pressure and the temperature of the air leaving the nozzle with this back pressure, the lowest back pressure for which there will be no supersonic flow in the nozzle, The back pressure below which there are no shock waves in the nozzle. 5. Air flows through a convergent divergent nozzle that has an inlet area of 25 cm2. The inlet temperature and pressure are 50 o C and 550 kpa respectively, and the velocity at the inlet is 80 m/s. If the flow is assumed to be isentropic, and if the exit pressure is 120 kpa, find the throat and exit areas and the exit velocity. 6. Air enters a convergent divergent nozzle at Mach number 0.2. The stagnation pressure is 700 kpa and the stagnation temperature is 5 o C. The throat area of the nozzle is 46 cm 2. If the pressure at the exit to the nozzle is 500 kpa, determine if there is a shock in the divergent portion of the nozzle. If there is a shock wave, determine the nozzle area at which the shock occurs and the Mach number and pressure just before and just after the shock wave. 7. Air with a stagnation pressure and temperature of 100 kpa and 150 o C is expanded through a convergent divergent nozzle that is designed to give an exit Mach number of 2. The nozzle exit area is 30 cm 2. Find the exit pressure and the mass rate of flow through the nozzle when operating at design conditions. Also find the exit pressure if a normal shock wave occurs in the divergent portion of the nozzle at a section where the area is half between the throat and exit areas. Oblique Shock and Expansion Waves 1. A flat plate airfoil of chord c is in a Mach 3 at an angle of attack of 8 deg. Use the shock expansion theory calculates the lift and drag coefficient C L & C D. 13

14 2. A symmetric double wedge two-dimensional airfoil having a thickness to chord ratio of 0.07 is placed at an angle of attack of 7 deg in a supersonic air stream of Mach number 2.5. Calculate the lift and drag coefficients. 3. Consider a symmetric double wedge airfoil. If the semi wedge angle is 10 deg and the free stream Mach number is 2, use shock expansion theory to compute the lift and drag coefficients, the moment coefficient about the leading edge point. Make these calculations for angle of attack 10 deg. 4. A thin two dimensional flapped flat plate airfoil is placed at an angle of attack α in a stream of Mach number 4. Calculate the lift and drag coefficients for the following cases: ( α = -2.5,2.5,5,7.5,10) and ( δ = -5,0,5,10) where δ is the deflection angle of the flap whose length is 20% of the total airfoil chord. 5. Consider a two dimensional flow about an infinite wedge whose cross sectional shape is a right angle. The free stream Mach number is 5 and the wedge angle is 10 deg. The upper surface is aligned with the free stream direction. Calculate the lift and drag coefficients if (P b is set equal to zero & P b is set equal to P ) Estimate without calculations the exact values of C L & C D. M P b Prof. Dr. Mohamed Madbouli Abdelrahman 14

One-Dimensional Isentropic Flow

One-Dimensional Isentropic Flow Cairo University Second Year Faculty of Engineering Gas Dynamics AER 201B Aerospace Department Sheet (1) 2011-2012 One-Dimensional Isentropic Flow 1. Assuming the flow of a perfect gas in an adiabatic,

More information

6.1 According to Handbook of Chemistry and Physics the composition of air is

6.1 According to Handbook of Chemistry and Physics the composition of air is 6. Compressible flow 6.1 According to Handbook of Chemistry and Physics the composition of air is From this, compute the gas constant R for air. 6. The figure shows a, Pitot-static tube used for velocity

More information

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

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

More information

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

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

More information

2 Navier-Stokes Equations

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

More information

Given the water behaves as shown above, which direction will the cylinder rotate?

Given the water behaves as shown above, which direction will the cylinder rotate? water stream fixed but free to rotate Given the water behaves as shown above, which direction will the cylinder rotate? ) Clockwise 2) Counter-clockwise 3) Not enough information F y U 0 U F x V=0 V=0

More information

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

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,

More information

IX. COMPRESSIBLE FLOW. ρ = P

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.

