ME 305 Fluid Mechanics I. Part 4 Integral Formulation of Fluid Flow

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "ME 305 Fluid Mechanics I. Part 4 Integral Formulation of Fluid Flow"

Transcription

1 ME 305 Fluid Mechanics I Part 4 Integral Formulation of Fluid Flow These presentations are prepared by Dr. Cüneyt Sert Mechanical Engineering Department Middle East Technical University Ankara, Turkey Please ask for permission before using them. You are NOT allowed to modify them. 4-1

2 Reynolds Transport Theorem dn sys dt = ρ η d + ρ η V n da t CV CS Rate of change of property N within the system. Rate of change of = property N in the corresponding CV + (zero for steady flows) Net rate at which property N exits the CV Conservation Eqn N η Left hand side Mass m 1 Zero Linear Momentum P V F Angular Momentum H r V T Energy E e Q + W 4-2

3 Conservation of Mass (Continuity Equation) Taking N = m and η = 1, RTT becomes dm sys dt = 0 = ρ d + ρ V n da t CV CS Rate of change of mass in the CV Net rate of mass exiting through the CS t CV ρ d < 0 : Mass inside the CV decreases in time CV CS ρ V n da > 0 : The amount of mass leaving the CV is in balance with the above term 4-3

4 Mass Flow Rate ( m) The surface integral of the continuity equation is known as the mass flow rate ( m). It has the units of kg/s. V m = ρ V n da CS [kg/s] CS n Usually the CS is separated into parts and the integral over each part is evaluated one by one. n V CV n V > 0 if V n > 0 outflow V m = = 0 if V n = 0 V = 0 or flow is parallel to the CS α n < 0 if V n < 0 inflow V n = V cos(α) 4-4

5 Mass Flow Rate ( m) Consider the following pipe branching into two. Section 1 is an inlet. V n & m are negative. 1 3 n Section 3 is an exit. V n & m are positive. V n V n, V 2 Section 2 is an exit. V n & m are positive. Alternative CS selection at section 3 (prefer this one) V n 4-5

6 Volumetric Flow Rate (Q) and Average Velocity (V) If the density is uniform across a cross section A volumetric flow rate (Q) can be defined as Q = m ρ = A V n da [m 3 /s] Average velocity over a section of a flow field is defined as V = m ρa = Q A (ρ is uniform over the section) m = ρav Q = AV u = U max 1 r2 R 2 V V is defined such that these two cases provide the same flow rate. 4-6

7 Volumetric Flow Rate and Average Velocity (cont d) Exercise: Consider the water exiting a pipe of diameter D = 2 cm. To find the flow rate we measured the time it will take to fill a bucket of volume V = 10 liters. It took 65 s to fill it. Determine a) the volumetric flow rate of water. b) the mass flow rate of water. c) Average velocity at the exit. c) the centerline velocity at the exit if the velocity profile is parabolic as given in the previous slide. 4-7

8 Continuity Equation for Steady Flows For a steady flow (time independent flow) partial time derivative of RTT is zero, and the continuity equation reduces to ρ V n da = 0 CS Continuity equation for a steady flow is inlets m i + outlets m o = 0 For a common case of unidirectional, uniform flow with a single inlet and single exit 1 inlet 2 Continuity : ρ 1 A 1 V 1 + ρ 2 A 2 V 2 = 0 ρ 1 A 1 V 1 = ρ 2 A 2 V 2 4-8

9 Continuity Equation for Incompressible Flow For an incompressible flow (not necessarily steady) density is constant and continuity equation simplifies as Zero since volume of a CV is constant ρ t CV d + ρ CS V n da = 0 ρ CV t + ρ CS V n da = 0 CS V n da = 0 For a common case of unidirectional, uniform flow with a single inlet and single exit 1 2 Continuity : A 1 V 1 + A 2 V 2 = 0 A 1 V 1 = A 2 V 2 (true even if the flow is unsteady) 4-9

10 Mass Conservation Exercises Exercise : Parabolic velocity profile for the steady, fully developed, laminar flow in a pipe is as given below. Calculate the mass flow rates at the inlet and exit of the shown CV and show that they are equal. ρ 60 2R u = U max 1 r2 R 2 Exercise : For the pipe flow given above how much i) the maximum velocity, and ii) wall shear stress will change if the same amount of fluid is forced to pass through a smaller pipe with a radius that is half of the one given above. 4-10

11 Mass Conservation Exercises (cont d) Exercise : A hair dryer can be considered as a duct of constant diameter in which layers of electric resistors are placed. A small fan pulls the air in and forces it through the resistors where it is heated. If the density of air is 1.2 kg/m 3 at the inlet and 1.05 kg/m 3 at the exit, determine the percent increase in the velocity of air as it flows through the dryer (Reference: Çengel s book). 1.2 kg/m kg/m

12 Mass Conservation Exercises (cont d) Exercise : A cylindrical tank, open at the top, has a diameter of 1 m. Water is flowing into the tank through pipe 1, and flowing out through pipe 2. Determine the rate at which the water level is rising / falling in the tank. 1 D 1 = 0.2 m V 1 = 3 m/s Water 2 D 2 = 0.1 m V 2 = 10 m/s Exercise : A tank of 0.05 m 3 volume contains air at 800 kpa (absolute) and 15 o C. At t = 0, air begins escaping from the tank through a valve with a flow area of 65 mm 2. The air passing through the valve has a speed of 300 m/s and a density of 6 kg/m 3. Determine the instantaneous rate of change of density in the tank at t = 0. Air 4-12

13 Moving CV Although we defined a CV to be fixed in space, in some problems a moving CV can be used. In such a case use a reference frame attached to the moving CV so that it becomes stationary. This is the same as using relative velocities at the inlets/exits. Relative velocity (W) is the fluid velocity seen by an observer moving with the CV. Absolute velocity (V) is the fluid velocity seen by a fixed observer. V CV V CV : Velocity of the CV W V W V : Relative velocity : Absolute velocity Exercise : An airplane moves forward in still air at a speed of 971 km/h. The frontal area of the jet engine is 0.8 m 2 and the entering air density is 1.2 kg/m 3. The exhaust area is m 2 and the exhaust gas density is kg/m 3. A stationary observer on the ground observes that the jet engine exhaust gases move with a speed of 1050 km/h. Estimate the mass flow rate of fuel into the engine. 4-13

