2 NavierStokes Equations


 Gertrude Bruce
 2 years ago
 Views:
Transcription
1 1 Integral analysis 1. Water enters a pipe bend horizontally with a uniform velocity, u 1 = 5 m/s. The pipe is bended at 90 so that the water leaves it vertically downwards. The input diameter d 1 = 0.1 m and the input pressure p 1 = Pa. The output diameter is d 2 = 0.05 m. The size of the bend is such that it contains 4 kg of water between its two flanges and the mass of the steel walls of the bend is 6 kg. Neglecting viscous forces and assuming steady state conditions, find the total force which acts on the bend, i.e.that force that the bolts at the bend connections must support. 2. The mass off a rocket and fuel together is m(t)= tkg where t is time (s). The crosssectional area of the rocket nozzle at the exit is m 2. The speed of the exhaust gas there is u e = 1350 m/s, relative to the nozzle. The atmospheric pressure around the rocket is p 0 = 10 5 Pa. (a) The rocket is fixed on a horizontal test bench and fired. The pressure of the gas at the exit is p e = Pa. The test bench is held in place by a dynamometer. Find the force read on the dynamometer. (b) The rocket is set with its nose upward and fired. Neglect the aerodynamic resistance and find its acceleration. 3. A singleengine jet airplane flies at the speed of V = 280 m/s. The atmospheric pressure is p a = 10 5 Pa. The welldesigned air intake of the engine has a crosssectional area of A 1 = 0.1 m 2. The exit cross section of the jet nozzle has the area of A 2 = 0.3 m 2. The gas pressure at the exit is p 2 = Pa. The fueltoair mass ratio of the engine is 1 : 20. The specific density of the air at the inlet is ρ=1.2 kg/m 3. The gas speed at the exit relative to the airplane is U = 650 m/s. What is the horizontal force transferred by the bolts connecting the engine to the airplane body? 4. A fireman hose ends with a nozzle as shown below. Measurements show that A F = 0.01 m 2, A E = m 2, u F = 8 m/s, p F = N/m 2, p E = N/m 2 and so is the atmospheric pressure. The nozzle is connected to the hose by a flange at G. Whare are the magnitude and direction of the forces acting on the flange? 1
2 5. A steel pipe of d= m, wall thickness of 6 mm and m long is used to supply water. The water flows at 10 m/s and the nominal stress allowed in the pipe wall is N/cm 2. To prevent high stresses due to water hammer, the valve at the end of the pipe must not be closed faster than a certain rate. What is the minimal time required to close the valve? 6. A floating anchor is a deviced used in lifeboats to keep the nose of the boat directed against the waves. It is made of heavy clothe and has the shape of a cone, with holes at both ends (see below). It is tied to the rear of the boat and is dragged underwater by the boat, which is itself dragged by the waves and the wind. The water is thus forced into the anchor at its larger opening (diameter d i = 1 m) and comes out at the narrower end (diameter d e = 0.4 m). Experiments show that the pressure at the exit, i.e.the narrow end, is close to the hydrostatic pressure for this depth but that the pressure at the wide end is above hydrostatic pressure by about 0.4ρV 2, where V is the speed of the anchor relative to the water. A good assumption is also that the water does not leave the anchor at a relative speed higher than V. Estimate the resistance force of this anchor to relative speeds of 1 m/s, 5 m/s and 10 m/s. 7. A jet of water has the diameter of 0.04 m and the average velocity of 8 m/s. The water hits a stationary flat vane which is tilted by the angle π/4. The pressure everywhere outside the water jet is atmospheric and so it is inside the jet well before it hits the vane. Viscous forces are neglected. Assume the flow twodimensional and find the force acting on the vane and the power extracted by the vane. 8. A round jet of water comes straight up from a nozzle in a water fountain. The jet diameter as it comes out of the nozzle is m and its velocity there is 20 m/s. A little boy places a small glass sphere in the jet and enjoys seeing it 2
