# Basic Fluid Mechanics

Size: px
Start display at page:

Transcription

1 Basic Fluid Mechanics Chapter 5: Application of Bernoulli Equation 4/16/2018 C5: Application of Bernoulli Equation Introduction In this chapter we will show that the equation of motion of a particle can be integrated (under certain circumstances) and related to the potential and kinetic energies of the particle. Initially we will consider incompressible flow, but later with the use of the first law of thermodynamics a similar form of the equations of motion for compressible flow can be developed. The following are different forms of the Bernoulli equation. Simple Form of the Bernoulli Equation Assumptions: 1. Steady 2. Incompressible 3. Inviscid 4. Along a streamline 5. Inertial reference frame 4/16/2018 C5: Application of Bernoulli Equation 2 1

2 5.1 Introduction Bernoulli Equation with Conservative Forces Assumptions: 1. Steady 2. Incompressible 3. Inviscid 4. Along a streamline 5. Inertial reference frame 6. Conservative Body Force U Bernoulli Equation with Conservative Forces Assumptions: 1. Steady 2. Incompressible 3. Inviscid 4. Along a streamline 5. Inertial reference frame 6. Conservative Gravitational Force 4/16/2018 C5: Application of Bernoulli Equation Introduction Unsteady Bernoulli Equation Assumptions: 1. Unsteady 2. Incompressible 3. Inviscid 4. Along a streamline 5. Inertial reference frame Extended Bernoulli Equation Assumptions: 1. Steady 2. Incompressible 3. Viscous (i.e., resistance) W f 4. Along a streamline 5. Shaft work, W s 6. Inertial reference frame 4/16/2018 C5: Application of Bernoulli Equation 4 2

3 5.1 Introduction Problem 5.1: Determine the pressure difference between two stations 1 and 2 as a function of the flow rate Q and density. V 1 V 2 A 1 Solution: 1) Assume steady state 2) Assume uniform flow 3) Assume inviscid fluid 4) Assume = constant 5) Apply the conservation of mass to determine V 2. 6) Apply the simple Bernoulli equation A 2 Recall Conservation of Mass: 4/16/2018 C5: Application of Bernoulli Equation Introduction For an Incompressible fluid, the Volume flow rate (Q) = constant and the conservation of mass reduces to continuity eq: Apply Bernoulli Eq; Rewriting Bernoulli Eq (5.2b); From continuity eq; Eq (EX5.1) Substituting for V 1 into the pressure difference equation (EX5.1); 4/16/2018 C5: Application of Bernoulli Equation 6 3

4 5.1 Introduction ====The End==== 4/16/2018 C5: Application of Bernoulli Equation Extended Bernoulli s Equation Consider the presence of non-conservative body forces (f nc ) as well as the presence of shear and normal stresses arising from friction (f f ). Including these forces in Bernoulli's Equation (5.4) leads to; A Assumptions: 1. Steady 2. Incompressible 3. Along a streamline 4. Inertial reference frame B (5.8) 4/16/2018 C5: Application of Bernoulli Equation 8 4

5 5.2 Extended Bernoulli s Equation A B Term "A represents the useful work done on the fluid by f nc (e.g., moving of pump vane or turbine blade) where W s is the shaft work performed or energy expended per unit mass. W s = Where W s is considered "+" for a pump and "-" for a turbine blade, since they add and remove energy from the flow respectively. Term B represents the work done by the fluid in overcoming viscous resistance (not useful work) which is always a loss in energy. W f = 4/16/2018 C5: Application of Bernoulli Equation Extended Bernoulli s Equation Therefore, Where each term is written as an energy/unit mass. In hydraulic engineering, the terms are rearranged and expressed as energy (or work)/unit weight g g (5.10) (5.11) Where each term is written with units of length, enabling the use of the term head. 4/16/2018 C5: Application of Bernoulli Equation 10 5