14 Deforming CV Although a CV is defined to have fixed position and shape, for some problems it may be useful to consider deforming CVs. Exercise: Solve the cylindrical tank problem of Slide 4-12 using a deforming CV such that the CS is attached to the free surface and goes up/down with it. Exercise: A syringe is used to inoculate a cow. The plunger has a face area of 500 mm 2. The liquid in the syringe is to be injected steadily at a rate of 300 cm 3 /min. The leakage rate past the plunger is 10% of the flow rate out of the needle. With what speed should the plunger be advanced? (Reference: Munson s book) 4-14

15 Conservation of Linear Momentum Taking N = P and η = V, RTT becomes dp sys dt = F = ρvd + ρv V n da t CV CS Sum of external forces acting on the CV Rate of change of linear momentum in the CV Net rate of flow of linear momentum through the CS Unlike the mass conservation equation, this one is a vector equation. For steady flows partial time derivative is zero. First term drops F = ρv V n da CS 4-15

16 Conservation of Linear Momentum (cont d) For the common case of steady, unidirectional, uniform flow with a single inlet and single exit 1 x 2 m = ρ 1 A 1 V 1 = ρ 2 A 2 V 2 F x = ρ 2 V 2 2 A 2 ρ 1 V 1 2 A 1 = m (V 2 V 1 ) 4-16

17 Cons. of Linear Momentum Important Points Direction of momentum flow rate at the inlets/exits is always in the direction of the outward normal n. In solving problems you can show them with arrows just like forces. Show the forces on a separately drawn CV (like drawing a free body diagram). 1 3 α 2 With this CV, forces acting on the fluid by the pipe can be calculated. Forces acting on the pipe by the fluid are the reverse of the calculated ones. 4-17

18 Cons. of Linear Momentum Important Points (cont d) Which forces to include depend on the selection of the CV. Work on the previous example, but this time select the CV outside the pipe With this CV, anchoring forces can be calculated. These are usually the desired ones in practice. Atmospheric pressure forces come into the picture. 4-18

19 Cons. of Linear Momentum Important Points (cont d) Effect of p atm can be simlified. For the outside CV of the previous slide, concentrate of the pressure forces. p atm acts p 3 A 3 p atm acts p 1 A 1 p atm acts p 2 A 2 p 3,gage A 3 These two systems are equivalent as far as the pressure forces are concerned. When calculating anchoring forces by selecting outside CVs, it is better to use gage pressures at inlets/exits. When this is done p atm s are gone. p 1,gage A 1 p 2,gage A

20 Cons. of Linear Momentum Important Points (cont d) Liquid jets exiting freely to atmosphere at subsonic speed are considered to be at atmospheric pressure. Exercise: The following vane deflects the liquid jet coming out of a nozzle by an angle of α. The jet exits the nozzle with an average velocity of V j through an exit area of A j. Jet s cross sectional area is assumed to remain constant. Select a proper CV and calculate the anchoring force necessary to hold the vane in its place. Nozzle Jet 2 1 Deflecting vane 4-20

21 Cons. of Linear Momentum Important Points (cont d) Conservation of linear momentum is a vector equation. It can be written in component form. Cartesian components are x component : F x = t CV ρ u d + ρ u V n da CS y component : F y = t CV ρ v d + ρ v V n da CS z component : F z = t CV ρ w d + ρ w V n da CS V remains as it is in the dot product 4-21

22 Cons. of Linear Momentum Important Points (cont d) When the velocity is not uniform at a cross section, the calculations can still be done as if the velocity is uniform and the results can be corrected using the momentum correction factor (β). u = U max 1 r2 R 2 V 1 Part of a CV 1 1 Previously we showed that U max = 2 V β = Momentum flow rate of the actual velocity profile Momentum flow rate of the uniform velocity profile = A ρu 1 V 1 1 n 1 da ρ V 2 1 A 1 For the parabolic velocity profile of laminar pipe flow given above β = 4/3. For a turbulent flow the velocity profile will be closer to uniform and β will be close to 1 (~ ) and usually neglected. 4-22

23 Linear Momentum Exercises Exercise : A jet engine operates on a test stand with the shown inlet and exit conditions. Fuel-to-air mass ratio is 1/30. Calculate the horizontal force to be applied by the stand to hold the engine in its place. Assume that the fuel is injected in a vertical direction. Air Fuel Combustion products V in = 250 m s T in = 20 A in = 0.5 m 2 P in = 1 atm V out = 900 m s A out = 0.4 m 2 P out = 1 atm 4-23

24 Linear Momentum Exercises (cont d) Exercise : Consider the flow of a fluid inside a converging duct. Determine the anchoring force force required to hold the duct in its place by using a) a CV inside the duct b) a CV outside the duct Take the pressure at the nozzle exit to be atmospheric. 1 Chamber Nozzle ρ 1 p 1 A 1 V 1 2 ρ 2 p 2 = p atm A 2 V 2 p atm 4-24

25 Linear Momentum Exercises (cont d) Exercise : Water flow inside a constant diameter pipe develops from uniform profile to parabolic profile. Contact force between the water and the pipe wall is F z. Determine an expression for the pressure drop between the inlet and the exit. x u = U max 1 r2 R 2 g r L R u = U 4-25

26 Linear Momentum Exercises (cont d) Exercise : A circular cylinder is immersed in a steady, incompressible flow. Velocities at the upstream and downstream locations are measured and simplified as follows. Calculate the drag force acting on the cylinder using the two control volumes shown below. Assume constant pressure everywhere (which is a questionable assumption). U U U Streamline U D 4D? D 4D Streamline 4-26

27 Linear Momentum Exercises (cont d) Exercise : Water exiting a stationary nozzle strikes a flat plate as shown. Water leaves the nozzle as a circular jet at 15 m/s. Nozzle exit area is 0.01 m 2. After striking the plate water leaves the plate tangentially as a circular disk. Determine the horizontal component of the anchoring force at the support. Solve the problem using two different CVs as shown. Which one is easier to use? Plate Nozzle 4-27

28 Linear Momentum Exercises (cont d) Exercise : Water flows steadily through the 90 o reducing elbow. At the inlet to the elbow, the absolute pressure is 220 kpa and the cross sectional area is 0.01 m 2. At the outlet, cross sectional area is m 2 and the velocity is 16 m/s. The elbow discharges to the atmosphere. Determine the force required to hold the elbow in its place. 4-28

29 Linear Momentum Exercises (cont d) Exercise : The vane with a turning angle of 60 o moves at a constant speed of U = 10 m/s. It receives a jet of water that leaves a stationary nozzle with speed V = 30 m/s. The nozzle exit area is m 2. Area of the jet leaving the vane is the same as the jet leaving the nozzle. Determine the force components that act on the vane by the ground. Select a CV that moves with the cart, i.e. consider relative velocities at the inlet and the exit (Reference: Munson s book). V 60 o Nozzle U 4-29