3 balances there. The glass sphere has a mass of 0.01 kg. Find the diameter of the water jet just before it hits the glass sphere. 9. A laminar flow (density ρ, viscosity µ) occurs trough a slender nozzle of length l and whose radius varies with the longitudinal coordinate x according to R(x)=R 1 +(R 2 R 1 ) x l where R 1 is the radius at the inlet and R 2 < R 1 is the radius at the outlet. The mass flux Q is constant. (a) Calculate the velocity distribution inside the nozzle assuming a parabolic velocity profile with a mean velocity Ū which is half the maximum velocity. (b) Determine the force acting on the nozzle. 10. After touchdown of aircrafts, the thrust reverser blocks the jet to the rear and redirects if forward to produce reverse thrust. The exiting jet (subsonic jet p 0, ρ 0, relative velocity w 0, section A 0 ) is divided into two symmetric jets with a deflection angle of π β. Thus, the aircraft experiences a deceleration a. Neglecting body forces and viscous forces and neglecting theengine inlet momentum flux (but not the mass flux), show that the deceleration is given by a= ρ 0w 2 0 A 0 cosβ m tot where m tot is the total mass of the aircraft. 2 NavierStokes Equations 1. An experimental system consists of a long tube of radius R 0 filled with glycerin. The pressure gradient along the tube is given and the flow is fully developed. The temperature in the glycerin at the center of the tube is sought, 3
4 and a suggestion is made to stretch a thin wire along the tube axis. It is claimed that, since the wire is very thin, the flow field is only slightly modified by the presence of the wire. Assess this claim by considering the ratio of the maximum velocity and the average velocity of the annular flow to that of the tube flow. 2. A metal wire of radius R i = 2mm is pulled vertically upward with the speed V i through a long pipe of radius R 0 = 5 mm. The gap between the wire and the pipe is filled with molten plastic material of density ρ and viscosity µ. As the wire comes out of the pipe, it carries on its surface a layer of plastic which cools and solidifies. The thickness of the solid layer is 0.1 mm. Find the speed with which the wire is pulled upward. 3. Coating of electric wire with insulating material is done by drawing the wire through a tubular die as shown below. The viscosity of the coating material is 100 poise. Write the equations for this case and calculate the force F required to draw the wire. 4. Glycerin (ρ=1.26 g/cm 3, µ = 10 poise) slides down on a semiinfinite vertical wall and form a laminar layer of thickness δ. Calculate the shear stress on the wall and the flowrate of glycerin. 5. An instrument for measuring viscosity consists of a rotating inner cylinder and a stationary outer cylinder. The inner cylinder rotates at 3600 r.p.m. and the viscosity of the fluid is 100 poise. (a) What is the moment acting on the outer cylinder? (b) What is the efficiency of this instrument as a hydraulic transmission of moment? Find the moment as a function the r.p.m. of the outer cylinder and the power transmitted. 4
5 6. The radial gap of an unloaded bearing which is filled with a Newtonian fluid can be modelled by a twodimensional gap if the radial dimension of the gap h is much smaller than the internal radius R. Assume a steady plane flow induced by the rotation of the journal at the constant angular velocity Ω. The material properties ρ, µ, k are constants. Body forces are neglected. (a) Calculate the torque exerted on the journal and the necessary power. (b) Determine the dissipation function. (c) Calculate the energy per unit time dissipated in the bearing gap. (Compare with the driving power). (d) Determine the heat flux that must be rejected from the fluid in steady operation. (e) Calculate the temperature gradient at the bushing (external axis) if the total heat flux flows through the bushing alone. (f) Determine the temperature distribution in the gap when the bushing is kept at the constant temperature T B. 7. Newtonian fluid flows through a channel with the height h and large extensions in the x 1 and x 3 directions. The plane flow is steady, the density ρ and viscosity µ are assumed to be constant, and body forces are neglected. The top and bottom wall are porous such that a constant normal velocity component V W can be established at the walls. The pressure gradient is constant in the x 1 direction and zero along x 3. Calculate the velocity distribution. What happens in the limiting case V W Incompressible Newtonian fluid flows steadily over a flat plate with large extensions in x and z directions. A boundary layer develops which normally would grow with increasing x. However, succion is applied over the length L such that the boundary layer thickness remains constant. The pressure p is assumed to be constant. Far from the plate, the velocity component u(y) has the value U. (a) Give the boundary condition for the velocity field. (b) Compute the velocity field and check that the mass flux entering the control volume DC is equal to the suction mass flux. (c) Calculate the drag per unit depth and plate length L by directly inegrating the wall shear stress and by application of a momentum balance to the control volume ABCD. 3 Compressible flow 1. A large pressure vessel contains at the total (stagnation) pressure p 0 = Pa and the total temperature T 0 = 350 K. The atmospheric pressure is p a = 5