6 5.2 Extended Bernoulli s Equation M pump work H f friction loss Y elevation head static pressure head velocity head h t total head h t2 = h t1 + M h f (5.12) The total head after the flow process is equal to the total head before the process plus any mechanical work performed minus losses due to friction. 4/16/2018 C5: Application of Bernoulli Equation Extended Bernoulli s Equation Aero engineers multiply Eq (5.10) by to obtain Bernoulli Equations in terms of work/unit volume. In this form, all terms have the dimensions of a pressure; so is the dynamic pressure total pressure (p t); (analogous to total head) Total pressure is also known as the stagnation pressure since it is the pressure which would result if a fluid stream was brought to rest isentropically. Each term in Eq (5.10) represents energy/unit mass. When multiplied by the mass flow rate (mass/time) one obtains the power () in watts. energy/unit mass * mass/time = energy/time = 4/16/2018 C5: Application of Bernoulli Equation 12 6

7 5.2 Extended Bernoulli s Equation Similarly, each term in Eq represents energy/unit weight. When multiplied by the weight flow rate, gq (weight/time), where Q is the volume flow rate, one also obtains power (). The function of a pump is to increase the total head of the flow, h t. The associated power () required for this increase Recall, the fluid power is considered positive for a pump and negative for a turbine. The actual power, act, necessary to run a pump is always larger than the ideal fluid power due to friction, internal leakage, and a variety of other losses. The ratio / act is called the pump "efficiency." Likewise, the ratio act / is turbine efficiency. 4/16/2018 C5: Application of Bernoulli Equation Engineering Application of Bernoulli s Equation Often it is possible to assume that the flow is "one-dimensional," i.e., no velocity variation normal to the axis of the conduit. This uniform velocity is taken to be equal to the average velocity over the flow cross section. This would be true of flow in pipe circuits. 4/16/2018 C5: Application of Bernoulli Equation 14 7

8 Problem 5.2: A constant diameter pipe (d) of length l is attached to a reservoir whose water level is y 1. For a length of pipe equal to one diameter the frictional loss is f, the friction coefficient, is constant. Determine the distributions of static pressure and total head, as well as the outlet velocity for the system shown. You may neglect frictional losses at the pipe entrance. The following info is available: f = 0.02 l /d = 1000 y 1 y 2 = 100 m 4/16/2018 C5: Application of Bernoulli Equation 15 Total Head Hydraulic gradeline y 1 y 1 <0 h f >0 Solution: y Pipe elevation y 2 y 3 Distance along the pipe Solution: 1. Apply the extended Bernoulli equation between points 1 & Note that no pump work is performed. 3. Assume that the reservoir is large so that the velocity at 1 due to the discharge is very small. 4. Assume that the pressures at 1 & 2 are equal to atmospheric. 5. Solve for the discharge velocity at 2. 4/16/2018 C5: Application of Bernoulli Equation 16 8

9 6. Write the extended Bernoulli equation between station 1 and some arbitrary station along the pipe, x. 7. Note that since the pipe diameter is constant, the pipe velocity is constant. 8. Solve for the total head as a function of x position. Apply Bernoulli's Eq (5.12 and 11), (work/unit weight) between points 1 and 2 written in terms of total head h t2 = h t1 + M h f (5.12) g g (5.11) but in the absence of a pump or turbine, M = 0 and if we assume the free surface at 1 is large; V 1 = 0 and p 2 = p 1, so 4/16/2018 C5: Application of Bernoulli Equation 17 /. /.. / 4/16/2018 C5: Application of Bernoulli Equation 18 9

10 One can now determine the total pressure distribution along the pipe between station 1 and some arbitrary station "x". h tx h t1 h fx h tx h t1 This equation shows that the total head decreases linearly with distance along the pipe. Substituting for the total head g h t1 4/16/2018 C5: Application of Bernoulli Equation 19 From continuity and the fact that the pipe diameter is constant, V x = V 2 and let y 1 = 0 and p 1 = p atm = 0 gage g therefore the static pressure is a linear function of pipe length x. The group (p/g + y) is sometimes called the piezometric head, and the graph of the piezometric head along the pipe is called the hydraulic grade line. Note: If the elevation of the pipe at any section exceeds that of the hydraulic grade line, the static pressure will fall below the atmospheric pressure. 4/16/2018 C5: Application of Bernoulli Equation 20 10