More information

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

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

More information

Chapter Four fluid flow mass, energy, Bernoulli and momentum

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

More information

GAS DYNAMICS AND JET PROPULSION

GAS DYNAMICS AND JET PROPULSION GAS DYNAMICS AND JE PROPULSION 1. What is the basic difference between compressible and incompressible fluid flow? Compressible Incompressible 1. Fluid velocities are appreciable 1. Fluid velocities are

More information

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

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.

More information

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

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

More information

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

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,

More information

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

4 Finite Control Volume Analysis Introduction Reynolds Transport Theorem Conservation of Mass iv 2.3.2 Bourdon Gage................................... 92 2.3.3 Pressure Transducer................................ 93 2.3.4 Manometer..................................... 95 2.3.4.1 Piezometer................................

More information

10.52 Mechanics of Fluids Spring 2006 Problem Set 3

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

More information

FE Exam Fluids Review October 23, Important Concepts

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

More information

Introduction to Aerospace Engineering

Introduction to Aerospace Engineering 4. Basic Fluid (Aero) Dynamics Introduction to Aerospace Engineering Here, we will try and look at a few basic ideas from the complicated field of fluid dynamics. The general area includes studies of incompressible,

More information

4 Compressible Fluid Dynamics

4 Compressible Fluid Dynamics 4 Compressible Fluid Dynamics 4. Compressible flow definitions Compressible flow describes the behaviour of fluids that experience significant variations in density under the application of external pressures.

More information

UNIT 1 COMPRESSIBLE FLOW FUNDAMENTALS

UNIT 1 COMPRESSIBLE FLOW FUNDAMENTALS UNIT 1 COMPRESSIBLE FLOW FUNDAMENTALS 1) State the difference between compressible fluid and incompressible fluid? 2) Define stagnation pressure? 3) Express the stagnation enthalpy in terms of static enthalpy

More information

Applied Gas Dynamics Flow With Friction and Heat Transfer

Applied Gas Dynamics Flow With Friction and Heat Transfer Applied Gas Dynamics Flow With Friction and Heat Transfer Ethirajan Rathakrishnan Applied Gas Dynamics, John Wiley & Sons (Asia) Pte Ltd c 2010 Ethirajan Rathakrishnan 1 / 121 Introduction So far, we have

More information

Jet Aircraft Propulsion Prof. Bhaskar Roy Prof. A.M. Pradeep Department of Aerospace Engineering

Jet Aircraft Propulsion Prof. Bhaskar Roy Prof. A.M. Pradeep Department of Aerospace Engineering Jet Aircraft Propulsion Prof. Bhaskar Roy Prof. A.M. Pradeep Department of Aerospace Engineering Indian Institute of Technology, IIT Bombay Module No. # 01 Lecture No. # 08 Cycle Components and Component

More information

Aerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved)

Aerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved) Flow with no friction (inviscid) Aerodynamics Basic Aerodynamics Continuity equation (mass conserved) Flow with friction (viscous) Momentum equation (F = ma) 1. Euler s equation 2. Bernoulli s equation

More information

Department of Energy Sciences, LTH

Department of Energy Sciences, LTH Department of Energy Sciences, LTH MMV11 Fluid Mechanics LABORATION 1 Flow Around Bodies OBJECTIVES (1) To understand how body shape and surface finish influence the flow-related forces () To understand

More information

Lecture with Numerical Examples of Ramjet, Pulsejet and Scramjet

Lecture with Numerical Examples of Ramjet, Pulsejet and Scramjet Lecture 41 1 Lecture with Numerical Examples of Ramjet, Pulsejet and Scramjet 2 Problem-1 Ramjet A ramjet is flying at Mach 1.818 at an altitude 16.750 km altitude (Pa = 9.122 kpa, Ta= - 56.5 0 C = 216.5

More information

Given a stream function for a cylinder in a uniform flow with circulation: a) Sketch the flow pattern in terms of streamlines.