6 10 5 Pa. Design a convergentdivergent nozzle that discharges 1.5 kg/s air to the atmosphere at atmospheric pressure. Find the speed of the discharged air. The nozzle is then made to discharge into another vessel where the pressure is (a) p e = Pa ; (b) p e = Pa ; (c) p e = Pa ; (d) p e = 10 5 Pa ; (e) p e = Pa Describe the resulting flows. 2. A large pressure vessel contains gas at the stagnation properties p 0 = 400 kpa, T 0 =420 K. The gas is approximately ideal with R = 287 J/kg/K and γ = 1.4. The outside atmospheric pressure is p a = 100 kpa. A convergentdivergent nozzle is designed to pass a mass flux of 1 kg/s from the vessel to the outside. Find (a) the speed of the gas at the exit from the nozzle, (b) the exit Mach number, (c) the critical crosssection area, (d) the exit crosssection area. 3. A normal shock wave moves through a quiescent air at p=10 5 Pa, T = 300 K. The speed of the shock is 694 m/s. Find the pressure left immediately behind the shock. Is the aire immediately behind the shock quiescent? If not, what is its velocity? 6
AEROSPACE ENGINEERING DEPARTMENT. Second Year  Second Term ( ) Fluid Mechanics & Gas Dynamics
AEROSPACE ENGINEERING DEPARTMENT Second Year  Second Term (20082009) Fluid Mechanics & Gas Dynamics Similitude,Dimensional Analysis &Modeling (1) [7.2R*] Some common variables in fluid mechanics include:
More informationREE Internal Fluid Flow Sheet 2  Solution Fundamentals of Fluid Mechanics
REE 307  Internal Fluid Flow Sheet 2  Solution Fundamentals of Fluid Mechanics 1. Is the following flows physically possible, that is, satisfy the continuity equation? Substitute the expressions for
More informationConsider a control volume in the form of a straight section of a streamtube ABCD.
6 MOMENTUM EQUATION 6.1 Momentum and Fluid Flow In mechanics, the momentum of a particle or object is defined as the product of its mass m and its velocity v: Momentum = mv The particles of a fluid stream
More informationFluid Dynamics Exercises and questions for the course
Fluid Dynamics Exercises and questions for the course January 15, 2014 A two dimensional flow field characterised by the following velocity components in polar coordinates is called a free vortex: u r
More information4 Mechanics of Fluids (I)
1. The x and y components of velocity for a twodimensional flow are u = 3.0 ft/s and v = 9.0x ft/s where x is in feet. Determine the equation for the streamlines and graph representative streamlines in
More informationFluids. Fluids in Motion or Fluid Dynamics
Fluids Fluids in Motion or Fluid Dynamics Resources: Serway  Chapter 9: 9.79.8 Physics B Lesson 3: Fluid Flow Continuity Physics B Lesson 4: Bernoulli's Equation MIT  8: Hydrostatics, Archimedes' Principle,
More informationIn which of the following scenarios is applying the following form of Bernoulli s equation: steady, inviscid, uniform stream of water. Ma = 0.
bernoulli_11 In which of the following scenarios is applying the following form of Bernoulli s equation: p V z constant! g + g + = from point 1 to point valid? a. 1 stagnant column of water steady, inviscid,
More informationequation 4.1 INTRODUCTION
4 The momentum equation 4.1 INTRODUCTION It is often important to determine the force produced on a solid body by fluid flowing steadily over or through it. For example, there is the force exerted on a
More informationShell Balances in Fluid Mechanics
Shell Balances in Fluid Mechanics R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University When fluid flow occurs in a single direction everywhere in a system, shell
More informationCENG 501 Examination Problem: Estimation of Viscosity with a Falling  Cylinder Viscometer
CENG 501 Examination Problem: Estimation of Viscosity with a Falling  Cylinder Viscometer You are assigned to design a fallingcylinder viscometer to measure the viscosity of Newtonian liquids. A schematic
More informationPart A: 1 pts each, 10 pts total, no partial credit.
Part A: 1 pts each, 10 pts total, no partial credit. 1) (Correct: 1 pt/ Wrong: 3 pts). The sum of static, dynamic, and hydrostatic pressures is constant when flow is steady, irrotational, incompressible,
More informationMiddle East Technical University Department of Mechanical Engineering ME 305 Fluid Mechanics I Fall 2018 Section 4 (Dr.