11 Note: If the elevation of the pipe at any section exceeds that of the hydraulic grade line, the static pressure will fall below the atmospheric pressure. Total Head Hydraulic gradeline y 1 y 1 <0 h f >0 y 3 Solution: y Pipe elevation y 2 Distance along the pipe ====The End==== 4/16/2018 C5: Application of Bernoulli Equation 21 Problem 5.5: Find the head across the pump and power necessary to transport water between the reservoirs shown. Given are the frictional losses between designated points, the respective elevations and volume flow rate. h f1 2 = h f3 4 = 5 m; y 1 = 20 m; y 5 =40 m; Q p = 0.5 m 3 /s; A 4 = 0.04 m y1 y 4 y 5 4/16/2018 C5: Application of Bernoulli Equation 22 11

12 Solution Strategy: 1 4 y1 y 4 y 5 1. Apply extended Bernoulli eq between points 1 & 5; solve for M. 2. Assume that the areas at stations 1 & 5 are large, therefore their respective velocities can be assumed small and neglected, use this to simplify the above expression. 3. Write the extended Bernouli equation between points 4 and Use the hydrostatic eq to write an expression for pressure at (4). 5. Solve for the losses between 4 and 5. 4/16/2018 C5: Application of Bernoulli Equation 23 Solution: To determine the head across the pump, it is only necessary to write the extended Bernoulli equation between points 5 and 1. h t5 = h t1 + M h f1 2 h f3 4 h f4 5 (5.5A) Recall the pressure acting on the two liquid surfaces (points 1 & 5) are equal, and the surface areas at these locations are large, which allows us to assume the velocities are small and thus can be neglected. g Since V 5 = V 1 0 and g g and g (5.5B) 4/16/2018 C5: Application of Bernoulli Equation 24 12

13 Solve for the total pressure difference (energy/unit volume),( ) in Eq. (5.5.B) recalling that p 1 = p 5 g or solving for h t in terms of an energy/weight viewpoint therefore, Eq 5.5.A becomes M = y 5 y 1 h f1 2 h f3 4 h f4 5 (5.5C.1) Except for h f4 5, all frictional losses are given. To estimate h f4 5, one assumes that as the jet discharges at point 4, the jet spreads and it's velocity goes to zero. 4/16/2018 C5: Application of Bernoulli Equation 25 Writing Bernoulli's Equation between points (4) and (5). h t5 = h t4 + M h f4 5 since the pump is located between points 2 and 3, M in the above equation is zero. Also recall V 5 = 0 g h f4 5 g g + h f4 5 (5.5D) But if the fluid in the reservoir surrounding the jet is approximately stationary, then the pressure is distributed hydrostatically and one can use the hydrostatic pressure equation. g or g g 4/16/2018 C5: Application of Bernoulli Equation 26 13

14 If we work in terms of atmospheric pressure (gage pressure), p 5 = 0 g (5.5E) Substituting Eq. (5.5.E) into Eq. (5.5.D) h f4 5 Now substituting h f4 5 into Eq. (5.5.C1) M = y 5 y 1 h f1 2 h f3 4 + (5.5F) Thus using the given conditions / M = 40m 20m + 5m + 5m +. / M = 30m +. /.. / = 38.0 m (5.5B2) 4/16/2018 C5: Application of Bernoulli Equation 27 The ideal pump power () required is; = Force/area volume/time = Total Pressure volume flow rate or = g(h t ) Q = p t Q = m Nm/s = 80.4 W ====The End==== 4/16/2018 C5: Application of Bernoulli Equation 28 14

### 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

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

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

### Chapter 7 The Energy Equation

Chapter 7 The Energy Equation 7.1 Energy, Work, and Power When matter has energy, the matter can be used to do work. A fluid can have several forms of energy. For example a fluid jet has kinetic energy,

