Chapter 6 The Impulse-Momentum Principle
|
|
- Annabel Strickland
- 5 years ago
- Views:
Transcription
1 Chapter 6 The Impulse-Momentum Principle 6. The Linear Impulse-Momentum Equation 6. Pipe Flow Applications 6.3 Open Channel Flow Applications 6.4 The Angular Impulse-Momentum Principle Objectives: - Develop impulse - momentum equation, the third of three basic equations of fluid mechanics, added to continuity and work-energy principles - Develop linear and angular momentum (moment of momentum) equations - 6-
2 6.0 Introduction Three basic tools for the solution of fluid flow problems Impulse - momentum equation Continuity principle Work-energy principle Impulse - momentum equation ~ derived from Newton's nd law in vector form F ma Multifly by dt F dt madt d( mv c ) F d ( mvc) dt where vc velocity of the center of mass of the system of mass mvc linear momentum 6-
3 m sys dm v c m sys vdm ( Fdt ) impulse in time dt - Define the fluid system to include all the fluid in a specified control volume whereas the Euler equations was developed for a small fluid system - Restrict the analysis to steady flow - Shear stress is not explicitly included - This equation will apply equally well to real fluids as well as ideal fluids. - Develop linear and angular momentum (moment of momentum) equations - Linear momentum equation: calculate magnitude and direction of resultant forces - Angular momentum equation: calculate line of action of the resultant forces, rotating fluid machinery (pump, turbine) 6-3
4 6. The Linear Impulse Momentum Equation Use the same control volume previously employed for conservation of mass and work-energy. For the individual fluid system in the control volume, d d F ma mv vdv dt dt (a) Sum them all d d F vdv vdv ext dt dt sys sys Use Reynolds Transport Theorem to evaluate RHS i v for momentum/mass d dt de vdv ivda vvda vvda dt sys c.. s c.. s out c.. s in (b) where E = momentum of fluid system in the control volume 6-4
5 iv momentum per unit mass Ch. 6 The Impulse-Momentum Principle Because the streamlines are straight and parallel at Sections and, velocity is constant over the cross sections. The cross-sectional area is normal to the velocity vector over the entire cross section. In Eq. (b) vv da v v nda vvda V Q c. s. out c. s. out c. s. out v Q vvda csinvv ndavq csin.... v Q Q Q By Continuity eq: R. H. S. of (b) Q V V (c) Substitute (c) into (a) F Q V V (6.) In -D flow, Fx Q Vx Vx (6.a) Fz Q Vz Vz (6.b) 6-5
6 General form in case momentum enters and leaves the control volume at more than one location: F Qv Qv out in (6.3) - The external forces include both normal (pressure) and tangential (shear) forces on the fluid in the control volume, as well as the weight of the fluid inside the control volume at a given time. - Advantages of impulse-momentum principle ~ Only flow conditions at inlets and exits of the control volume are needed for successful application. ~ Detailed flow processes within the control volume need not be known to apply the principle. 6-6
7 6. Pipe Flow Applications Forces exerted by a flowing fluid on a pipe bend, enlargement, or contraction in a pipeline may be computed by a application of the impulse-momentum principle. The reducing pipe bend Known: flowrate, Q; pressures,, p p ; velocities, v, v Find: F (equal & opposite of the force exerted by the fluid on the bend) = force exerted by the bend on the fluid 6-7
8 Pressures: For streamlines essentially straight and parallel at section and, the forces F, and F result from hydrostatic pressure distributions. If mean pressure p and p are large, and the pipe areas are small, then F pa and F p A, and assumed to act at the centerline of the pipe instead of the center of pressure. Body forces: = total weight of fluid, W Force exerted by the bend on the fluid, F = resultant of the pressure distribution over the entire interior of the bend between sections &. ~ distribution is unknown in detail ~ resultant can be predicted by Impulse-momentum Eq. Now apply Impulse-momentum equation, Eq. (6.) (i) x-direction: 6-8