Reading Assignments Middle East Technical University Department of Mechanical Engineering ME 305 Fluid Mechanics I Fall 2018 Section 4 (Dr. Sert) Study Set 1 You can find the answers of some of the following
More informationChapter 4 DYNAMICS OF FLUID FLOW
Faculty Of Engineering at Shobra nd Year Civil  016 Chapter 4 DYNAMICS OF FLUID FLOW 41 Types of Energy 4 Euler s Equation 43 Bernoulli s Equation 44 Total Energy Line (TEL) and Hydraulic Grade Line
More informationCE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK 3 0 0 3 UNIT I FLUID PROPERTIES AND FLUID STATICS PART  A 1. Define fluid and fluid mechanics. 2. Define real and ideal fluids. 3. Define mass density
More informationTherefore, the control volume in this case can be treated as a solid body, with a net force or thrust of. bm # V
When the mass m of the control volume remains nearly constant, the first term of the Eq. 6 8 simply becomes mass times acceleration since 39 CHAPTER 6 d(mv ) CV m dv CV CV (ma ) CV Therefore, the control
More informationENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids
CHAPTER 1 Properties of Fluids ENGINEERING FLUID MECHANICS 1.1 Introduction 1.2 Development of Fluid Mechanics 1.3 Units of Measurement (SI units) 1.4 Mass, Density, Specific Weight, Specific Volume, Specific
More informationTutorial 10. Boundary layer theory
Tutorial 10 Boundary layer theory 1. If the velocity distribution law in a laminar boundary layer over a flat plate is assumes to be of the form, determine the velocity distribution law. At y = 0, u= 0
More informationLesson 6 Review of fundamentals: Fluid flow
Lesson 6 Review of fundamentals: Fluid flow The specific objective of this lesson is to conduct a brief review of the fundamentals of fluid flow and present: A general equation for conservation of mass
More informationFigure 3: Problem 7. (a) 0.9 m (b) 1.8 m (c) 2.7 m (d) 3.6 m
1. For the manometer shown in figure 1, if the absolute pressure at point A is 1.013 10 5 Pa, the absolute pressure at point B is (ρ water =10 3 kg/m 3, ρ Hg =13.56 10 3 kg/m 3, ρ oil = 800kg/m 3 ): (a)
More informationThe online of midtermtests of Fluid Mechanics 1
The online of midtermtests of Fluid Mechanics 1 1) The information on a can of pop indicates that the can contains 460 ml. The mass of a full can of pop is 3.75 lbm while an empty can weights 80.5 lbf.
More informationFinal 1. (25) 2. (10) 3. (10) 4. (10) 5. (10) 6. (10) TOTAL = HW = % MIDTERM = % FINAL = % COURSE GRADE =
MAE101B: Advanced Fluid Mechanics Winter Quarter 2017 http://web.eng.ucsd.edu/~sgls/mae101b_2017/ Name: Final This is a three hour openbook exam. Please put your name on the top sheet of the exam. Answer
More information10.52 Mechanics of Fluids Spring 2006 Problem Set 3
10.52 Mechanics of Fluids Spring 2006 Problem Set 3 Problem 1 Mass transfer studies involving the transport of a solute from a gas to a liquid often involve the use of a laminar jet of liquid. The situation
More informationMOMENTUM PRINCIPLE. Review: Last time, we derived the Reynolds Transport Theorem: Chapter 6. where B is any extensive property (proportional to mass),
Chapter 6 MOMENTUM PRINCIPLE Review: Last time, we derived the Reynolds Transport Theorem: where B is any extensive property (proportional to mass), and b is the corresponding intensive property (B / m
More informationFluid Mechanics Qualifying Examination Sample Exam 2
Fluid Mechanics Qualifying Examination Sample Exam 2 Allotted Time: 3 Hours The exam is closed book and closed notes. Students are allowed one (doublesided) formula sheet. There are five questions on
More informationLecture 3 The energy equation
Lecture 3 The energy equation Dr Tim Gough: t.gough@bradford.ac.uk General information Lab groups now assigned Timetable up to week 6 published Is there anyone not yet on the list? Week 3 Week 4 Week 5
More information4 Finite Control Volume Analysis Introduction Reynolds Transport Theorem Conservation of Mass
iv 2.3.2 Bourdon Gage................................... 92 2.3.3 Pressure Transducer................................ 93 2.3.4 Manometer..................................... 95 2.3.4.1 Piezometer................................
More information150A Review Session 2/13/2014 Fluid Statics. Pressure acts in all directions, normal to the surrounding surfaces
Fluid Statics Pressure acts in all directions, normal to the surrounding surfaces or Whenever a pressure difference is the driving force, use gauge pressure o Bernoulli equation o Momentum balance with
More informationTable of Contents. Foreword... xiii. Preface... xv
Table of Contents Foreword.... xiii Preface... xv Chapter 1. Fundamental Equations, Dimensionless Numbers... 1 1.1. Fundamental equations... 1 1.1.1. Local equations... 1 1.1.2. Integral conservation equations...