### 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

### 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.

### CEE 3310 Control Volume Analysis, Oct. 7, D Steady State Head Form of the Energy Equation P. P 2g + z h f + h p h s.

CEE 3310 Control Volume Analysis, Oct. 7, 2015 81 3.21 Review 1-D Steady State Head Form of the Energy Equation ( ) ( ) 2g + z = 2g + z h f + h p h s out where h f is the friction head loss (which combines

### Chapter 3 Bernoulli Equation

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

### Fluid Mechanics-61341

An-Najah National University College of Engineering Fluid Mechanics-61341 Chapter [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed 1 Fluid Mechanics-2nd Semester 2010- [5] Flow of An Incompressible

### Basics of fluid flow. Types of flow. Fluid Ideal/Real Compressible/Incompressible

Basics of fluid flow Types of flow Fluid Ideal/Real Compressible/Incompressible Flow Steady/Unsteady Uniform/Non-uniform Laminar/Turbulent Pressure/Gravity (free surface) 1 Basics of fluid flow (Chapter

### 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:

### 3.8 The First Law of Thermodynamics and the Energy Equation

CEE 3310 Control Volume Analysis, Sep 30, 2011 65 Review Conservation of angular momentum 1-D form ( r F )ext = [ˆ ] ( r v)d + ( r v) out ṁ out ( r v) in ṁ in t CV 3.8 The First Law of Thermodynamics and

### 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

### Introduction to Fluid Machines, and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Introduction to Fluid Machines, and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 09 Introduction to Reaction Type of Hydraulic

### 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

### 3.25 Pressure form of Bernoulli Equation

CEE 3310 Control Volume Analysis, Oct 3, 2012 83 3.24 Review The Energy Equation Q Ẇshaft = d dt CV ) (û + v2 2 + gz ρ d + (û + v2 CS 2 + gz + ) ρ( v n) da ρ where Q is the heat energy transfer rate, Ẇ

### MASS, MOMENTUM, AND ENERGY EQUATIONS

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

### CEE 3310 Control Volume Analysis, Oct. 10, = dt. sys

CEE 3310 Control Volume Analysis, Oct. 10, 2018 77 3.16 Review First Law of Thermodynamics ( ) de = dt Q Ẇ sys Sign convention: Work done by the surroundings on the system < 0, example, a pump! Work done

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

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

### 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

### 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,

### 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

### 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

### 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

### ME3560 Tentative Schedule Spring 2019

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

### 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.

### 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

### ME3560 Tentative Schedule Fall 2018

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

### Rate of Flow Quantity of fluid passing through any section (area) per unit time

Kinematics of Fluid Flow Kinematics is the science which deals with study of motion of liquids without considering the forces causing the motion. Rate of Flow Quantity of fluid passing through any section

### 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

### 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

### Chapter 5: Mass, Bernoulli, and Energy Equations

Chapter 5: Mass, Bernoulli, and Energy Equations Introduction This chapter deals with 3 equations commonly used in fluid mechanics The mass equation is an expression of the conservation of mass principle.

### BERNOULLI EQUATION. The motion of a fluid is usually extremely complex.

BERNOULLI EQUATION The motion of a fluid is usually extremely complex. The study of a fluid at rest, or in relative equilibrium, was simplified by the absence of shear stress, but when a fluid flows over

### 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

### 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

### Useful concepts associated with the Bernoulli equation. Dynamic

Useful concets associated with the Bernoulli equation - Static, Stagnation, and Dynamic Pressures Bernoulli eq. along a streamline + ρ v + γ z = constant (Unit of Pressure Static (Thermodynamic Dynamic

### EGN 3353C Fluid Mechanics

Lecture 8 Bernoulli s Equation: Limitations and Applications Last time, we derived the steady form of Bernoulli s Equation along a streamline p + ρv + ρgz = P t static hydrostatic total pressure q = dynamic

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

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

### Dimensions represent classes of units we use to describe a physical quantity. Most fluid problems involve four primary dimensions

BEE 5330 Fluids FE Review, Feb 24, 2010 1 A fluid is a substance that can not support a shear stress. Liquids differ from gasses in that liquids that do not completely fill a container will form a free