9 F p A p A F x cos x cos x x Q V V Q V V Combining the two equations to develop an expression for F x F p A p A cos Q( V V cos ) (6.4.a) x (ii) z-direction F sin z W pa F z sin 0 z z Q V V Q V F W p A sin QV sin (6.4.b) z If the bend is relatively sharp, the weight may be negligible, depending on the magnitudes of the pressure and velocities. 6-9
10 [IP 6.] 300 l/s of water flow through the vertical reducing pipe bend. Calculate the force exerted by the fluid on the bend if the volume of the bend is m N Given: 3 Q 300 l s 0.3 m s ; Vol. of bend m 3 A (0.3) 0.07 m 4 ; A (0.) 0.03 m 4 3 p 70 kpa 70 0 N m ) Continuity Eq. Q AV AV (4.5) 0.3 V 4.4 m/s
11 0.3 V 9.55 m/s 0.03 ) Bernoulli Eq. between and p V p V g g z z (4.4) p (9.55) 0.5 9,800 (9.8) 9,800 (9.8) p 8.8 kpa 3) Momentum Eq. Apply Eqs. 6.4a and 6.4b F p A p A cos Q( V V cos ) x F W p A sin QV sin z F pa 4948 N F 3 pa N W (volume) N 6-
12 F 4,948 (590.6) cos0 (9980.3)( cos0 ) 7,94 N x F 833 (590.6)sin0 (9980.3)(9.55sin0 0) 3,80 N z F F F 8,83 N x z F F z tan 5.7 x 6-
13 Abrupt enlargement in a closed passage ~ Real fluid flow The impulse-momentum principle can be employed to predict the fall of the energy line (energy loss due to a rise in the internal energy of the fluid caused by viscous dissipation) at an abrupt axisymmetric enlargement in a passage. Energy loss Consider the control surface ABCD assuming a one-dimensional flow i) Continuity Q AV AV Result from hydrostatic pressure distribution over the area ii) Momentum For area AB it is an approximation because of the dynamics of eddies in the dead water zone. F p A p A Q( V V) x 6-3
14 VA ( p p) A ( V V) g p p V ( V V ) g (a) iii) Bernoulli equation p V p V H g g p p V V H g g (b) where H Borda-Carnot Head loss Combine (a) and (b) V( V V) V V H g g g V VV V V ( V V ) H g g g g 6-4
15 6.3 Open Channel Flow Applications Applications impulse-momentum principle for Open Channel Flow - Computation of forces exerted by flowing water on overflow or underflow structures (weirs or gates) - Hydraulic jump - Wave propagation [Case ] Sluice gate Shear force is neglected Consider a control volume that has uniform flow and straight and parallel streamlines at the entrance and exit Apply first Bernoulli and continuity equations to find values of depths y and y and flowrate per unit width q Then, apply the impulse-momentum equation to find the force the water exerts on the sluice gate 6-5
16 F Q( V V ) x Discharge per unit width F F F F Q( V V ) q V V x x x x where q Q W discharge per unit width yv yv Assume that the pressure distribution is hydrostatic at sections and, replace V with q/y y y Fx q ( ) (6.6) y y [Re] Hydrostatic pressure distribution y y F h A y c ( ) 3 ( y) Ic l p l c y la y c ( y 6 ) Cp y y y
17 For ideal fluid (to a good approximation, for a real fluid), the force tnagent to the gate is zero. shear stress is neglected. Hence, the resultant force is normal to the gate. F F cos x We don t need to apply the impulse-momentum equation in the z-direction. [Re] The impulse-momentum equation in the z-direction F Q( V V ) z z z F F W F Q(0 0) z OB z F W F z OB Non-uniform distribution pressure 6-7
18 [IP 6.] For the two-dimensional overflow structure, calculate the horizontal component of the resultant force the fluid exerts on the structure Lift gate Ideal fluid Continuity Eq. q5v V (4.7) Bernoulli's equation between () and () 0 5m V V 0 m g g (5.7) Combine two equations V 3.33 m s V 8.33 m s 3 q 5(3.33) 6.65 m s m 6-8
19 Hydrostatic pressure principle kn m y (5) F hc A y kn m () F kn m Impulse-Momentum Eq. ( kg m ) F,500 F 9,600 ( )( ) x x F 9.65 kn m x [Cf] What is the force if the gate is closed? 6-9
20 Jamshil submerged weir (Seo, 999) Jamshil submerged weir with gate opened (Q = 00 m 3 /s) 6-0
21 Bucket roller Jamshil submerged weir Model Test; Q = 00 m 3 /s (Seo, 999) Jamshil submerged weir Model Test (Q = 5,000 m 3 /s) 6-