More informationWhat s important: viscosity Poiseuille's law Stokes' law Demo: dissipation in flow through a tube
PHYS 101 Lecture 29x  Viscosity 29x  1 Lecture 29x Viscosity (extended version) What s important: viscosity Poiseuille's law Stokes' law Demo: dissipation in flow through a tube Viscosity We introduced
More informationPage 1. Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.)
Page 1 Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (1 point if not circled, or circled incorrectly): Prof. Vlachos Prof. Ardekani
More informationChapter Four fluid flow mass, energy, Bernoulli and momentum
41Conservation of Mass Principle Consider a control volume of arbitrary shape, as shown in Fig (41). Figure (41): the differential control volume and differential control volume (Total mass entering
More informationConservation 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
More informationAnswers to questions in each section should be tied together and handed in separately.
EGT0 ENGINEERING TRIPOS PART IA Wednesday 4 June 014 9 to 1 Paper 1 MECHANICAL ENGINEERING Answer all questions. The approximate number of marks allocated to each part of a question is indicated in the
More informationSPC Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30
SPC 307  Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30 1. The maximum velocity at which an aircraft can cruise occurs when the thrust available with the engines operating with the
More informationIran University of Science & Technology School of Mechanical Engineering Advance Fluid Mechanics
1. Consider a sphere of radius R immersed in a uniform stream U0, as shown in 3 R Fig.1. The fluid velocity along streamline AB is given by V ui U i x 1. 0 3 Find (a) the position of maximum fluid acceleration
More informationContents. I Introduction 1. Preface. xiii
Contents Preface xiii I Introduction 1 1 Continuous matter 3 1.1 Molecules................................ 4 1.2 The continuum approximation.................... 6 1.3 Newtonian mechanics.........................
More informationSignature: (Note that unsigned exams will be given a score of zero.)
Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (1 point if not circled, or circled incorrectly): Prof. Dabiri Prof. Wassgren Prof.
More informationV/ t = 0 p/ t = 0 ρ/ t = 0. V/ s = 0 p/ s = 0 ρ/ s = 0
UNIT III FLOW THROUGH PIPES 1. List the types of fluid flow. Steady and unsteady flow Uniform and nonuniform flow Laminar and Turbulent flow Compressible and incompressible flow Rotational and irrotational
More informationLecture 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
More information2 Internal Fluid Flow
Internal Fluid Flow.1 Definitions Fluid Dynamics The study of fluids in motion. Static Pressure The pressure at a given point exerted by the static head of the fluid present directly above that point.
More informationMECHANICAL PROPERTIES OF FLUIDS
CHAPTER10 MECHANICAL PROPERTIES OF FLUIDS QUESTIONS 1 marks questions 1. What are fluids? 2. How are fluids different from solids? 3. Define thrust of a liquid. 4. Define liquid pressure. 5. Is pressure
More informationName : Applied Physics II Exam One Winter Multiple Choice ( 7 Points ):
Name : email: Applied Physics II Exam One Winter 20062007 Multiple Choice ( 7 Points ): 1. Pure nitrogen gas is contained in a sealed tank containing a movable piston. The initial volume, pressure and
More information11.1 Mass Density. Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an
Chapter 11 Fluids 11.1 Mass Density Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an important factor that determines its behavior
More informationS.E. (Mech.) (First Sem.) EXAMINATION, (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum Marks : 100
Total No. of Questions 12] [Total No. of Printed Pages 8 Seat No. [4262]113 S.E. (Mech.) (First Sem.) EXAMINATION, 2012 (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum
More informationFriction Factors and Drag Coefficients
Levicky 1 Friction Factors and Drag Coefficients Several equations that we have seen have included terms to represent dissipation of energy due to the viscous nature of fluid flow. For example, in the
More informationFLUID MECHANICS PROF. DR. METİN GÜNER COMPILER
FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER ANKARA UNIVERSITY FACULTY OF AGRICULTURE DEPARTMENT OF AGRICULTURAL MACHINERY AND TECHNOLOGIES ENGINEERING 1 5. FLOW IN PIPES 5.1.3. Pressure and Shear Stress
More informationConvective Mass Transfer
Convective Mass Transfer Definition of convective mass transfer: The transport of material between a boundary surface and a moving fluid or between two immiscible moving fluids separated by a mobile interface
More informationPh.D. Qualifying Exam in Fluid Mechanics
Student ID Department of Mechanical Engineering Michigan State University East Lansing, Michigan Ph.D. Qualifying Exam in Fluid Mechanics Closed book and Notes, Some basic equations are provided on an
More informationME 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
More informationNicholas J. Giordano. Chapter 10 Fluids
Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 10 Fluids Fluids A fluid may be either a liquid or a gas Some characteristics of a fluid Flows from one place to another Shape varies according
More informationFE Fluids Review March 23, 2012 Steve Burian (Civil & Environmental Engineering)
Topic: Fluid Properties 1. If 6 m 3 of oil weighs 47 kn, calculate its specific weight, density, and specific gravity. 2. 10.0 L of an incompressible liquid exert a force of 20 N at the earth s surface.
