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

Size: px
Start display at page:

Transcription

1 CEE 3310 Control Volume Analysis, Oct. 10, 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 by the system on the surroundings > 0, example, a turbine! Work and ower Ẇ pres = v n da CS This term is usually moved to the right-hand-side flux term of the energy equation as it is a flux, which is how we will treat it. Ẇ visc = τ v da which is often zero The Energy Equation Q Ẇshaft = d dt CV CS ) (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 shaft is the shaft power (work rate), û is the internal energy per unit mass, v 2 /2 is the kinetic energy per unit mass, and gz is the potential energy per unit mass. 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 the net change in internal energy and heat flux terms), h p is work added by pumps and h s is work removed by shafts. in 3.17 Variations From Uniform Flow As we have discussed we frequently assume that a flow is 1-D while we know in actuality it is not. Often this is an excellent assumption but sometimes the assumption is not as

2 CEE 3310 Control Volume Analysis, Oct. 10, good and we may wish to correct for the effects of the dependence of the velocity on position. The term that is effected in the energy equation is the flux term. If we wish to use the average velocity, V, as representative of a 1-D velocity equivalent to the 2-D velocity then we have CS v 2 ( 2 ρ( v n) da = ṁ αout 2 V 2 out α ) in 2 V 2 in where α is known as the kinetic constant and it accounts for the effect of the non-uniform velocity profile on the surface flux of energy. The definition of the mean velocity is V = ρ( v n) da ρa which for incompressible flows with the velocity vector normal to the control surface reduces to simply V = Q/A. Hence and Example ṁ α out 2 V 2 = α = CS v 2 ρ( v n) da 2 CS v2 ρ( v n) da ṁ V 2 Consider the Laminar flow through a pipe sitting in a uniform velocity field in water: What is the head loss? h L = V 2 2g

3 CEE 3310 Control Volume Analysis, Oct. 10, Bernoulli Equation Bernoulli wrote down a verbal form of his famous equation in 1738 and Euler completed the analytic derivation in The differential form of the Bernoulli Equation is known as the Euler Equation. Consider our 1-D head form of the energy equation and let s apply it along a streamline of a flow. If the flow is steady then the integral over the control volume vanishes. Further, since by definition there is no flow normal to the streamline we only have flux terms at the starting and ending points along the streamline (really we are talking about a volume and hence a streamtube just a cylindrical volume element defined by a family of streamlines - a virtual pipe!). Clearly there is no shaft work along the streamline. If we assume the flow is frictionless (i.e., inviscid or ν = 0) h f =0 and we have ( ) ( ) 2g + z = out 2g + z in This is the Bernoulli equation. Clearly anywhere along a streamline, as long as no work is done between analysis points and the assumption of frictionless flow is good, we can write 2g + z = h 0 where the constant h 0 is referred to as the Bernoulli constant and varies across streamlines. The Bernoulli Equation can be derived by considering Newton s second law F = m a along a streamline (conservation of linear momentum). This leads to the steady form of the Bernoulli equation. If we add conservation of mass we can derive the unsteady form. Bernoulli Equation Assumptions Flow along single streamline different streamlines, different h 0. Steady flow (can be generalized to unsteady flow).

4 CEE 3310 Control Volume Analysis, Oct. 10, Incompressible flow. Inviscid or frictionless flow, very restrictive! No w s between analysis points on streamline. No q between points on streamline.

5 CEE 3310 Control Volume Analysis, Oct. 10, Illustrations of Valid and Invalid Regions for the Application of the Bernoulli Equation 3.19 ressure form of Bernoulli Equation If we multiply our head form of the Bernoulli equation by the specific weight we arrive at the pressure form of the Bernoulli Equation: + ρ v2 2 + γz = t where we call the first term the static pressure, the second the dynamic pressure, the third the hydrostatic pressure, and the right-hand-side the total pressure. Hence the Bernoulli Equation says that in inviscid flows the total pressure along a streamline is constant.

6 CEE 3310 Control Volume Analysis, Oct. 10, If we remain at a constant elevation the above equation reduces to + ρ v2 2 = s where we refer to s as the stagnation pressure. Thus by definition the stagnation pressure is the pressure along horizontal streamlines when the velocity is zero Stagnation oint and ressure Consider the flow around a circular cylinder: + ρ v2 2 + γz = t We see that the stagnation pressure is simply the conversion of all kinetic energy to potential energy and hence there is a subsequent pressure rise. The elevation head simply accounts for any change in the potential energy due to vertical changes in elevation.