22 [Case ] Hydraulic Jump When liquid at high velocity discharges into a zone of lower velocity, a rather abrupt rise (a standing wave) occurs in water surface and is accompanied by violent turbulence, eddying, air entrainment, surface undulation. such as a wave is known as a hydraulic jump large head loss (energy dissipation) Head loss due to hydraulic jump turbulence, eddying, air entrainment, surface undulation in the hydraulic jump Neglect shear force Apply impulse-momentum equation to find the relation between the depths for a given flowrate Construct a control volume enclosing the hydraulic jump between two sections and where the streamlines are straight and parallel y y Fx FF q( V V) where q flowrate per unit width 6-
23 Substitute the continuity relations V q y ; V q y Rearrange (divide by ) q y q y gy gy Solve for y y y 8 8 q V 3 y gy gy (6.7) Set Fr V gy Fr V gy William Froude (80~879) where Fr Froude number Inertia Force Gravity Force V gy 6-3
24 Then, we have y y 8Fr Jump Equation (a) Fr : critical flow y y 8 y y No jump (b) Fr : super-critical flow y y yy Hydraulic jump (c) Fr : sub-critical flow y y y y physically impossible ( rise of energy line through the jump is impossible) Conclusion: For a hydraulic jump to occur, the upstream conditions must be such that V gy. 6-4
25 [IP 6.3] p. 99 ; Water flows in a horizontal open channel. y 0.6 m 3 q 3.7 m s m Find y, and power dissipated in hydraulic jump. [Sol] (i) Continuity q yv yv 3.7 V 6.7 m s 0.6 Fr V hydraulic jump occurs gy 9.8(0.6) (ii) Jump Eq. y y 8Fr 0.6 8(.54).88 m 6-5
26 V m s.88 (iii) Bernoulli Eq. (Work-Energy Eq.) V V y y E g g (6.7) (.97) E (9.8) (9.8) E 0.46 m Power QE kw meter of width The hydraulic jump is excellent energy dissipator (used in the spillway). 6-6
27 Pulsating jump E/E ~ 85% 6-7
28 [Case 3] Wave Propagation The velocity (celerity) of small gravity waves in a body of water can be calculated by the impulse-momentum equation. small gravity waves ~ appears as a small localized rise in the liquid surface which propagate at a velocity a ~ extends over the full depth of the flow [Cf] small surface disturbance (ripple) ~ liquid movement is restricted to a region near the surface For the steady flow, assign the velocity under the wave as a From continuity 6-8
29 ' ay a y dy From impulse-momentum y y dy ' ay a (6.a) Combining these two equations gives a g y dy Letting dy approach zero results in a gy (6.8) The celerity of the samll gravity wave depends only on the depth of flow. 6-9
30 6.4 The Angular Impulse-Momentum Principle The angular impulse-momentum equation can be developed using moments of the force and momentum vectors V z V V x (x, z ) (x, z ) Fig Take a moment of forces and momentum vectors for the small individual fluid system about d d r F ( r mv) ( r dvolv) dt dt Sum this for control volume d rfext ( rv) dvol. dt sys (a) 6-30
31 Use Reynolds Transport Theorem to evaluate the integral de d ( r v) dvol. iv da dt dt sys C. S. ( r v ) v da ( rv ) vda CSout.. CSin.. irv (b) where E moment of momentum of fluid system irv = moment of momentum per unit mass Restrict to control volume where the fluid enters and leaves at sections where the streamlines are straight and parallel and with the velocity normal to the cross-sectional area d dt ( rv) dvol. ( rv) dq ( rv) dq sys C. S. out C. S. in Because velocity is uniform over the flow cross sections d dt sys ( rv) dvol. Q( r V ) Q( r V ) out out in in Q ( rv) out ( rv) in (c) where r position vector from the moment center to the centroid of entering or leaving flow cross section of the control volume 6-3
32 Substitute (c) into (a) ( rf ) M Q ( rv) ( rv) ext 0 out in (6.3) In -D flow, M Q( rv rv ) (6.4) 0 t t where Vt component of velocity normal to the moment arm r. In rectangular components, assuming V is directed with positive components in both x and z- direction, and with the moment center at the origin of the x-z coordinate system, for clockwise positive moments, M Q ( zv xv ) ( zv xv ) (6.5) 0 x z x z where x, z coordinates of centroid of the entering cross section x, z coordinates of centroid of the leaving cross section For the fluid that enter or leave the control volume at more than one cross-section, M 0 ( QrVt) out( QrVt) in (6.6) 6-3