More informationFluid Mechanics. du dy
FLUID MECHANICS Technical English  I 1 th week Fluid Mechanics FLUID STATICS FLUID DYNAMICS Fluid Statics or Hydrostatics is the study of fluids at rest. The main equation required for this is Newton's
More informationFE Exam Fluids Review October 23, Important Concepts
FE Exam Fluids Review October 3, 013 mportant Concepts Density, specific volume, specific weight, specific gravity (Water 1000 kg/m^3, Air 1. kg/m^3) Meaning & Symbols? Stress, Pressure, Viscosity; Meaning
More informationPiping Systems and Flow Analysis (Chapter 3)
Piping Systems and Flow Analysis (Chapter 3) 2 Learning Outcomes (Chapter 3) Losses in Piping Systems Major losses Minor losses Pipe Networks Pipes in series Pipes in parallel Manifolds and Distribution
More informationINTRODUCTION TO FLUID MECHANICS June 27, 2013
INTRODUCTION TO FLUID MECHANICS June 27, 2013 PROBLEM 3 (1 hour) A perfect liquid of constant density ρ and constant viscosity µ fills the space between two infinite parallel walls separated by a distance
More informationEXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER
EXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER 1.1 AIM: To determine the coefficient of discharge of the orifice meter 1.2 EQUIPMENTS REQUIRED: Orifice meter test rig, Stopwatch 1.3 PREPARATION 1.3.1
More informationCOURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour. Basic Equations in fluid Dynamics
COURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour Basic Equations in fluid Dynamics Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 Description of Fluid
More informationControl Volume Revisited
Civil Engineering Hydraulics Control Volume Revisited Previously, we considered developing a control volume so that we could isolate mass flowing into and out of the control volume Our goal in developing
More informationLEAKLESS COOLING SYSTEM V.2 PRESSURE DROP CALCULATIONS AND ASSUMPTIONS
CH1211 Geneva 23 Switzerland EDMS No. ST/CV  Cooling of Electronics & Detectors GUIDE LEAKLESS COOLING SYSTEM V.2 PRESSURE DROP CALCULATIONS AND ASSUMPTIONS Objectives Guide to Leakless Cooling System
More information2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False A. True B.
CHAPTER 03 1. Write Newton's second law of motion. YOUR ANSWER: F = ma 2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False 3.Streamwise
More informationFLUID MECHANICS PROF. DR. METİN GÜNER COMPILER
FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER ANKARA UNIVERSITY FACULTY OF AGRICULTURE DEPARTMENT OF AGRICULTURAL MACHINERY AND TECHNOLOGIES ENGINEERING 1 4. ELEMENTARY FLUID DYNAMICS THE BERNOULLI EQUATION
More informationBenha University College of Engineering at Benha Questions For Corrective Final Examination Subject: Fluid Mechanics M 201 May 24/ 2016
Benha University College of Engineering at Benha Questions For Corrective Final Examination Subject: Fluid Mechanics M 01 May 4/ 016 Second year Mech. Time :180 min. Examiner:Dr.Mohamed Elsharnoby Attempt
More informationf= flow rate (m 3 /s) A = crosssectional area of the pipe (m 2 ) v= flow speed (m/s)
Fluid Mechanics Flow Rate and Continuity Equation If you have a pipe that is flowing a liquid you will have a flow rate. The flow rate is the volume of fluid that passes any particular point per unit of
More information6.1 According to Handbook of Chemistry and Physics the composition of air is
6. Compressible flow 6.1 According to Handbook of Chemistry and Physics the composition of air is From this, compute the gas constant R for air. 6. The figure shows a, Pitotstatic tube used for velocity
More informationIntroduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD)
Introduction to Aerodynamics Dr. Guven Aerospace Engineer (P.hD) Aerodynamic Forces All aerodynamic forces are generated wither through pressure distribution or a shear stress distribution on a body. The
More informationCHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS NOOR ALIZA AHMAD
CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS 1 INTRODUCTION Flow often referred as an ideal fluid. We presume that such a fluid has no viscosity. However, this is an idealized situation that does not exist.
