Chapter 6 The Impulse-Momentum Principle

Size: px
Start display at page:

Download "Chapter 6 The Impulse-Momentum Principle"

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

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 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

Chapter 4 Continuity Equation and Reynolds Transport Theorem

Chapter 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 information

Fluid Mechanics. du dy

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

More information

In this section, mathematical description of the motion of fluid elements moving in a flow field is

In 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 information

1.060 Engineering Mechanics II Spring Problem Set 4

1.060 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 information

VARIED FLOW IN OPEN CHANNELS

VARIED 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 information

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

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

NPTEL Quiz Hydraulics

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

More information

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

Consider a control volume in the form of a straight section of a streamtube ABCD. 6 MOMENTUM EQUATION 6.1 Momentum and Fluid Flow In mechanics, the momentum of a particle or object is defined as the product of its mass m and its velocity v: Momentum = mv The particles of a fluid stream

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

FLUID MECHANICS. Chapter 3 Elementary Fluid Dynamics - The Bernoulli Equation

FLUID 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 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

Closed duct flows are full of fluid, have no free surface within, and are driven by a pressure gradient along the duct axis.

Closed 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 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

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

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

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

HOMEWORK ASSIGNMENT ON BERNOULLI S EQUATION

HOMEWORK 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 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

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

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

Closed duct flows are full of fluid, have no free surface within, and are driven by a pressure gradient along the duct axis.

Closed 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 information

PROPERTIES OF FLUIDS

PROPERTIES 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 information

Chapter 5 Control Volume Approach and Continuity Equation

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

More information

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

Q1 Give answers to all of the following questions (5 marks each): FLUID MECHANICS First Year Exam Solutions 03 Q Give answers to all of the following questions (5 marks each): (a) A cylinder of m in diameter is made with material of relative density 0.5. It is moored

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

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

Experiment (4): Flow measurement

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

More information

Hydraulics for Urban Storm Drainage

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

More information

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

s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum equations E. Pipe and other internal flow 7% of FE Morning Session I Fundamentals of Engineering (FE) Exam General Section Steven Burian Civil & Environmental Engineering October 26, 2010 s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum

More information

Chapter 2: Basic Governing Equations

Chapter 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 information

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

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

More information

Basic Fluid Mechanics

Basic 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 information

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

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

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

The Bernoulli Equation

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

More information

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

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

More information

FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER

FLUID 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 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

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

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

Basic equations of motion in fluid mechanics

Basic 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 information

CIE4491 Lecture. Hydraulic design

CIE4491 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 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

APPLIED FLUID DYNAMICS HANDBOOK

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

More information

Sourabh V. Apte. 308 Rogers Hall

Sourabh 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 information

UNIT I FLUID PROPERTIES AND STATICS

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

More information

28.2 Classification of Jumps

28.2 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 information

Chapter 4: Non uniform flow in open channels

Chapter 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 information

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

6.1 Momentum Equation for Frictionless Flow: Euler s Equation The equations of motion for frictionless flow, called Euler s Chapter 6 INCOMPRESSIBLE INVISCID FLOW All real fluids possess viscosity. However in many flow cases it is reasonable to neglect the effects of viscosity. It is useful to investigate the dynamics of an

More information

FREE SURFACE HYDRODYNAMICS (module 2)

FREE 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 information

CEE 3310 Open Channel Flow, Nov. 26,

CEE 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 information

Chapter (6) Energy Equation and Its Applications

Chapter (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 information

Open Channel Flow Part 2. Ch 10 Young, notes, handouts

Open 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 information

Control Volume Revisited

Control 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 information

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

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

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

Chapter 6: Momentum Analysis

Chapter 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 information

CLASS SCHEDULE 2013 FALL

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

More information

Chapter Two. Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency. Laith Batarseh

Chapter 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 information

Hydraulics Part: Open Channel Flow

Hydraulics 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 information

conservation of linear momentum 1+8Fr = 1+ Sufficiently short that energy loss due to channel friction is negligible h L = 0 Bernoulli s equation.

conservation 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 information

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

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

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

Fluid 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 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 information

P10.5 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 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!! +!"!! +!!"!"!"

!! +! 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 information

Angular momentum equation

Angular 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 information

Friction Factors and Drag Coefficients

Friction 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 information

Lecture 3 The energy equation

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

More information

NPTEL Course Developer for Fluid Mechanics DYMAMICS OF FLUID FLOW

NPTEL 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 information

Chapter 1 INTRODUCTION

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

More information

Pressure in stationary and moving fluid Lab- Lab On- On Chip: Lecture 2

Pressure 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 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

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

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

More information

Chapter (3) Water Flow in Pipes

Chapter (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 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 most common methods to identify velocity of flow are pathlines, streaklines and streamlines.

The 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 information

ENERGY 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 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 information

Chapter 8: Flow in Pipes

Chapter 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 information

Lesson 37 Transmission Of Air In Air Conditioning Ducts

Lesson 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 information

Chapter (3) Water Flow in Pipes

Chapter (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 information

y 2 = 1 + y 1 This is known as the broad-crested weir which is characterized by:

y 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 information

Lecture 4. Differential Analysis of Fluid Flow Navier-Stockes equation

Lecture 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 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

Mechanical Engineering Programme of Study

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

More information

Shell Balances in Fluid Mechanics

Shell 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 information

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

Answers to questions in each section should be tied together and handed in separately. EGT0 ENGINEERING TRIPOS PART IA Wednesday 4 June 014 9 to 1 Paper 1 MECHANICAL ENGINEERING Answer all questions. The approximate number of marks allocated to each part of a question is indicated in the

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

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

V/ t = 0 p/ t = 0 ρ/ t = 0. V/ s = 0 p/ s = 0 ρ/ s = 0 UNIT III FLOW THROUGH PIPES 1. List the types of fluid flow. Steady and unsteady flow Uniform and non-uniform flow Laminar and Turbulent flow Compressible and incompressible flow Rotational and ir-rotational

More information

Chapter 8: Flow in Pipes

Chapter 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 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

Benha 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 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 information

1.060 Engineering Mechanics II Spring Problem Set 8

1.060 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 information

Bernoulli s equation may be developed as a special form of the momentum or energy equation.

Bernoulli 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 information

Conservation of Angular Momentum

Conservation 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 information

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING Urban Drainage: Hydraulics. Solutions to problem sheet 2: Flows in open channels

DEPARTMENT 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 information

Introduction to Turbomachinery

Introduction 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 information

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

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

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