33 [IP 6.6] Compute the location of the resultant force exerted by the water on the pipe bend. 590 N 8,83 N Assume that center of gravity of the fluid is 0.55 m to the right of section, and the forces F and F act at the centroid of the sections rather than at the center of pressure. Take moments about the center of section M Q ( z v x v ) ( zv xv ) 0 x x x x x 0, z 0, x 0.6, z.5 For this case, T r(8,83) 0.55(833).5(590cos60 ) 0.6( 590sin 60 ) (0.3998).5( 9.55 cos60 ) 0.6(9.55sin 60 ) r 0.59 m 6-33
34 [Re] Torque for rotating system d T ( rf) ( rmvc) dt Where T torque Tdt torque impulse rmv c angular momentum (moment of momentum) r radius vector from the origin 0 to the point of application of a force [Re] Vector product (cross product) V FG -Magnitude: V F G sin -Direction: perpendicular to the plane of F and G (right-hand rule) If F, G are in the plane of x and y, then the V is in the z plane. 6-34
35 Homework Assignment # 6 Due: week from today Prob. 6. Prob. 6.6 Prob. 6.4 Prob. 6.6 Prob Prob Prob Prob Prob Prob
The Impulse-Momentum Principle
Chapter 6 /60 The Impulse-Momentum Principle F F Chapter 6 The Impulse-Momentum Principle /60 Contents 6.0 Introduction 6. The Linear Impulse-Momentum Equation 6. Pipe Flow Applications 6.3 Open Channel
More informationCHAPTER 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 informationChapter 4 Continuity Equation and Reynolds Transport Theorem
Chapter 4 Continuity Equation and Reynolds Transport Theorem 4.1 Control Volume 4. The Continuity Equation for One-Dimensional Steady Flow 4.3 The Continuity Equation for Two-Dimensional Steady Flow 4.4
More informationFluid 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
More informationIn this section, mathematical description of the motion of fluid elements moving in a flow field is
Jun. 05, 015 Chapter 6. Differential Analysis of Fluid Flow 6.1 Fluid Element Kinematics In this section, mathematical description of the motion of fluid elements moving in a flow field is given. A small
More information1.060 Engineering Mechanics II Spring Problem Set 4
1.060 Engineering Mechanics II Spring 2006 Due on Monday, March 20th Problem Set 4 Important note: Please start a new sheet of paper for each problem in the problem set. Write the names of the group members
More informationVARIED FLOW IN OPEN CHANNELS
Chapter 15 Open Channels vs. Closed Conduits VARIED FLOW IN OPEN CHANNELS Fluid Mechanics, Spring Term 2011 In a closed conduit there can be a pressure gradient that drives the flow. An open channel has
More informationCOURSE 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
More informationNPTEL 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
More informationConsider 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
More information5 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 informationFLUID MECHANICS. Chapter 3 Elementary Fluid Dynamics - The Bernoulli Equation
FLUID MECHANICS Chapter 3 Elementary Fluid Dynamics - The Bernoulli Equation CHAP 3. ELEMENTARY FLUID DYNAMICS - THE BERNOULLI EQUATION CONTENTS 3. Newton s Second Law 3. F = ma along a Streamline 3.3
More informationFE 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 informationClosed duct flows are full of fluid, have no free surface within, and are driven by a pressure gradient along the duct axis.
OPEN CHANNEL FLOW Open channel flow is a flow of liquid, basically water in a conduit with a free surface. The open channel flows are driven by gravity alone, and the pressure gradient at the atmospheric
More informationChapter 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 informationVisualization 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:
More informationChapter 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 informationHOMEWORK ASSIGNMENT ON BERNOULLI S EQUATION
AMEE 0 Introduction to Fluid Mechanics Instructor: Marios M. Fyrillas Email: m.fyrillas@frederick.ac.cy HOMEWORK ASSIGNMENT ON BERNOULLI S EQUATION. Conventional spray-guns operate by achieving a low pressure
More informationLesson 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 informationvector 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 informationR09. 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 informationClosed duct flows are full of fluid, have no free surface within, and are driven by a pressure gradient along the duct axis.