30 Conservation of Angular Momentum Taking N = H and η = r V, RTT becomes dh sys dt = T = ρ( r V)d + ρ( r V) V n da t CV CS Sum of external torques acting on the CV Rate of change of angular momentum in the CV Rate of angular momentum exiting through the CS For a steady flow partial time derivative is zero. First term drops T = ρ( r V) V n da CS 4-30

31 Conservation of Angular Momentum Exercises Exercise : Underground water is pumped to the surface through a 10 cm diameter pipe that consists of a 2 m long vertical and 1 m long horizontal section. Water discharges to atmospheric air at an average velocity of 3 m/s. Mass of the horizontal pipe section when filled with water is 12 kg per meter length. The pipe is anchored on the ground by a concrete base. Determine a) the moment acting at the base of the pipe (point A) b) length of the horizontal section that would make the moment at point A zero. 1 m V = 3 m/s 2 m A Diameter : 10 cm 4-31

32 Conservation of Angular Momentum Exercises (cont d) Exercise : A large lawn sprinkler with four identical arms is to be converted into a turbine to generate electric power by attaching a generator to its rotating head. Water enters the sprinkler from the base along the axis of rotation at a rate of 20 L/s and leaves the nozzles in the tangential direction. The sprinkler rotates at 300 rpm in a horizontal plane. The diameter of each jet is 1 cm, and the normal distance between the axis of rotation and the center of each nozzle is 0.6 m. a) Calculate the torque transmitted to the shaft. b) Calculate the generated power. c) Plot a curve of generated power vs. rotation speed. Determine the maximum possible power generation and the speed at which it is obtained. (Reference: Cengel and Cimbala) 4-32

33 Conservation of Energy Taking N = E and η = e, RTT becomes de sys dt = Q + W = ρed + ρe V n da t CV CS Rate of heat transfer into the system and rate of work done on the system Rate of change of energy in the CV Rate of energy exiting through the CS Q > 0 if heat is added into the system. W > 0 if work is done on the system. Specific energy, e, includes internal, kinetic and potential energy terms e = u + V2 2 + gz 4-33

34 Conservation of Energy (cont d) Q + W = ρ u + V2 t CV 2 + gz d + ρ u + V2 CS 2 + gz V n da Most common forms of work in fluid systems are shear work : work done on the CS due to viscous stresses. Can be made negligibly small by a proper CV selection. shaft work : e.g. energy delivered to the fluid by a pump or energy extracted from the fluid by a turbine. flow work : energy necessary to push a certain amount of fluid into the CV or out of the CV. It depends on the pressure and velocity at an inlet or an exit. W f = A p V n da 4-34

35 Conservation of Energy (cont d) W f is treated separately from other types of work and it is added to the last integral of the energy equation. Q + W = ρ u + V2 t CV 2 + gz d + ρ u + p CS ρ + V2 2 + gz V n da Using the definition of enthaply h = u + p ρ energy equation becomes Q + W = ρ u + V2 t CV 2 + gz d + ρ h + V2 CS 2 + gz V n da W no longer includes flow work Flow work is accounted inside the enthalpy term 4-35

36 Conservation of Energy (cont d) For a steady, single inlet - single exit flow with uniform properties at inlet and exit sections exit m inlet z Datum for potential energy Q + W = m h + V2 2 + gz exit h + V2 2 + gz inlet Dividing both sides by the constant mass flow rate q + w = h + V2 2 + gz exit h + V2 2 + gz inlet 4-36

37 Conservation of Energy Exercises Exercise : A water pump is powered by a 15 kw electric motor whose efficiency is 90 %. Water flow rate through the pump is 50 L/s. Diameters of the inlet and outlet pipes are the same. Elevation difference across the pump is negligible. The pump is known to be working at 75 % efficiency. If the inlet pressure is measured as 100 kpa determine the exit pressure. Assume adiabatic conditions. 50 L/s p 2 =? η pump = 75 % η motor = 90 % 100 kpa 15 kw 4-37

38 Conservation of Energy Exercises (cont d) Exercise : A pump delivers water at a steady rate of 1150 L/min. Inlet and exit pipe diameters are 10 cm and 3 cm, respectively. Inlet and exit pressures are 130 kpa and 400 kpa, respectively. There is no significant elevation difference between the inlet and exit of the pump. The rise in internal energy of water, due to the temperature rise across the pump is 250 Nm/kg. Considering adiabatic pumping process determine the power delivered to the fluid by the pump. Pump W shaft =? 1150 L/min Inlet D 1 = 10 cm p 1 = 130 kpa Exit D 1 = 3 cm p 1 = 400 kpa u 2 u 1 = 250 Nm/kg 4-38

39 Conservation of Energy Exercises (cont d) Exercise : A steam turbine is used to produce electricity. Steam enters the turbine with a velocity of 30 m/s and enthalpy of 3500 kj/kg. The steam leaves the turbine as a mixture of vapor and liquid having a velocity of 60 m/s and enthalpy of 2300 kj/kg. Assuming adiabatic conditions and negligible elevation changes, determine the work output of the turbine per unit mass of fluid flowing. Turbine w shaft =? Inlet V 1 = 30 m/s h 1 = 3500 kj/kg Exit V 2 = 60 m/s h 1 = 2300 kj/kg 4-39

Sheet 5:Chapter 5 5 1C Name four physical quantities that are conserved and two quantities that are not conserved during a process.

Sheet 5:Chapter 5 5 1C Name four physical quantities that are conserved and two quantities that are not conserved during a process. Thermo 1 (MEP 261) Thermodynamics An Engineering Approach Yunus A. Cengel & Michael A. Boles 7 th Edition, McGraw-Hill Companies, ISBN-978-0-07-352932-5, 2008 Sheet 5:Chapter 5 5 1C Name four physical

More information

Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 20 Conservation Equations in Fluid Flow Part VIII Good morning. I welcome you all

More information

Mass and Energy Analysis of Control Volumes

Mass and Energy Analysis of Control Volumes MAE 320-Chapter 5 Mass and Energy Analysis of Control Volumes Objectives Develop the conservation of mass principle. Apply the conservation of mass principle to various systems including steady- and unsteady-flow

More information

Chapter 6 Energy Equation for a Control Volume

Chapter 6 Energy Equation for a Control Volume Chapter 6 Energy Equation for a Control Volume Conservation of Mass and the Control Volume Closed systems: The mass of the system remain constant during a process. Control volumes: Mass can cross the boundaries,