7 CEE 3310 Control Volume Analysis, Oct. 10, itot-static Tube The static and stagnation pressures can be measured simultaneously using a itot-static tube. Consider the following geometry: Now, we see the streamlines around the tube, either at the tip or away from the tip (but not around the curved front end), are horizontal. If the tube is not very long it is very reasonable to assume friction is negligible for this analysis. Now the velocity at the tip of the itot-static tube is zero hence the pressure at this point (and hence along the entire horizontal leg of the itot tube as this portion of the device is known) is the stagnation pressure. The holes perpendicular to the flow are similar to piezometers - they simply measure the static pressure in the fluid flow. If we write the equation for the itot tube we have 1 + ρ v2 1 2 = 2 = γh Now, at the static tube we have the free-stream pressure, 2o but at this point, which is along the streamline from point 1 to point 2, the velocity is the same as it is for point 1 (assuming the itot-static tube is small and does not affect the flow) and there is no elevation change so the Bernoulli Equation gives us: 1 = 2o = γh Substituting this expression into the equation for the itot tube we arrive at the itot formula or in terms of heads V 1 = ρ V = 2g(H h)

8 CEE 3310 Control Volume Analysis, Oct. 10, Example Flow accelerating out of a reservoir 2gh V 2 = 1 ( ) 2 A2 A and if A 1 A 2 1 ( A2 A 1 ) 2 1 V 2 2gh, again! Let s look at this a bit further by asking the question what speed will a parcel of fluid dropped a distance h be traveling at? Therefore v = t 0 g dt = gt! h = t = 2h g and t 0 v dt = t v = gt = 2gh aha! 0 gt dt = 1 2 gt2 Thus we see that in an inviscid flow, which by definition has no frictional energy losses, we simply convert potential energy to kinetic energy and hence the same result, v = 2gh keeps showing up. This was first noted by Torricelli Energy and the Hydraulic Grade Line As we have seen we can write the head form of the Energy equation as + z = H = Energy Grade Line (EGL) 2g In the case of Bernoulli flows the energy grade line is simply a constant since by assumption energy is conserved (there is no mechanism to gain/lose energy). For other flows it will drop due to frictional losses or work done on the surroundings (e.g., a turbine)

9 CEE 3310 Control Volume Analysis, Oct. 10, or increase due to work input (e.g., a pump). Note that this is the head that would be measured by a itot tube. We can also write γ + z = Hydraluic Grade Line (HGL) and we see that the HGL is due to static pressure the height a column of fluid would rise due to pressure at a given elevation or in other words the head measured by a static pressure tap or the piezometric head Example Venturi Flow Meter Consider 2g h Q = A 2 V 2 = A 2 ( A2 1 A 1 ) 2 1 2

10 CEE 3310 Control Volume Analysis, Oct. 10, Frictional Effects If we have abrupt losses, say at a contraction, a simple way of accounting for this is through a discharge coefficient. We can write a modified form of Torricelli s formula for incompressible flow V = Q A = C d 2gh where C d is the discharge coefficient and is 1 for frictionless (inviscid) flow and can range down to about 0.6 for flows strongly effected by friction. Note we can handle non-uniform (violation of 1-D assumption) flow effects with a C d as well Vena Contracta Effect For a flow to get around a sharp corner there would need to be an infinite pressure gradient, which of course does not happen. Hence if the boundary changes directions too rapidly at an exit, the flow separates from the exit and forms what is known as a vena contracta Clearly A j /A 1. For a round sharp-cornered exit the coefficient is C c = A j /A = 0.61 and typical values of the coefficient fall in the range 0.5 C c 1.0.

### 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

### 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

### 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

### 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

### 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 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

### 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

### 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.

### 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

### 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

### 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

### 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

### 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:

### 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.

### 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

### 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

### 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

### 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

### 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,

### 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

### 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

### 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

### 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

### Basic Fluid Mechanics

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

### 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

### 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.

### 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

### 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

### 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

### 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.

### 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 4. ELEMENTARY FLUID DYNAMICS -THE BERNOULLI EQUATION

### 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

### Lecture23. Flowmeter Design.

Lecture23 Flowmeter Design. Contents of lecture Design of flowmeter Principles of flow measurement; i) Venturi and ii) Orifice meter and nozzle Relationship between flow rate and pressure drop Relation

### !! +! 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

### 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

### 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

### 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

### 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

### 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

### Where does Bernoulli's Equation come from?

Where does Bernoulli's Equation come from? Introduction By now, you have seen the following equation many times, using it to solve simple fluid problems. P ρ + v + gz = constant (along a streamline) This

### 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

### 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

### 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 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.

### 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

### 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

### Unit C-1: List of Subjects

Unit C-: List of Subjects The elocity Field The Acceleration Field The Material or Substantial Derivative Steady Flow and Streamlines Fluid Particle in a Flow Field F=ma along a Streamline Bernoulli s

### 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

### Chapter 11 - Fluids in Motion. Sections 7-9

Chapter - Fluids in Motion Sections 7-9 Fluid Motion The lower falls at Yellowstone National Park: the water at the top of the falls passes through a narrow slot, causing the velocity to increase at that