OPEN CHANNEL FLOW Open channel flow is a flow of liquid, basically water in a conduit with a free surface. The open channel flows are driven by gravity alone, and the pressure gradient at the atmospheric
More informationPROPERTIES OF FLUIDS
Unit - I Chapter - PROPERTIES OF FLUIDS Solutions of Examples for Practice Example.9 : Given data : u = y y, = 8 Poise = 0.8 Pa-s To find : Shear stress. Step - : Calculate the shear stress at various
More informationChapter 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,
More informationQ1 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
More informationFE 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 information2.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 informationExperiment (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
More informationHydraulics 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
More informations 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
More informationChapter 2: Basic Governing Equations
-1 Reynolds Transport Theorem (RTT) - Continuity Equation -3 The Linear Momentum Equation -4 The First Law of Thermodynamics -5 General Equation in Conservative Form -6 General Equation in Non-Conservative
More informationExperiment- 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
More informationBasic Fluid Mechanics
Basic Fluid Mechanics Chapter 6A: Internal Incompressible Viscous Flow 4/16/2018 C6A: Internal Incompressible Viscous Flow 1 6.1 Introduction For the present chapter we will limit our study to incompressible
More informationINSTITUTE 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
More information2 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 informationThe 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
More information11.1 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
More informationFLUID MECHANICS PROF. DR. METİN GÜNER COMPILER
FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER ANKARA UNIVERSITY FACULTY OF AGRICULTURE DEPARTMENT OF AGRICULTURAL MACHINERY AND TECHNOLOGIES ENGINEERING 1 5. FLOW IN PIPES 5.1.3. Pressure and Shear Stress
More informationCE 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 informationApproximate 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 information10.52 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 informationBasic equations of motion in fluid mechanics
1 Annex 1 Basic equations of motion in fluid mechanics 1.1 Introduction It is assumed that the reader of this book is familiar with the basic laws of fluid mechanics. Nevertheless some of these laws will
More informationCIE4491 Lecture. Hydraulic design
CIE4491 Lecture. Hydraulic design Marie-claire ten Veldhuis 19-9-013 Delft University of Technology Challenge the future Hydraulic design of urban stormwater systems Focus on sewer pipes Pressurized and
More informationTherefore, 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 informationAPPLIED 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 /
More informationSourabh V. Apte. 308 Rogers Hall
Sourabh V. Apte 308 Rogers Hall sva@engr.orst.edu 1 Topics Quick overview of Fluid properties, units Hydrostatic forces Conservation laws (mass, momentum, energy) Flow through pipes (friction loss, Moody
More informationUNIT 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:
More information28.2 Classification of Jumps
28.2 Classification of Jumps As mentioned earlier, the supercritical flow Froude number influences the characteristics of the hydraulic jump. Bradley and Peterka, after extensive experimental investigations,
More informationChapter 4: Non uniform flow in open channels
Chapter 4: Non uniform flow in open channels Learning outcomes By the end of this lesson, students should be able to: Relate the concept of specific energy and momentum equations in the effect of change
More information6.1 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
More informationFREE SURFACE HYDRODYNAMICS (module 2)
Introduction to FREE SURFACE HYDRODYNAMICS (module 2) Prof Arthur E Mynett Professor of Hydraulic Engineering in addition to the lecture notes by Maskey et al. Introduction to FREE SURFACE HYDRODYNAMICS
More informationCEE 3310 Open Channel Flow, Nov. 26,
CEE 3310 Open Channel Flow, Nov. 6, 018 175 8.10 Review Open Channel Flow Gravity friction balance. y Uniform Flow x = 0 z = S 0L = h f y Rapidly Varied Flow x 1 y Gradually Varied Flow x 1 In general
More informationChapter (6) Energy Equation and Its Applications
Chapter (6) Energy Equation and Its Applications Bernoulli Equation Bernoulli equation is one of the most useful equations in fluid mechanics and hydraulics. And it s a statement of the principle of conservation