More information

Chapter 5 MASS, BERNOULLI AND ENERGY EQUATIONS

Chapter 5 MASS, BERNOULLI AND ENERGY EQUATIONS Fluid Mechanics: Fundamentals and Applications, 2nd Edition Yunus A. Cengel, John M. Cimbala McGraw-Hill, 2010 Chapter 5 MASS, BERNOULLI AND ENERGY EQUATIONS Lecture slides by Hasan Hacışevki Copyright

More information

h b b h Q u da u 1 1 dy dz u 1 dy 1 dz u b h b h

h b b h Q u da u 1 1 dy dz u 1 dy 1 dz u b h b h P3.18 An incompressible fluid flows steadily through the rectangular duct in the figure. The exit velocity profile is given by u umax(1 y /b )(1 z /h ). (a) Does this profile satisfy the correct boundary

More information

Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of

More information

Chapter 8: Flow in Pipes

Chapter 8: Flow in Pipes Objectives 1. Have a deeper understanding of laminar and turbulent flow in pipes and the analysis of fully developed flow 2. Calculate the major and minor losses associated with pipe flow in piping networks

More information

CO 2 41.2 MPa (abs) 20 C

CO 2 41.2 MPa (abs) 20 C comp_02 A CO 2 cartridge is used to propel a small rocket cart. Compressed CO 2, stored at a pressure of 41.2 MPa (abs) and a temperature of 20 C, is expanded through a smoothly contoured converging nozzle

More information

FLUID MECHANICS. TUTORIAL No.7 FLUID FORCES. When you have completed this tutorial you should be able to. Solve forces due to pressure difference.

FLUID MECHANICS. TUTORIAL No.7 FLUID FORCES. When you have completed this tutorial you should be able to. Solve forces due to pressure difference. FLUID MECHANICS TUTORIAL No.7 FLUID FORCES When you have completed this tutorial you should be able to Solve forces due to pressure difference. Solve problems due to momentum changes. Solve problems involving

More information

CH-205: Fluid Dynamics

CH-205: Fluid Dynamics CH-05: Fluid Dynamics nd Year, B.Tech. & Integrated Dual Degree (Chemical Engineering) Solutions of Mid Semester Examination Data Given: Density of water, ρ = 1000 kg/m 3, gravitational acceleration, g

More information

Fluent Software Training TRN Boundary Conditions. Fluent Inc. 2/20/01

Fluent Software Training TRN Boundary Conditions. Fluent Inc. 2/20/01 Boundary Conditions C1 Overview Inlet and Outlet Boundaries Velocity Outline Profiles Turbulence Parameters Pressure Boundaries and others... Wall, Symmetry, Periodic and Axis Boundaries Internal Cell

More information

Practice Problems on Conservation of Energy. heat loss of 50,000 kj/hr. house maintained at 22 C

Practice Problems on Conservation of Energy. heat loss of 50,000 kj/hr. house maintained at 22 C COE_10 A passive solar house that is losing heat to the outdoors at an average rate of 50,000 kj/hr is maintained at 22 C at all times during a winter night for 10 hr. The house is to be heated by 50 glass

More information

du u U 0 U dy y b 0 b

du u U 0 U dy y b 0 b BASIC CONCEPTS/DEFINITIONS OF FLUID MECHANICS (by Marios M. Fyrillas) 1. Density (πυκνότητα) Symbol: 3 Units of measure: kg / m Equation: m ( m mass, V volume) V. Pressure (πίεση) Alternative definition:

More information

These slides contain some notes, thoughts about what to study, and some practice problems. The answers to the problems are given in the last slide.

These slides contain some notes, thoughts about what to study, and some practice problems. The answers to the problems are given in the last slide. Fluid Mechanics FE Review Carrie (CJ) McClelland, P.E. cmcclell@mines.edu Fluid Mechanics FE Review These slides contain some notes, thoughts about what to study, and some practice problems. The answers

More information

Energy : ṁ (h i + ½V i 2 ) = ṁ(h e + ½V e 2 ) Due to high T take h from table A.7.1

Energy : ṁ (h i + ½V i 2 ) = ṁ(h e + ½V e 2 ) Due to high T take h from table A.7.1 6.33 In a jet engine a flow of air at 000 K, 00 kpa and 30 m/s enters a nozzle, as shown in Fig. P6.33, where the air exits at 850 K, 90 kpa. What is the exit velocity assuming no heat loss? C.V. nozzle.

More information

When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid.

When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Fluid Statics When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Consider a small wedge of fluid at rest of size Δx, Δz, Δs

More information

This chapter deals with three equations commonly used in fluid mechanics:

This chapter deals with three equations commonly used in fluid mechanics: MASS, BERNOULLI, AND ENERGY EQUATIONS CHAPTER 5 This chapter deals with three equations commonly used in fluid mechanics: the mass, Bernoulli, and energy equations. The mass equation is an expression of

More information

Practice Problems on Pumps. Answer(s): Q 2 = 1850 gpm H 2 = 41.7 ft W = 24.1 hp. C. Wassgren, Purdue University Page 1 of 16 Last Updated: 2010 Oct 29

Practice Problems on Pumps. Answer(s): Q 2 = 1850 gpm H 2 = 41.7 ft W = 24.1 hp. C. Wassgren, Purdue University Page 1 of 16 Last Updated: 2010 Oct 29 _02 A centrifugal with a 12 in. diameter impeller requires a power input of 60 hp when the flowrate is 3200 gpm against a 60 ft head. The impeller is changed to one with a 10 in. diameter. Determine the

More information

FIGURE P8 50E FIGURE P8 62. Minor Losses

FIGURE P8 50E FIGURE P8 62. Minor Losses 8 48 Glycerin at 40 C with r 1252 kg/m 3 and m 0.27 kg/m s is flowing through a 4-cm-diameter horizontal smooth pipe with an average velocity of 3.5 m/s. Determine the pressure drop per 10 m of the pipe.

More information

Applied Fluid Mechanics

Applied Fluid Mechanics Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 7. General Energy Equation

More information

CENTRIFUGAL PUMP OVERVIEW Presented by Matt Prosoli Of Pumps Plus Inc.