More informationINTRODUCTION DEFINITION OF FLUID. U p F FLUID IS A SUBSTANCE THAT CAN NOT SUPPORT SHEAR FORCES OF ANY MAGNITUDE WITHOUT CONTINUOUS DEFORMATION
INTRODUCTION DEFINITION OF FLUID plate solid F at t = 0 t > 0 = F/A plate U p F fluid t 0 t 1 t 2 t 3 FLUID IS A SUBSTANCE THAT CAN NOT SUPPORT SHEAR FORCES OF ANY MAGNITUDE WITHOUT CONTINUOUS DEFORMATION
More informationApplied Gas Dynamics Flow With Friction and Heat Transfer
Applied Gas Dynamics Flow With Friction and Heat Transfer Ethirajan Rathakrishnan Applied Gas Dynamics, John Wiley & Sons (Asia) Pte Ltd c 2010 Ethirajan Rathakrishnan 1 / 121 Introduction So far, we have
More informationPhysics 196 Final Test Point
Physics 196 Final Test  120 Point Name You need to complete six 5point problems and six 10point problems. Cross off one 5point problem and one 10point problem. 1. Two small silver spheres, each with
More informationExperiment (4): Flow measurement
Experiment (4): Flow measurement Introduction: The flow measuring apparatus is used to familiarize the students with typical methods of flow measurement of an incompressible fluid and, at the same time
More informationExperiment (3): Impact of jet
Experiment (3): Impact of jet Introduction: Impact of jets apparatus enables experiments to be carried out on the reaction force produced on vanes when a jet of water impacts on to the vane. The study
More informationEmpirical Co  Relations approach for solving problems of convection 10:06:43
Empirical Co  Relations approach for solving problems of convection 10:06:43 10:06:44 Empirical Corelations for Free Convection Use T f or T b for getting various properties like Re = VL c / ν β = thermal
More information3/10/2019. What Is a Force? What Is a Force? Tactics: Drawing Force Vectors
What Is a Force? A force acts on an object. A force requires an agent, something that acts on the object. If you throw a ball, your hand is the agent or cause of the force exerted on the ball. A force
More informationKing Fahd University of Petroleum and Minerals Department of Physics. Final Exam 041. Answer key  First choice is the correct answer
King Fahd University of Petroleum and Minerals Department of Physics MSK Final Exam 041 Answer key  First choice is the correct answer Q1 A 20 kg uniform ladder is leaning against a frictionless wall
More informationTOPICS. Density. Pressure. Variation of Pressure with Depth. Pressure Measurements. Buoyant ForcesArchimedes Principle
Lecture 6 Fluids TOPICS Density Pressure Variation of Pressure with Depth Pressure Measurements Buoyant ForcesArchimedes Principle Surface Tension ( External source ) Viscosity ( External source ) Equation
More informationPlease welcome for any correction or misprint in the entire manuscript and your valuable suggestions kindly mail us
Problems of Practices Of Fluid Mechanics Compressible Fluid Flow Prepared By Brij Bhooshan Asst. Professor B. S. A. College of Engg. And Technology Mathura, Uttar Pradesh, (India) Supported By: Purvi Bhooshan
More informationPrinciples of Food and Bioprocess Engineering (FS 231) Problems on Heat Transfer
Principles of Food and Bioprocess Engineering (FS 1) Problems on Heat Transfer 1. What is the thermal conductivity of a material 8 cm thick if the temperature at one end of the product is 0 C and the temperature
More informationWhat Is a Force? Slide Pearson Education, Inc.
What Is a Force? A force acts on an object. A force requires an agent, something that acts on the object. If you throw a ball, your hand is the agent or cause of the force exerted on the ball. A force
More informationFluid Dynamics. Equation of continuity Bernoulli s Equation Bernoulli s Application Viscosity Poiseuilles law Stokes law Reynolds Number
Fluid Dynamics Equation of continuity Bernoulli s Equation Bernoulli s Application Viscosity Poiseuilles law Stokes law Reynolds Number Fluids in Motion steady or laminar flow, if each particle of the
More informationAPPLIED FLUID DYNAMICS HANDBOOK
APPLIED FLUID DYNAMICS HANDBOOK ROBERT D. BLEVINS H imhnisdia ttodisdiule Darmstadt Fachbereich Mechanik 'rw.nr.. [VNR1 VAN NOSTRAND REINHOLD COMPANY ' ' New York Contents Preface / v 1. Definitions /
More informationSliding Contact Bearings
Sliding Contact Bearings Classification of Bearings 1. According to the direction of load to be supported. The bearings under this group are classified as: (a) Radial bearings (b) Thrust bearings. In radial
More informationFluid Mechanics II Viscosity and shear stresses
Fluid Mechanics II Viscosity and shear stresses Shear stresses in a Newtonian fluid A fluid at rest can not resist shearing forces. Under the action of such forces it deforms continuously, however small
More informationChemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017
Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017 Objective: Text: To introduce the basic concepts of fluid mechanics and heat transfer necessary for solution of engineering
More informationFluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture  17 Laminar and Turbulent flows
Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture  17 Laminar and Turbulent flows Welcome back to the video course on fluid mechanics. In
More informationINSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad AERONAUTICAL ENGINEERING QUESTION BANK : AERONAUTICAL ENGINEERING.