Given a stream function for a cylinder in a uniform flow with circulation: a) Sketch the flow pattern in terms of streamlines. Question Given a stream function for a cylinder in a uniform flow with circulation: R Γ r ψ = U r sinθ + ln r π R a) Sketch the flow pattern in terms of streamlines. b) Derive an expression for the angular

More information

Orifice and Venturi Pipe Flow Meters

Orifice and Venturi Pipe Flow Meters Orifice and Venturi Pipe Flow Meters by Harlan H. Bengtson, PhD, P.E. 1. Introduction Your Course Title Here The flow rate of a fluid flowing in a pipe under pressure is measured for a variety of applications,

More information

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

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.

More information

Lesson 6 Review of fundamentals: Fluid flow

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

More information

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. 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

More information

Richard Nakka's Experimental Rocketry Web Site

Richard Nakka's Experimental Rocketry Web Site Página 1 de 7 Richard Nakka's Experimental Rocketry Web Site Solid Rocket Motor Theory -- Nozzle Theory Nozzle Theory The rocket nozzle can surely be described as the epitome of elegant simplicity. The

More information

Fundamentals of Gas Dynamics (NOC16 - ME05) Assignment - 8 : Solutions

Fundamentals of Gas Dynamics (NOC16 - ME05) Assignment - 8 : Solutions Fundamentals of Gas Dynamics (NOC16 - ME05) Assignment - 8 : Solutions Manjul Sharma & Aswathy Nair K. Department of Aerospace Engineering IIT Madras April 5, 016 (Note : The solutions discussed below

More information

Fundamentals of Fluid Mechanics

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

More information

The E80 Wind Tunnel Experiment the experience will blow you away. by Professor Duron Spring 2012

The E80 Wind Tunnel Experiment the experience will blow you away. by Professor Duron Spring 2012 The E80 Wind Tunnel Experiment the experience will blow you away by Professor Duron Spring 2012 Objectives To familiarize the student with the basic operation and instrumentation of the HMC wind tunnel

More information

ENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids

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

More information

Flow Measurement in Pipes and Ducts COURSE CONTENT

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.

More information

Tutorial 10. Boundary layer theory

Tutorial 10. Boundary layer theory Tutorial 10 Boundary layer theory 1. If the velocity distribution law in a laminar boundary layer over a flat plate is assumes to be of the form, determine the velocity distribution law. At y = 0, u= 0

More information

Lecture 22. Mechanical Energy Balance

Lecture 22. Mechanical Energy Balance Lecture 22 Mechanical Energy Balance Contents Exercise 1 Exercise 2 Exercise 3 Key Words: Fluid flow, Macroscopic Balance, Frictional Losses, Turbulent Flow Exercise 1 It is proposed to install a fan to

More information

1. (20 pts total 2pts each) - Circle the most correct answer for the following questions.

1. (20 pts total 2pts each) - Circle the most correct answer for the following questions. ME 50 Gas Dynamics Spring 009 Final Exam NME:. (0 pts total pts each) - Circle the most correct answer for the following questions. i. normal shock propagated into still air travels with a speed (a) equal

More information

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

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

More information

ME332 FLUID MECHANICS LABORATORY (PART I)

ME332 FLUID MECHANICS LABORATORY (PART I) ME332 FLUID MECHANICS LABORATORY (PART I) Mihir Sen Department of Aerospace and Mechanical Engineering University of Notre Dame Notre Dame, IN 46556 Version: January 14, 2002 Contents Unit 1: Hydrostatics

More information

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

More information

Only if handing in. Name: Student No.: Page 2 of 7

Only if handing in. Name: Student No.: Page 2 of 7 UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING FINAL EXAMINATION, DECEMBER 10, 2014 2:00 PM 2.5 HOURS CHE 211F FLUID MECHANICS EXAMINER: PROFESSOR D.G. ALLEN ANSWER ALL SEVEN (7) QUESTIONS

More information

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 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

More information

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

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.

More information

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

More information

Introduction. In general, gases are highly compressible and liquids have a very low compressibility. COMPRESSIBLE FLOW

Introduction. In general, gases are highly compressible and liquids have a very low compressibility. COMPRESSIBLE FLOW COMRESSIBLE FLOW COMRESSIBLE FLOW Introduction he compressibility of a fluid is, basically, a measure of the change in density that will be produced in the fluid by a specific change in pressure and temperature.