### 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

### 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

### An-Najah National University Civil Engineering Department. Fluid Mechanics. Chapter 1. General Introduction

1 An-Najah National University Civil Engineering Department Fluid Mechanics Chapter 1 General Introduction 2 What is Fluid Mechanics? Mechanics deals with the behavior of both stationary and moving bodies

### 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

### where = rate of change of total energy of the system, = rate of heat added to the system, = rate of work done by the system

The Energy Equation for Control Volumes Recall, the First Law of Thermodynamics: where = rate of change of total energy of the system, = rate of heat added to the system, = rate of work done by the system

### 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

### ME 316: Thermofluids Laboratory

ME 316 Thermofluid Laboratory 6.1 KING FAHD UNIVERSITY OF PETROLEUM & MINERALS ME 316: Thermofluids Laboratory PELTON IMPULSE TURBINE 1) OBJECTIVES a) To introduce the operational principle of an impulse

### AA210A Fundamentals of Compressible Flow. Chapter 5 -The conservation equations

AA210A Fundamentals of Compressible Flow Chapter 5 -The conservation equations 1 5.1 Leibniz rule for differentiation of integrals Differentiation under the integral sign. According to the fundamental

### 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.

### 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

### 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

### Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 07 Analysis of Force on the Bucket of Pelton

### 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

### AA210A Fundamentals of Compressible Flow. Chapter 1 - Introduction to fluid flow

AA210A Fundamentals of Compressible Flow Chapter 1 - Introduction to fluid flow 1 1.2 Conservation of mass Mass flux in the x-direction [ ρu ] = M L 3 L T = M L 2 T Momentum per unit volume Mass per unit

### FLUID MECHANICS. Dynamics of Viscous Fluid Flow in Closed Pipe: Darcy-Weisbach equation for flow in pipes. Major and minor losses in pipe lines.

FLUID MECHANICS Dynamics of iscous Fluid Flow in Closed Pipe: Darcy-Weisbach equation for flow in pipes. Major and minor losses in pipe lines. Dr. Mohsin Siddique Assistant Professor Steady Flow Through

### 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

### 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

### Lecture 2 Flow classifications and continuity

Lecture 2 Flow classifications and continuity Dr Tim Gough: t.gough@bradford.ac.uk General information 1 No tutorial week 3 3 rd October 2013 this Thursday. Attempt tutorial based on examples from today

### 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

### Conservation of Momentum using Control Volumes

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

### Stream Tube. When density do not depend explicitly on time then from continuity equation, we have V 2 V 1. δa 2. δa 1 PH6L24 1

Stream Tube A region of the moving fluid bounded on the all sides by streamlines is called a tube of flow or stream tube. As streamline does not intersect each other, no fluid enters or leaves across the

### 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

### 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

### Introduction to Fluid Machines and Compressible Flow Prof. S.K Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Introduction to Fluid Machines and Compressible Flow Prof. S.K Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture No. # 24 Axial Flow Compressor Part I Good morning

### If a stream of uniform velocity flows into a blunt body, the stream lines take a pattern similar to this: Streamlines around a blunt body

Venturimeter & Orificemeter ELEMENTARY HYDRAULICS National Certificate in Technology (Civil Engineering) Chapter 5 Applications of the Bernoulli Equation The Bernoulli equation can be applied to a great

### 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

### 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

### 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

### 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................................

### CLASS Fourth Units (Second part)

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

### Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 21 Centrifugal Compressor Part I Good morning

### 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

### Introduction to Chemical Engineering Thermodynamics. Chapter 7. KFUPM Housam Binous CHE 303

Introduction to Chemical Engineering Thermodynamics Chapter 7 1 Thermodynamics of flow is based on mass, energy and entropy balances Fluid mechanics encompasses the above balances and conservation of momentum

### Steven Burian Civil & Environmental Engineering September 25, 2013

Fundamentals of Engineering (FE) Exam Mechanics Steven Burian Civil & Environmental Engineering September 25, 2013 s and FE Morning ( Mechanics) A. Flow measurement 7% of FE Morning B. properties Session

### 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

### Lecture Note for Open Channel Hydraulics

Chapter -one Introduction to Open Channel Hydraulics 1.1 Definitions Simply stated, Open channel flow is a flow of liquid in a conduit with free space. Open channel flow is particularly applied to understand

### 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

### 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.

### Shell/Integral Balances (SIB)

Shell/Integral Balances (SIB) Shell/Integral Balances Shell or integral (macroscopic) balances are often relatively simple to solve, both conceptually and mechanically, as only limited data is necessary.