Course Name Course Code Class Branch INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad  00 0 AERONAUTICAL ENGINEERING : Mechanics of Fluids : A00 : III B. Tech Year : 0 0 Course Coordinator
More informationRecap: Static Fluids
Recap: Static Fluids Archimedes principal states that the buoyant force acting on an object is equal to the weight of fluid displaced. If the average density of object is greater than density of fluid
More informationThe Bernoulli Equation
The Bernoulli Equation The most used and the most abused equation in fluid mechanics. Newton s Second Law: F = ma In general, most real flows are 3D, unsteady (x, y, z, t; r,θ, z, t; etc) Let consider
More informationWilliam В. Brower, Jr. A PRIMER IN FLUID MECHANICS. Dynamics of Flows in One Space Dimension. CRC Press Boca Raton London New York Washington, D.C.
William В. Brower, Jr. A PRIMER IN FLUID MECHANICS Dynamics of Flows in One Space Dimension CRC Press Boca Raton London New York Washington, D.C. Table of Contents Chapter 1 Fluid Properties Kinetic Theory
More informationThe E80 Wind Tunnel Experiment the experience will blow you away. by Professor Duron Spring 2012
The E80 Wind Tunnel Experiment the experience will blow you away by Professor Duron Spring 2012 Objectives To familiarize the student with the basic operation and instrumentation of the HMC wind tunnel
More informationFluids. Fluid = Gas or Liquid. Density Pressure in a Fluid Buoyancy and Archimedes Principle Fluids in Motion
Chapter 14 Fluids Fluids Density Pressure in a Fluid Buoyancy and Archimedes Principle Fluids in Motion Fluid = Gas or Liquid MFMcGrawPHY45 Chap_14HaFluidsRevised 10/13/01 Densities MFMcGrawPHY45 Chap_14HaFluidsRevised
More informationPage 1. Chapters 2, 3 (linear) 9 (rotational) Final Exam: Wednesday, May 11, 10:05 am  12:05 pm, BASCOM 272
Final Exam: Wednesday, May 11, 10:05 am  12:05 pm, BASCOM 272 The exam will cover chapters 1 14 The exam will have about 30 multiple choice questions Consultations hours the same as before. Another review
More information5 ENERGY EQUATION OF FLUID MOTION
5 ENERGY EQUATION OF FLUID MOTION 5.1 Introduction In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics. The pertinent laws
More informationHigh Speed Aerodynamics. Copyright 2009 Narayanan Komerath
Welcome to High Speed Aerodynamics 1 Lift, drag and pitching moment? Linearized Potential Flow Transformations Compressible Boundary Layer WHAT IS HIGH SPEED AERODYNAMICS? Airfoil section? Thin airfoil
More informationChapter 10  Mechanical Properties of Fluids. The blood pressure in humans is greater at the feet than at the brain
Question 10.1: Explain why The blood pressure in humans is greater at the feet than at the brain Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at the sea level, though
More informationMass of fluid leaving per unit time
5 ENERGY EQUATION OF FLUID MOTION 5.1 Eulerian Approach & Control Volume In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics.
More informationIX. COMPRESSIBLE FLOW. ρ = P
IX. COMPRESSIBLE FLOW Compressible flow is the study of fluids flowing at speeds comparable to the local speed of sound. This occurs when fluid speeds are about 30% or more of the local acoustic velocity.
More informationCHARACTERISTIC OF FLUIDS. A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude.
CHARACTERISTIC OF FLUIDS A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude. In a fluid at rest, normal stress is called pressure. 1 Dimensions,
More informationR09. d water surface. Prove that the depth of pressure is equal to p +.
Code No:A109210105 R09 SET1 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 informationCLASS SCHEDULE 2013 FALL
CLASS SCHEDULE 2013 FALL Class # or Lab # 1 Date Aug 26 2 28 Important Concepts (Section # in Text Reading, Lecture note) Examples/Lab Activities Definition fluid; continuum hypothesis; fluid properties
More informationFor 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
More information