More informationOpen Channel Flow Part 2. Ch 10 Young, notes, handouts
Open Channel Flow Part 2 Ch 10 Young, notes, handouts Uniform Channel Flow Many situations have a good approximation d(v,y,q)/dx=0 Uniform flow Look at extended Bernoulli equation Friction slope exactly
More informationControl Volume Revisited
Civil Engineering Hydraulics Control Volume Revisited Previously, we considered developing a control volume so that we could isolate mass flowing into and out of the control volume Our goal in developing
More informationExam #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
More informationHydraulics. 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 informationChapter 6: Momentum Analysis
6-1 Introduction 6-2Newton s Law and Conservation of Momentum 6-3 Choosing a Control Volume 6-4 Forces Acting on a Control Volume 6-5Linear Momentum Equation 6-6 Angular Momentum 6-7 The Second Law of
More informationCLASS 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
More informationChapter Two. Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency. Laith Batarseh
Chapter Two Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency Laith Batarseh The equation of continuity Most analyses in this book are limited to one-dimensional steady flows where the velocity
More informationHydraulics Part: Open Channel Flow
Hydraulics Part: Open Channel Flow Tutorial solutions -by Dr. K.N. Dulal Uniform flow 1. Show that discharge through a channel with steady flow is given by where A 1 and A 2 are the sectional areas of
More informationconservation of linear momentum 1+8Fr = 1+ Sufficiently short that energy loss due to channel friction is negligible h L = 0 Bernoulli s equation.
174 Review Flow through a contraction Critical and choked flows The hydraulic jump conservation of linear momentum y y 1 = 1+ 1+8Fr 1 8.1 Rapidly Varied Flows Weirs 8.1.1 Broad-Crested Weir Consider the
More informationMULTIPLE-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.
More informationMass 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 informationFluid Mechanics Prof. S.K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur
Fluid Mechanics Prof. S.K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 42 Flows with a Free Surface Part II Good morning. I welcome you to this session
More informationP10.5 Water flows down a rectangular channel that is 4 ft wide and 3 ft deep. The flow rate is 15,000 gal/min. Estimate the Froude number of the flow.
P10.5 Water flows down a rectangular channel that is 4 ft wide and ft deep. The flow rate is 15,000 gal/min. Estimate the Froude number of the flow. Solution: Convert the flow rate from 15,000 gal/min
More information!! +! 2!! +!"!! =!! +! 2!! +!"!! +!!"!"!"
Homework 4 Solutions 1. (15 points) Bernoulli s equation can be adapted for use in evaluating unsteady flow conditions, such as those encountered during start- up processes. For example, consider the large
More informationAngular momentum equation
Angular momentum equation For angular momentum equation, B =H O the angular momentum vector about point O which moments are desired. Where β is The Reynolds transport equation can be written as follows:
More informationFriction Factors and Drag Coefficients
Levicky 1 Friction Factors and Drag Coefficients Several equations that we have seen have included terms to represent dissipation of energy due to the viscous nature of fluid flow. For example, in the
More informationLecture 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
More informationNPTEL Course Developer for Fluid Mechanics DYMAMICS OF FLUID FLOW
Module 04; Lecture DYMAMICS OF FLUID FLOW Energy Equation (Conservation of Energy) In words, the conservation of energy can be stated as, Time rate of increase in stored energy of the system = Net time
More informationChapter 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
More informationPressure in stationary and moving fluid Lab- Lab On- On Chip: Lecture 2
Pressure in stationary and moving fluid Lab-On-Chip: Lecture Lecture plan what is pressure e and how it s distributed in static fluid water pressure in engineering problems buoyancy y and archimedes law;
More informationEXPERIMENT 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 informationMULTIPLE-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
More informationChapter (3) Water Flow in Pipes
Chapter (3) Water Flow in Pipes Water Flow in Pipes Bernoulli Equation Recall fluid mechanics course, the Bernoulli equation is: P 1 ρg + v 1 g + z 1 = P ρg + v g + z h P + h T + h L Here, we want to study
More informationFundamentals 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 informationThe most common methods to identify velocity of flow are pathlines, streaklines and streamlines.