CENTRIFUGAL PUMP OVERVIEW Presented by Matt Prosoli Of Pumps Plus Inc. CENTRIFUGAL PUMP OVERVIEW Presented by Matt Prosoli Of Pumps Plus Inc. 1 Centrifugal Pump- Definition Centrifugal Pump can be defined as a mechanical device used to transfer liquid of various types. As

More information

Objective - Determining characteristic curve of a four-stroke Diesel engine - Calculating thermal efficiency of the engine

Objective - Determining characteristic curve of a four-stroke Diesel engine - Calculating thermal efficiency of the engine Objective - Determining characteristic curve of a four-stroke Diesel engine - Calculating thermal efficiency of the engine Apparatus The experimental setup, shown in Fig. 1, has three main parts: engine,

More information

oil liquid water water liquid Answer, Key Homework 2 David McIntyre 1

oil liquid water water liquid Answer, Key Homework 2 David McIntyre 1 Answer, Key Homework 2 David McIntyre 1 This print-out should have 14 questions, check that it is complete. Multiple-choice questions may continue on the next column or page: find all choices before making

More information

(b) 1. Look up c p for air in Table A.6. c p = 1004 J/kg K 2. Use equation (1) and given and looked up values to find s 2 s 1.

(b) 1. Look up c p for air in Table A.6. c p = 1004 J/kg K 2. Use equation (1) and given and looked up values to find s 2 s 1. Problem 1 Given: Air cooled where: T 1 = 858K, P 1 = P = 4.5 MPa gage, T = 15 o C = 88K Find: (a) Show process on a T-s diagram (b) Calculate change in specific entropy if air is an ideal gas (c) Evaluate

More information

20 m neon m propane 20

20 m neon m propane 20 Problems with solutions:. A -m 3 tank is filled with a gas at room temperature 0 C and pressure 00 Kpa. How much mass is there if the gas is a) Air b) Neon, or c) Propane? Given: T73K; P00KPa; M air 9;

More information

Applied Fluid Mechanics

Applied Fluid Mechanics Applied Fluid Mechanics Sixth Edition Robert L. Mott University of Dayton PEARSON Prentkv Pearson Education International CHAPTER 1 THE NATURE OF FLUIDS AND THE STUDY OF FLUID MECHANICS 1.1 The Big Picture

More information

ME 6404 THERMAL ENGINEERING. Part-B (16Marks questions)

ME 6404 THERMAL ENGINEERING. Part-B (16Marks questions) ME 6404 THERMAL ENGINEERING Part-B (16Marks questions) 1. Drive and expression for the air standard efficiency of Otto cycle in terms of volume ratio. (16) 2. Drive an expression for the air standard efficiency

More information

THERMODYNAMICS NOTES - BOOK 2 OF 2

THERMODYNAMICS NOTES - BOOK 2 OF 2 THERMODYNAMICS & FLUIDS (Thermodynamics level 1\Thermo & Fluids Module -Thermo Book 2-Contents-December 07.doc) UFMEQU-20-1 THERMODYNAMICS NOTES - BOOK 2 OF 2 Students must read through these notes and

More information

The First Law of Thermodynamics: Closed Systems. Heat Transfer

The First Law of Thermodynamics: Closed Systems. Heat Transfer The First Law of Thermodynamics: Closed Systems The first law of thermodynamics can be simply stated as follows: during an interaction between a system and its surroundings, the amount of energy gained

More information

INTRODUCTION TO FLUID MECHANICS

INTRODUCTION TO FLUID MECHANICS INTRODUCTION TO FLUID MECHANICS SIXTH EDITION ROBERT W. FOX Purdue University ALAN T. MCDONALD Purdue University PHILIP J. PRITCHARD Manhattan College JOHN WILEY & SONS, INC. CONTENTS CHAPTER 1 INTRODUCTION

More information

Practice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22

Practice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22 BL_01 A thin flat plate 55 by 110 cm is immersed in a 6 m/s stream of SAE 10 oil at 20 C. Compute the total skin friction drag if the stream is parallel to (a) the long side and (b) the short side. D =

More information

ME 305 Fluid Mechanics I. Part 8 Viscous Flow in Pipes and Ducts

ME 305 Fluid Mechanics I. Part 8 Viscous Flow in Pipes and Ducts ME 305 Fluid Mechanics I Part 8 Viscous Flow in Pipes and Ducts These presentations are prepared by Dr. Cüneyt Sert Mechanical Engineering Department Middle East Technical University Ankara, Turkey csert@metu.edu.tr

More information

Lecture 6 - Boundary Conditions. Applied Computational Fluid Dynamics

Lecture 6 - Boundary Conditions. Applied Computational Fluid Dynamics Lecture 6 - Boundary Conditions Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (2002-2006) Fluent Inc. (2002) 1 Outline Overview. Inlet and outlet boundaries.

More information

Fluids and Solids: Fundamentals

Fluids and Solids: Fundamentals Fluids and Solids: Fundamentals We normally recognize three states of matter: solid; liquid and gas. However, liquid and gas are both fluids: in contrast to solids they lack the ability to resist deformation.

More information

NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES

NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Vol. XX 2012 No. 4 28 34 J. ŠIMIČEK O. HUBOVÁ NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Jozef ŠIMIČEK email: jozef.simicek@stuba.sk Research field: Statics and Dynamics Fluids mechanics

More information

Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture No. # 36 Pipe Flow Systems

Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture No. # 36 Pipe Flow Systems Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture No. # 36 Pipe Flow Systems Welcome back to the video course on Fluid Mechanics. In today

More information

CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK PART - A

CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK PART - A CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK 3 0 0 3 UNIT I FLUID PROPERTIES AND FLUID STATICS PART - A 1. Define fluid and fluid mechanics. 2. Define real and ideal fluids. 3. Define mass density

More information

p atmospheric Statics : Pressure Hydrostatic Pressure: linear change in pressure with depth Measure depth, h, from free surface Pressure Head p gh

p atmospheric Statics : Pressure Hydrostatic Pressure: linear change in pressure with depth Measure depth, h, from free surface Pressure Head p gh IVE1400: n Introduction to Fluid Mechanics Statics : Pressure : Statics r P Sleigh: P..Sleigh@leeds.ac.uk r J Noakes:.J.Noakes@leeds.ac.uk January 008 Module web site: www.efm.leeds.ac.uk/ive/fluidslevel1

More information

Chapter 10. Flow Rate. Flow Rate. Flow Measurements. The velocity of the flow is described at any

Chapter 10. Flow Rate. Flow Rate. Flow Measurements. The velocity of the flow is described at any Chapter 10 Flow Measurements Material from Theory and Design for Mechanical Measurements; Figliola, Third Edition Flow Rate Flow rate can be expressed in terms of volume flow rate (volume/time) or mass

More information

Engineering Software P.O. Box 2134, Kensington, MD 20891 Phone: (301) 919-9670 Web Site:

Engineering Software P.O. Box 2134, Kensington, MD 20891 Phone: (301) 919-9670   Web Site: Engineering Software P.O. Box 2134, Kensington, MD 20891 Phone: (301) 919-9670 E-Mail: info@engineering-4e.com Web Site: http://www.engineering-4e.com Brayton Cycle (Gas Turbine) for Propulsion Application

More information

PHYSICS 111 HOMEWORK SOLUTION #9. April 5, 2013

PHYSICS 111 HOMEWORK SOLUTION #9. April 5, 2013 PHYSICS 111 HOMEWORK SOLUTION #9 April 5, 2013 0.1 A potter s wheel moves uniformly from rest to an angular speed of 0.16 rev/s in 33 s. Find its angular acceleration in radians per second per second.