### Pressure and Flow Characteristics

Pressure and Flow Characteristics Continuing Education from the American Society of Plumbing Engineers August 2015 ASPE.ORG/ReadLearnEarn CEU 226 READ, LEARN, EARN Note: In determining your answers to

### 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

### Homework 6. Solution 1. r ( V jet sin( θ) + ω r) ( ρ Q r) Vjet

Problem 1 Water enters the rotating sprinkler along the axis of rotation and leaves through three nozzles. How large is the resisting torque required to hold the rotor stationary for the angle that produces

### 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

### SYSTEMS VS. CONTROL VOLUMES. Control volume CV (open system): Arbitrary geometric space, surrounded by control surfaces (CS)

SYSTEMS VS. CONTROL VOLUMES System (closed system): Predefined mass m, surrounded by a system boundary Control volume CV (open system): Arbitrary geometric space, surrounded by control surfaces (CS) Many

### 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

### Engineering Fluid Mechanics

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

### Turbomachinery. Hasan Ozcan Assistant Professor. Mechanical Engineering Department Faculty of Engineering Karabuk University

Turbomachinery Hasan Ozcan Assistant Professor Mechanical Engineering Department Faculty of Engineering Karabuk University Introduction Hasan Ozcan, Ph.D, (Assistant Professor) B.Sc :Erciyes University,

### ME 309 Fluid Mechanics Fall 2010 Exam 2 1A. 1B.

Fall 010 Exam 1A. 1B. Fall 010 Exam 1C. Water is flowing through a 180º bend. The inner and outer radii of the bend are 0.75 and 1.5 m, respectively. The velocity profile is approximated as C/r where C

### Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 1 Introduction to Fluid Machines Well, good

### 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,

### 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

### CVE 372 HYDROMECHANICS EXERCISE PROBLEMS

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

### CHAPTER TWO CENTRIFUGAL PUMPS 2.1 Energy Transfer In Turbo Machines

7 CHAPTER TWO CENTRIFUGAL PUMPS 21 Energy Transfer In Turbo Machines Fig21 Now consider a turbomachine (pump or turbine) the total head (H) supplied by it is The power delivered to/by the fluid simply

### 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

### Hydraulic (Piezometric) Grade Lines (HGL) and

Hydraulic (Piezometric) Grade Lines (HGL) and Energy Grade Lines (EGL) When the energy equation is written between two points it is expresses as in the form of: Each term has a name and all terms have

### 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

### Chapter 5: Mass, Bernoulli, and

and Energy Equations 5-1 Introduction 5-2 Conservation of Mass 5-3 Mechanical Energy 5-4 General Energy Equation 5-5 Energy Analysis of Steady Flows 5-6 The Bernoulli Equation 5-1 Introduction This chapter

### MAE 3130: Fluid Mechanics Lecture 7: Differential Analysis/Part 1 Spring Dr. Jason Roney Mechanical and Aerospace Engineering

MAE 3130: Fluid Mechanics Lecture 7: Differential Analysis/Part 1 Spring 2003 Dr. Jason Roney Mechanical and Aerospace Engineering Outline Introduction Kinematics Review Conservation of Mass Stream Function

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

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

### Chapter Four Hydraulic Machines

Contents 1- Introduction. - Pumps. Chapter Four Hydraulic Machines (لفرع الميكانيك العام فقط ( Turbines. -3 4- Cavitation in hydraulic machines. 5- Examples. 6- Problems; sheet No. 4 (Pumps) 7- Problems;