4 FLUID FLOW 4.1 Introduction Many civil engineering problems in fluid mechanics are concerned with fluids in motion. The distribution of potable water, the collection of domestic sewage and storm water,
More informationENERGY TRANSFER BETWEEN FLUID AND ROTOR. Dr. Ir. Harinaldi, M.Eng Mechanical Engineering Department Faculty of Engineering University of Indonesia
ENERGY TRANSFER BETWEEN FLUID AND ROTOR Dr. Ir. Harinaldi, M.Eng Mechanical Engineering Department Faculty of Engineering University of Indonesia Basic Laws and Equations Continuity Equation m m ρ mass
More informationChapter 8: Flow in Pipes
8-1 Introduction 8-2 Laminar and Turbulent Flows 8-3 The Entrance Region 8-4 Laminar Flow in Pipes 8-5 Turbulent Flow in Pipes 8-6 Fully Developed Pipe Flow 8-7 Minor Losses 8-8 Piping Networks and Pump
More informationLesson 37 Transmission Of Air In Air Conditioning Ducts
Lesson 37 Transmission Of Air In Air Conditioning Ducts Version 1 ME, IIT Kharagpur 1 The specific objectives of this chapter are to: 1. Describe an Air Handling Unit (AHU) and its functions (Section 37.1).
More informationChapter (3) Water Flow in Pipes
Chapter (3) Water Flow in Pipes Water Flow in Pipes Bernoulli Equation Recall fluid mechanics course, the Bernoulli equation is: P 1 ρg + v 1 g + z 1 = P ρg + v g + z h P + h T + h L Here, we want to study
More informationy 2 = 1 + y 1 This is known as the broad-crested weir which is characterized by:
CEE 10 Open Channel Flow, Dec. 1, 010 18 8.16 Review Flow through a contraction Critical and choked flows The hydraulic jump conservation of linear momentum y = 1 + y 1 1 + 8Fr 1 8.17 Rapidly Varied Flows
More informationLecture 4. Differential Analysis of Fluid Flow Navier-Stockes equation
Lecture 4 Differential Analysis of Fluid Flow Navier-Stockes equation Newton second law and conservation of momentum & momentum-of-momentum A jet of fluid deflected by an object puts a force on the object.
More informationChapter 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 informationMechanical 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
More informationShell Balances in Fluid Mechanics
Shell Balances in Fluid Mechanics R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University When fluid flow occurs in a single direction everywhere in a system, shell
More informationAnswers 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
More informationHydraulics 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 informationV/ 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
More informationChapter 8: Flow in Pipes
Objectives 1. Have a deeper understanding of laminar and turbulent flow in pipes and the analysis of fully developed flow 2. Calculate the major and minor losses associated with pipe flow in piping networks
More informationChapter 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 informationBenha University College of Engineering at Benha Questions For Corrective Final Examination Subject: Fluid Mechanics M 201 May 24/ 2016
Benha University College of Engineering at Benha Questions For Corrective Final Examination Subject: Fluid Mechanics M 01 May 4/ 016 Second year Mech. Time :180 min. Examiner:Dr.Mohamed Elsharnoby Attempt
More information1.060 Engineering Mechanics II Spring Problem Set 8
1.060 Engineering Mechanics II Spring 2006 Due on Monday, May 1st Problem Set 8 Important note: Please start a new sheet of paper for each problem in the problem set. Write the names of the group members
More informationBernoulli s equation may be developed as a special form of the momentum or energy equation.
BERNOULLI S EQUATION Bernoulli equation may be developed a a pecial form of the momentum or energy equation. Here, we will develop it a pecial cae of momentum equation. Conider a teady incompreible flow
More informationConservation of Angular Momentum
10 March 2017 Conservation of ngular Momentum Lecture 23 In the last class, we discussed about the conservation of angular momentum principle. Using RTT, the angular momentum principle was given as DHo
More informationDEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING Urban Drainage: Hydraulics. Solutions to problem sheet 2: Flows in open channels
DEPRTMENT OF CIVIL ND ENVIRONMENTL ENGINEERING Urban Drainage: Hydraulics Solutions to problem sheet 2: Flows in open channels 1. rectangular channel of 1 m width carries water at a rate 0.1 m 3 /s. Plot
More informationIntroduction to Turbomachinery
1. Coordinate System Introduction to Turbomachinery Since there are stationary and rotating blades in turbomachines, they tend to form a cylindrical form, represented in three directions; 1. Axial 2. Radial
More informationMOMENTUM 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
More informationApplied 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