More information

1. For an ideal gas, internal energy is considered to be a function of only. YOUR ANSWER: Temperature

1. For an ideal gas, internal energy is considered to be a function of only. YOUR ANSWER: Temperature CHAPTER 11 1. For an ideal gas, internal energy is considered to be a function of only. YOUR ANSWER: Temperature 2.In Equation 11.7 the subscript p on the partial derivative refers to differentiation at

More information

FLUID MECHANICS D203 SAE SOLUTIONS TUTORIAL 2 APPLICATIONS OF BERNOULLI SELF ASSESSMENT EXERCISE 1

FLUID MECHANICS D203 SAE SOLUTIONS TUTORIAL 2 APPLICATIONS OF BERNOULLI SELF ASSESSMENT EXERCISE 1 FLUID MECHANICS D203 SAE SOLUTIONS TUTORIAL 2 APPLICATIONS OF BERNOULLI SELF ASSESSMENT EXERCISE 1 1. A pipe 100 mm bore diameter carries oil of density 900 kg/m3 at a rate of 4 kg/s. The pipe reduces

More information

Middle East Technical University Department of Mechanical Engineering ME 305 Fluid Mechanics I Fall 2018 Section 4 (Dr.

Middle East Technical University Department of Mechanical Engineering ME 305 Fluid Mechanics I Fall 2018 Section 4 (Dr. Middle East Technical University Department of Mechanical Engineering ME 305 Fluid Mechanics I Fall 2018 Section 4 (Dr. Sert) Study Set 7 Reading Assignment R1. Read the section Common Dimensionless Groups

More information

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

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

More information

CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS NOOR ALIZA AHMAD

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.

More information

Introduction to Aerospace Engineering

Introduction to Aerospace Engineering Introduction to Aerospace Engineering Lecture slides Challenge the future 3-0-0 Introduction to Aerospace Engineering Aerodynamics 5 & 6 Prof. H. Bijl ir. N. Timmer Delft University of Technology 5. Compressibility

More information

Review of Fundamentals - Fluid Mechanics

Review of Fundamentals - Fluid Mechanics Review of Fundamentals - Fluid Mechanics Introduction Properties of Compressible Fluid Flow Basics of One-Dimensional Gas Dynamics Nozzle Operating Characteristics Characteristics of Shock Wave A gas turbine

More information

Section 4.1: Introduction to Jet Propulsion. MAE Propulsion Systems II

Section 4.1: Introduction to Jet Propulsion. MAE Propulsion Systems II Section 4.1: Introduction to Jet Propulsion Jet Propulsion Basics Squeeze Bang Blow Suck Credit: USAF Test Pilot School 2 Basic Types of Jet Engines Ramjet High Speed, Supersonic Propulsion, Passive Compression/Expansion

More information

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

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

More information

Chapter 17. For the most part, we have limited our consideration so COMPRESSIBLE FLOW. Objectives

Chapter 17. For the most part, we have limited our consideration so COMPRESSIBLE FLOW. Objectives Chapter 17 COMPRESSIBLE FLOW For the most part, we have limited our consideration so far to flows for which density variations and thus compressibility effects are negligible. In this chapter we lift this

More information

Fluids. Fluids in Motion or Fluid Dynamics

Fluids. Fluids in Motion or Fluid Dynamics Fluids Fluids in Motion or Fluid Dynamics Resources: Serway - Chapter 9: 9.7-9.8 Physics B Lesson 3: Fluid Flow Continuity Physics B Lesson 4: Bernoulli's Equation MIT - 8: Hydrostatics, Archimedes' Principle,

More information

Performance. 5. More Aerodynamic Considerations

Performance. 5. More Aerodynamic Considerations Performance 5. More Aerodynamic Considerations There is an alternative way of looking at aerodynamic flow problems that is useful for understanding certain phenomena. Rather than tracking a particle of

More information

Introduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD)

Introduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD) Introduction to Aerodynamics Dr. Guven Aerospace Engineer (P.hD) Aerodynamic Forces All aerodynamic forces are generated wither through pressure distribution or a shear stress distribution on a body. The