More information

Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids

Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids Dr. J. M. Meyers Dr. D. G. Fletcher Dr. Y. Dubief 1. Introduction Last lab you investigated flow loss in a pipe due to the roughness

More information

Fundamentals of Fluid Mechanics

Fundamentals of Fluid Mechanics Sixth Edition. Fundamentals of Fluid Mechanics International Student Version BRUCE R. MUNSON DONALD F. YOUNG Department of Aerospace Engineering and Engineering Mechanics THEODORE H. OKIISHI Department

More information

XI / PHYSICS FLUIDS IN MOTION 11/PA

XI / PHYSICS FLUIDS IN MOTION 11/PA Viscosity It is the property of a liquid due to which it flows in the form of layers and each layer opposes the motion of its adjacent layer. Cause of viscosity Consider two neighboring liquid layers A

More information

Minor losses include head losses through/past hydrants, couplers, valves,

Minor losses include head losses through/past hydrants, couplers, valves, Lecture 10 Minor Losses & Pressure Requirements I. Minor Losses Minor (or fitting, or local ) hydraulic losses along pipes can often be estimated as a function of the velocity head of the water within

More information

Chapter 7 Energy and Energy Balances

Chapter 7 Energy and Energy Balances CBE14, Levicky Chapter 7 Energy and Energy Balances The concept of energy conservation as expressed by an energy balance equation is central to chemical engineering calculations. Similar to mass balances

More information

Experiment # 3: Pipe Flow

Experiment # 3: Pipe Flow ME 05 Mechanical Engineering Lab Page ME 05 Mechanical Engineering Laboratory Spring Quarter 00 Experiment # 3: Pipe Flow Objectives: a) Calibrate a pressure transducer and two different flowmeters (paddlewheel

More information

Civil Engineering Hydraulics Mechanics of Fluids. Flow in Pipes

Civil Engineering Hydraulics Mechanics of Fluids. Flow in Pipes Civil Engineering Hydraulics Mechanics of Fluids Flow in Pipes 2 Now we will move from the purely theoretical discussion of nondimensional parameters to a topic with a bit more that you can see and feel

More information

Experiment 3 Pipe Friction

Experiment 3 Pipe Friction EML 316L Experiment 3 Pipe Friction Laboratory Manual Mechanical and Materials Engineering Department College of Engineering FLORIDA INTERNATIONAL UNIVERSITY Nomenclature Symbol Description Unit A cross-sectional

More information

SOLUTION MANUAL SI UNIT PROBLEMS CHAPTER 9 SONNTAG BORGNAKKE VAN WYLEN. FUNDAMENTALS of. Thermodynamics. Sixth Edition

SOLUTION MANUAL SI UNIT PROBLEMS CHAPTER 9 SONNTAG BORGNAKKE VAN WYLEN. FUNDAMENTALS of. Thermodynamics. Sixth Edition SOLUTION MANUAL SI UNIT PROBLEMS CHAPTER 9 SONNTAG BORGNAKKE VAN WYLEN FUNDAMENTALS of Thermodynamics Sixth Edition CONTENT SUBSECTION PROB NO. Correspondence table Concept-Study Guide Problems -20 Steady

More information

5.2 Rotational Kinematics, Moment of Inertia

5.2 Rotational Kinematics, Moment of Inertia 5 ANGULAR MOTION 5.2 Rotational Kinematics, Moment of Inertia Name: 5.2 Rotational Kinematics, Moment of Inertia 5.2.1 Rotational Kinematics In (translational) kinematics, we started out with the position

More information

Macroscopic Balances for Nonisothermal Systems

Macroscopic Balances for Nonisothermal Systems Transport Phenomena Macroscopic Balances for Nonisothermal Systems 1 Macroscopic Balances for Nonisothermal Systems 1. The macroscopic energy balance 2. The macroscopic mechanical energy balance 3. Use

More information

Tank Draining Exercise

Tank Draining Exercise Tank Draining Exercise EAS 361, Fall 009 Before coming to the lab, read sections 1 through 5 of this document. Engineering of Everyday Things Gerald Recktenwald Portland State University gerry@me.pdx.edu

More information

is the stagnation (or total) pressure, constant along a streamline.

is the stagnation (or total) pressure, constant along a streamline. 70 Incompressible flow (page 60): Bernoulli s equation (steady, inviscid, incompressible): p 0 is the stagnation (or total) pressure, constant along a streamline. Pressure tapping in a wall parallel to

More information

EXPERIMENT NUMBER 7 PERFORMANCE TEST OF A CENTRIFUGAL PUMP

EXPERIMENT NUMBER 7 PERFORMANCE TEST OF A CENTRIFUGAL PUMP EXPERIMENT NUMBER 7 PERFORMANCE TEST OF A CENTRIFUGAL PUMP OBJECTIVE The primary objectives of this experiment is to measure the performance of a centrifugal pump and compare the results to the manufacturers

More information

Ch 6 Forces. Question: 9 Problems: 3, 5, 13, 23, 29, 31, 37, 41, 45, 47, 55, 79

Ch 6 Forces. Question: 9 Problems: 3, 5, 13, 23, 29, 31, 37, 41, 45, 47, 55, 79 Ch 6 Forces Question: 9 Problems: 3, 5, 13, 23, 29, 31, 37, 41, 45, 47, 55, 79 Friction When is friction present in ordinary life? - car brakes - driving around a turn - walking - rubbing your hands together

More information

Pumps: Convert mechanical energy (often developed from electrical source) into hydraulic energy (position, pressure and kinetic energy).