### HYDRAULICS 1 (HYDRODYNAMICS) SPRING 2005

HYDRAULICS (HYDRODYNAMICS) SPRING 005 Part. Fluid-Flow Principles. Introduction. Definitions. Notation and fluid properties.3 Hydrostatics.4 Fluid dynamics.5 Control volumes.6 Visualising fluid flow.7

### 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

### 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

### 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

### 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

### 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

### 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

### PART II. Fluid Mechanics Pressure. Fluid Mechanics Pressure. Fluid Mechanics Specific Gravity. Some applications of fluid mechanics

ART II Some applications of fluid mechanics Fluid Mechanics ressure ressure = F/A Units: Newton's per square meter, Nm -, kgm - s - The same unit is also known as a ascal, a, i.e. a = Nm - ) English units:

### 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

### CHEN 3200 Fluid Mechanics Spring Homework 3 solutions

Homework 3 solutions 1. An artery with an inner diameter of 15 mm contains blood flowing at a rate of 5000 ml/min. Further along the artery, arterial plaque has partially clogged the artery, reducing the

### 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

### V (r,t) = i ˆ u( x, y,z,t) + ˆ j v( x, y,z,t) + k ˆ w( x, y, z,t)

IV. DIFFERENTIAL RELATIONS FOR A FLUID PARTICLE This chapter presents the development and application of the basic differential equations of fluid motion. Simplifications in the general equations and common

### FLOW MEASUREMENT IN PIPES EXPERIMENT

University of Leicester Engineering Department FLOW MEASUREMENT IN PIPES EXPERIMENT Page 1 FORMAL LABORATORY REPORT Name of the experiment: FLOW MEASUREMENT IN PIPES Author: Apollin nana chaazou Partner

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

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

### Chapter 15B - Fluids in Motion. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 15B - Fluids in Motion A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 007 Paul E. Tippens Fluid Motion The lower falls at Yellowstone National

### 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

### Physics 3 Summer 1990 Lab 7 - Hydrodynamics

Physics 3 Summer 1990 Lab 7 - Hydrodynamics Theory Consider an ideal liquid, one which is incompressible and which has no internal friction, flowing through pipe of varying cross section as shown in figure

### 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

### 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

### FACULTY OF CHEMICAL & ENERGY ENGINEERING FLUID MECHANICS LABORATORY TITLE OF EXPERIMENT: MINOR LOSSES IN PIPE (E4)

FACULTY OF CHEMICAL & ENERGY ENGINEERING FLUID MECHANICS LABORATORY TITLE OF EXPERIMENT: MINOR LOSSES IN PIPE (E4) 1 1.0 Objectives The objective of this experiment is to calculate loss coefficient (K

### 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

### Chapter 5 Mass, Bernoulli, and Energy Equations Chapter 5 MASS, BERNOULLI, AND ENERGY EQUATIONS

Chapter 5 MASS, BERNOULLI, AND ENERGY EQUATIONS Conservation of Mass 5-C Mass, energy, momentum, and electric charge are conserved, and volume and entropy are not conserved during a process. 5-C Mass flow

### Chapter 14. Lecture 1 Fluid Mechanics. Dr. Armen Kocharian

Chapter 14 Lecture 1 Fluid Mechanics Dr. Armen Kocharian States of Matter Solid Has a definite volume and shape Liquid Has a definite volume but not a definite shape Gas unconfined Has neither a definite

### 1 st Law Analysis of Control Volume (open system) Chapter 6

1 st Law Analysis of Control Volume (open system) Chapter 6 In chapter 5, we did 1st law analysis for a control mass (closed system). In this chapter the analysis of the 1st law will be on a control volume

### 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

### Chapter 7 Energy Principle

Chater 7: Energy Princile By Dr Ali Jawarneh Hashemite University Outline In this chater we will: Derive and analyse the Energy equation. Analyse the flow and shaft work. Derive the equation for steady

### 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

### equation 4.1 INTRODUCTION

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

### Fluids. Fluids in Motion or Fluid Dynamics

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

### 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).

### 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

### 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

### 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:

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

Chapter 5 Fluid in Motion The Bernoulli Equation 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

### 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

### 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

### CH.1 Overview of Fluid Mechanics/22 MARKS. 1.1 Fluid Fundamentals.

Content : 1.1 Fluid Fundamentals. 08 Marks Classification of Fluid, Properties of fluids like Specific Weight, Specific gravity, Surface tension, Capillarity, Viscosity. Specification of hydraulic oil

### 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,

### 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

### 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;

### 주요명칭 수직날개. Vertical Wing. Flap. Rudder. Elevator 수평날개

High Lift Devices 주요명칭 동체 Flap 수직날개 Vertical Wing Rudder Elevator 수평날개 방향전환 () Rolling Yawing Pitching 방향전환 () Rolling Yawing Pitching Potential Flow of Helicopter PNU ME CFD LAB. =0 o =60 o =90 o =0 o

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

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

### 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

### 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:

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

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

### 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

### 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