More information

Piping Systems and Flow Analysis (Chapter 3)

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

More information

Applied Fluid Mechanics

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

More information

Multistage Rocket Performance Project Two

Multistage Rocket Performance Project Two 41 Multistage Rocket Performance Project Two Charles R. O Neill School of Mechanical and Aerospace Engineering Oklahoma State University Stillwater, OK 74078 Project Two in MAE 3293 Compressible Flow December

More information

Applied Fluid Mechanics

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

More information

for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory?

for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory? 1. 5% short answers for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory? in what country (per Anderson) was the first

More information

Civil aeroengines for subsonic cruise have convergent nozzles (page 83):

Civil aeroengines for subsonic cruise have convergent nozzles (page 83): 120 Civil aeroengines for subsonic cruise have convergent nozzles (page 83): Choked convergent nozzle must be sonic at the exit A N. Consequently, the pressure (p 19 ) at the nozzle exit will be above

More information

The ramjet cycle. Chapter Ramjet flow field

The ramjet cycle. Chapter Ramjet flow field Chapter 3 The ramjet cycle 3. Ramjet flow field Before we begin to analyze the ramjet cycle we will consider an example that can help us understand how the flow through a ramjet comes about. The key to

More information

Steady waves in compressible flow

Steady waves in compressible flow Chapter Steady waves in compressible flow. Oblique shock waves Figure. shows an oblique shock wave produced when a supersonic flow is deflected by an angle. Figure.: Flow geometry near a plane oblique

More information

EXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER

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

More information

Orifice and Venturi Pipe Flow Meters

Orifice and Venturi Pipe Flow Meters Orifice and Venturi Pipe Flow Meters For Liquid and Gas Flow by Harlan H. Bengtson, PhD, P.E. 1. Introduction Orifice and Venturi Pipe Flow Meters The flow rate of a fluid flowing in a pipe under pressure

More information

2 Internal Fluid Flow

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.

More information

5 ENERGY EQUATION OF FLUID MOTION

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

More information

Measurements using Bernoulli s equation

Measurements using Bernoulli s equation An Internet Book on Fluid Dynamics Measurements using Bernoulli s equation Many fluid measurement devices and techniques are based on Bernoulli s equation and we list them here with analysis and discussion.

More information

Unified Quiz: Thermodynamics

Unified Quiz: Thermodynamics Unified Quiz: Thermodynamics October 14, 2005 Calculators allowed. No books or notes allowed. A list of equations is provided. Put your ID number on each page of the exam. Read all questions carefully.

More information

ME332 FLUID MECHANICS LABORATORY (PART II)

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

More information

SPC 407 Sheet 2 - Solution Compressible Flow - Governing Equations

SPC 407 Sheet 2 - Solution Compressible Flow - Governing Equations SPC 407 Sheet 2 - Solution Compressible Flow - Governing Equations 1. Is it possible to accelerate a gas to a supersonic velocity in a converging nozzle? Explain. No, it is not possible. The only way to

More information

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.

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

More information

AEROSPACE ENGINEERING

AEROSPACE ENGINEERING AEROSPACE ENGINEERING Subject Code: AE Course Structure Sections/Units Topics Section A Engineering Mathematics Topics (Core) 1 Linear Algebra 2 Calculus 3 Differential Equations 1 Fourier Series Topics

More information

SPC 407 Sheet 5 - Solution Compressible Flow Rayleigh Flow

SPC 407 Sheet 5 - Solution Compressible Flow Rayleigh Flow SPC 407 Sheet 5 - Solution Compressible Flow Rayleigh Flow 1. Consider subsonic Rayleigh flow of air with a Mach number of 0.92. Heat is now transferred to the fluid and the Mach number increases to 0.95.

More information

Mass of fluid leaving per unit time

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.