Pumps: Convert mechanical energy (often developed from electrical source) into hydraulic energy (position, pressure and kinetic energy). HYDRAULIC MACHINES Used to convert between hydraulic and mechanical energies. Pumps: Convert mechanical energy (often developed from electrical source) into hydraulic energy (position, pressure and kinetic

More information

Commercial CFD Software Modelling

Commercial CFD Software Modelling Commercial CFD Software Modelling Dr. Nor Azwadi bin Che Sidik Faculty of Mechanical Engineering Universiti Teknologi Malaysia INSPIRING CREATIVE AND INNOVATIVE MINDS 1 CFD Modeling CFD modeling can be

More information

Mercury is poured into a U-tube as in Figure (14.18a). The left arm of the tube has crosssectional

Mercury is poured into a U-tube as in Figure (14.18a). The left arm of the tube has crosssectional Chapter 14 Fluid Mechanics. Solutions of Selected Problems 14.1 Problem 14.18 (In the text book) Mercury is poured into a U-tube as in Figure (14.18a). The left arm of the tube has crosssectional area

More information

15. The Kinetic Theory of Gases

15. The Kinetic Theory of Gases 5. The Kinetic Theory of Gases Introduction and Summary Previously the ideal gas law was discussed from an experimental point of view. The relationship between pressure, density, and temperature was later

More information

State Newton's second law of motion for a particle, defining carefully each term used.

State Newton's second law of motion for a particle, defining carefully each term used. 5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding

More information

UNIVERSITY ESSAY QUESTIONS:

UNIVERSITY ESSAY QUESTIONS: UNIT I 1. What is a thermodynamic cycle? 2. What is meant by air standard cycle? 3. Name the various gas power cycles". 4. What are the assumptions made for air standard cycle analysis 5. Mention the various

More information

CE 3500 Fluid Mechanics / Fall 2014 / City College of New York

CE 3500 Fluid Mechanics / Fall 2014 / City College of New York 1 Drag Coefficient The force ( F ) of the wind blowing against a building is given by F=C D ρu 2 A/2, where U is the wind speed, ρ is density of the air, A the cross-sectional area of the building, and

More information

Introduction to COMSOL. The Navier-Stokes Equations

Introduction to COMSOL. The Navier-Stokes Equations Flow Between Parallel Plates Modified from the COMSOL ChE Library module rev 10/13/08 Modified by Robert P. Hesketh, Chemical Engineering, Rowan University Fall 2008 Introduction to COMSOL The following

More information

Chapter 10 Rotational Motion. Copyright 2009 Pearson Education, Inc.

Chapter 10 Rotational Motion. Copyright 2009 Pearson Education, Inc. Chapter 10 Rotational Motion Angular Quantities Units of Chapter 10 Vector Nature of Angular Quantities Constant Angular Acceleration Torque Rotational Dynamics; Torque and Rotational Inertia Solving Problems

More information

For Water to Move a driving force is needed

For Water to Move a driving force is needed RECALL FIRST CLASS: Q K Head Difference Area Distance between Heads Q 0.01 cm 0.19 m 6cm 0.75cm 1 liter 86400sec 1.17 liter ~ 1 liter sec 0.63 m 1000cm 3 day day day constant head 0.4 m 0.1 m FINE SAND

More information

Theory of turbo machinery / Turbomaskinernas teori. Chapter 4

Theory of turbo machinery / Turbomaskinernas teori. Chapter 4 Theory of turbo machinery / Turbomaskinernas teori Chapter 4 Note direction of α 2 FIG. 4.1. Turbine stage velocity diagrams. Assumptions: Hub to tip ratio high (close to 1) Negligible radial velocities

More information

COMPUTATIONAL FLUID DYNAMICS (CFD) ANALYSIS OF INTERMEDIATE PRESSURE STEAM TURBINE

COMPUTATIONAL FLUID DYNAMICS (CFD) ANALYSIS OF INTERMEDIATE PRESSURE STEAM TURBINE Research Paper ISSN 2278 0149 www.ijmerr.com Vol. 3, No. 4, October, 2014 2014 IJMERR. All Rights Reserved COMPUTATIONAL FLUID DYNAMICS (CFD) ANALYSIS OF INTERMEDIATE PRESSURE STEAM TURBINE Shivakumar

More information

Higher Technological Institute Civil Engineering Department. Lectures of. Fluid Mechanics. Dr. Amir M. Mobasher

Higher Technological Institute Civil Engineering Department. Lectures of. Fluid Mechanics. Dr. Amir M. Mobasher Higher Technological Institute Civil Engineering Department Lectures of Fluid Mechanics Dr. Amir M. Mobasher 1/14/2013 Fluid Mechanics Dr. Amir Mobasher Department of Civil Engineering Faculty of Engineering

More information

Compressor and turbines

Compressor and turbines Compressor and turbines In this chapter, we will look at the compressor and the turbine. They are both turbomachinery: machines that transfer energy from a rotor to a fluid, or the other way around. The

More information

CHE 253M Experiment No. 3 LIQUID FLOW MEASUREMENT

CHE 253M Experiment No. 3 LIQUID FLOW MEASUREMENT Rev 8/15 AW/GW CHE 253M Experiment No. 3 LIQUID FLOW MEASUREMENT The objective of this experiment is to familiarize the student with several types of flow-measuring devices commonly used in the laboratory

More information

Introduction to basic principles of fluid mechanics

Introduction to basic principles of fluid mechanics 2.016 Hydrodynamics Prof. A.H. Techet Introduction to basic principles of fluid mechanics I. Flow Descriptions 1. Lagrangian (following the particle): In rigid body mechanics the motion of a body is described

More information

SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS

SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS This work covers elements of the syllabus for the Engineering Council exams C105 Mechanical and Structural Engineering

More information

Rotation: Moment of Inertia and Torque

Rotation: Moment of Inertia and Torque Rotation: Moment of Inertia and Torque Every time we push a door open or tighten a bolt using a wrench, we apply a force that results in a rotational motion about a fixed axis. Through experience we learn

More information

Physics 200A FINALS Shankar 180mins December 13, 2005 Formulas and figures at the end. Do problems in 4 books as indicated

Physics 200A FINALS Shankar 180mins December 13, 2005 Formulas and figures at the end. Do problems in 4 books as indicated 1 Physics 200A FINALS Shankar 180mins December 13, 2005 Formulas and figures at the end. Do problems in 4 books as indicated I. Book I A camper is trying to boil water. The 55 g aluminum pan has specific

More information

Module 3. First law of thermodynamics

Module 3. First law of thermodynamics Module 3 First law of thermodynamics First Law of Thermodynamics Statement: When a closed system executes a complete cycle the sum of heat 1 B interactions is equal to the sum of work interactions. Y A

More information

Solution: (a) 1. Look up properties for air, Table A.6: k = 1.4, R = 287 J/kg K, c p = 1004 J/kgK 2. Calculate ρ. using the ideal gas equation:

Solution: (a) 1. Look up properties for air, Table A.6: k = 1.4, R = 287 J/kg K, c p = 1004 J/kgK 2. Calculate ρ. using the ideal gas equation: Problem Given: Air entering a combustion chamber with: 0., T 580 K, and.0 Pa (abs). Heat addition, then 0.4, T 77 K, and 86.7 Find: (a) Local isentroic stagnation conditions at the inlet (b) Local isentroic