More information

Experiment No.4: Flow through Venturi meter. Background and Theory

Experiment No.4: Flow through Venturi meter. Background and Theory Experiment No.4: Flow through Venturi meter Background and Theory Introduction Flow meters are used in the industry to measure the volumetric flow rate of fluids. Differential pressure type flow meters

More information

Applied Fluid Mechanics

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

More information

Propulsion Thermodynamics

Propulsion Thermodynamics Chapter 1 Propulsion Thermodynamics 1.1 Introduction The Figure below shows a cross-section of a Pratt and Whitney JT9D-7 high bypass ratio turbofan engine. The engine is depicted without any inlet, nacelle

More information

equation 4.1 INTRODUCTION

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

More information

Jet Aircraft Propulsion Prof. Bhaskar Roy Prof A M Pradeep Department of Aerospace Engineering Indian Institute of Technology, Bombay

Jet Aircraft Propulsion Prof. Bhaskar Roy Prof A M Pradeep Department of Aerospace Engineering Indian Institute of Technology, Bombay Jet Aircraft Propulsion Prof. Bhaskar Roy Prof A M Pradeep Department of Aerospace Engineering Indian Institute of Technology, Bombay Module No. #01 Lecture No. # 07 Jet Engine Cycles For Aircraft propulsion

More information

Atmospheric pressure. 9 ft. 6 ft

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):

More information

Chapter 4 DYNAMICS OF FLUID FLOW

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

More information

4 Mechanics of Fluids (I)

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

More information

Modelling Nozzle throat as Rocket exhaust

Modelling Nozzle throat as Rocket exhaust Vol. 3, Issue. 4, Jul - Aug. 2013 pp-2502-2506 ISSN: 2249-6645 Modelling Nozzle throat as Rocket exhaust Keshava Rao P. 1, Komma Rahul 2, Souda Dinesh 3 1 (Mechanical Engineering, CBIT College, India)

More information

Contents. Preface... xvii

Contents. Preface... xvii Contents Preface... xvii CHAPTER 1 Idealized Flow Machines...1 1.1 Conservation Equations... 1 1.1.1 Conservation of mass... 2 1.1.2 Conservation of momentum... 3 1.1.3 Conservation of energy... 3 1.2

More information

ME 6139: High Speed Aerodynamics

ME 6139: High Speed Aerodynamics Dr. A.B.M. Toufique Hasan Professor Department of Mechanical Engineering, BUET Lecture-01 04 November 2017 teacher.buet.ac.bd/toufiquehasan/ toufiquehasan@me.buet.ac.bd 1 Aerodynamics is the study of dynamics

More information

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 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

More information

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

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

More information

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

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

More information

Hydraulics and hydrology

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

More information

Chapter 6. Losses due to Fluid Friction

Chapter 6. Losses due to Fluid Friction Chapter 6 Losses due to Fluid Friction 1 Objectives ä To measure the pressure drop in the straight section of smooth, rough, and packed pipes as a function of flow rate. ä To correlate this in terms of

More information

Fundamentals of Gas Dynamics (NOC16 - ME05) Assignment - 10 : Solutions

Fundamentals of Gas Dynamics (NOC16 - ME05) Assignment - 10 : Solutions Fundamentals of Gas Dynamics (NOC16 - ME05) Assignment - 10 : Solutions Manjul Sharma & Aswathy Nair K. Department of Aerospace Engineering IIT Madras April 18, 016 (Note : The solutions discussed below

More information

Effect of Mach number on Wall Pressure Flow Field for Area Ratio 2.56

Effect of Mach number on Wall Pressure Flow Field for Area Ratio 2.56 IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) e-issn: 2278-1684,p-ISSN: 2320-334X, Volume 11, Issue 2 Ver. I (Mar- Apr. 2014), PP 56-64 Effect of Mach number on Wall Pressure Flow Field

More information

Chapter 3 Bernoulli Equation

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

More information

Hydraulics. B.E. (Civil), Year/Part: II/II. Tutorial solutions: Pipe flow. Tutorial 1

Hydraulics. B.E. (Civil), Year/Part: II/II. Tutorial solutions: Pipe flow. Tutorial 1 Hydraulics B.E. (Civil), Year/Part: II/II Tutorial solutions: Pipe flow Tutorial 1 -by Dr. K.N. Dulal Laminar flow 1. A pipe 200mm in diameter and 20km long conveys oil of density 900 kg/m 3 and viscosity

More information