More information

Laboratory Experience with a Model Jet Turbine

Laboratory Experience with a Model Jet Turbine Session 2166 Laboratory Experience with a Model Jet Turbine John E. Matsson Oral Roberts University Abstract This paper describes the experience gained from the operation of a JetCat model turbojet engine

More information

Physics 1114: Unit 6 Homework: Answers

Physics 1114: Unit 6 Homework: Answers Physics 1114: Unit 6 Homework: Answers Problem set 1 1. A rod 4.2 m long and 0.50 cm 2 in cross-sectional area is stretched 0.20 cm under a tension of 12,000 N. a) The stress is the Force (1.2 10 4 N)

More information

Fall 12 PHY 122 Homework Solutions #8

Fall 12 PHY 122 Homework Solutions #8 Fall 12 PHY 122 Homework Solutions #8 Chapter 27 Problem 22 An electron moves with velocity v= (7.0i - 6.0j)10 4 m/s in a magnetic field B= (-0.80i + 0.60j)T. Determine the magnitude and direction of the

More information

Chapter 28 Fluid Dynamics

Chapter 28 Fluid Dynamics Chapter 28 Fluid Dynamics 28.1 Ideal Fluids... 1 28.2 Velocity Vector Field... 1 28.3 Mass Continuity Equation... 3 28.4 Bernoulli s Principle... 4 28.5 Worked Examples: Bernoulli s Equation... 7 Example

More information

CBE 6333, R. Levicky 1 Differential Balance Equations

CBE 6333, R. Levicky 1 Differential Balance Equations CBE 6333, R. Levicky 1 Differential Balance Equations We have previously derived integral balances for mass, momentum, and energy for a control volume. The control volume was assumed to be some large object,

More information

Homework 4. problems: 5.61, 5.67, 6.63, 13.21

Homework 4. problems: 5.61, 5.67, 6.63, 13.21 Homework 4 problems: 5.6, 5.67, 6.6,. Problem 5.6 An object of mass M is held in place by an applied force F. and a pulley system as shown in the figure. he pulleys are massless and frictionless. Find

More information

Unit 24: Applications of Pneumatics and Hydraulics

Unit 24: Applications of Pneumatics and Hydraulics Unit 24: Applications of Pneumatics and Hydraulics Unit code: J/601/1496 QCF level: 4 Credit value: 15 OUTCOME 2 TUTORIAL 3 HYDRAULIC AND PNEUMATIC MOTORS The material needed for outcome 2 is very extensive

More information

Lecture 3 Fluid Dynamics and Balance Equa6ons for Reac6ng Flows

Lecture 3 Fluid Dynamics and Balance Equa6ons for Reac6ng Flows Lecture 3 Fluid Dynamics and Balance Equa6ons for Reac6ng Flows 3.- 1 Basics: equations of continuum mechanics - balance equations for mass and momentum - balance equations for the energy and the chemical

More information

Unit 4 Practice Test: Rotational Motion

Unit 4 Practice Test: Rotational Motion Unit 4 Practice Test: Rotational Motion Multiple Guess Identify the letter of the choice that best completes the statement or answers the question. 1. How would an angle in radians be converted to an angle

More information

OUTCOME 2 KINEMATICS AND DYNAMICS TUTORIAL 2 PLANE MECHANISMS. You should judge your progress by completing the self assessment exercises.

OUTCOME 2 KINEMATICS AND DYNAMICS TUTORIAL 2 PLANE MECHANISMS. You should judge your progress by completing the self assessment exercises. Unit 60: Dynamics of Machines Unit code: H/601/1411 QCF Level:4 Credit value:15 OUTCOME 2 KINEMATICS AND DYNAMICS TUTORIAL 2 PLANE MECHANISMS 2 Be able to determine the kinetic and dynamic parameters of

More information

Abaqus/CFD Sample Problems. Abaqus 6.10

Abaqus/CFD Sample Problems. Abaqus 6.10 Abaqus/CFD Sample Problems Abaqus 6.10 Contents 1. Oscillatory Laminar Plane Poiseuille Flow 2. Flow in Shear Driven Cavities 3. Buoyancy Driven Flow in Cavities 4. Turbulent Flow in a Rectangular Channel

More information

Chapter 13 OPEN-CHANNEL FLOW

Chapter 13 OPEN-CHANNEL FLOW Fluid Mechanics: Fundamentals and Applications, 2nd Edition Yunus A. Cengel, John M. Cimbala McGraw-Hill, 2010 Lecture slides by Mehmet Kanoglu Copyright The McGraw-Hill Companies, Inc. Permission required

More information

JET ENGINE PERFORMANCE. Charles Robert O Neill. School of Mechanical and Aerospace Engineering. Oklahoma State University. Stillwater, OK 74078

JET ENGINE PERFORMANCE. Charles Robert O Neill. School of Mechanical and Aerospace Engineering. Oklahoma State University. Stillwater, OK 74078 JET ENGINE PERFORMANCE Charles Robert O Neill School of Mechanical and Aerospace Engineering Oklahoma State University Stillwater, OK 74078 Honors Project in ENGSC 3233 Fluid Mechanics December 1998 JET

More information

Lab 7: Rotational Motion

Lab 7: Rotational Motion Lab 7: Rotational Motion Equipment: DataStudio, rotary motion sensor mounted on 80 cm rod and heavy duty bench clamp (PASCO ME-9472), string with loop at one end and small white bead at the other end (125

More information

Unit 24: Applications of Pneumatics and Hydraulics

Unit 24: Applications of Pneumatics and Hydraulics Unit 24: Applications of Pneumatics and Hydraulics Unit code: J/601/1496 QCF level: 4 Credit value: 15 OUTCOME 2 TUTORIAL 1 HYDRAULIC PUMPS The material needed for outcome 2 is very extensive so there

More information

charge is detonated, causing the smaller glider with mass M, to move off to the right at 5 m/s. What is the

charge is detonated, causing the smaller glider with mass M, to move off to the right at 5 m/s. What is the This test covers momentum, impulse, conservation of momentum, elastic collisions, inelastic collisions, perfectly inelastic collisions, 2-D collisions, and center-of-mass, with some problems requiring

More information

Chapter 17. For the most part, we have limited our consideration so COMPRESSIBLE FLOW. Objectives

Chapter 17. For the most part, we have limited our consideration so COMPRESSIBLE FLOW. Objectives Chapter 17 COMPRESSIBLE FLOW For the most part, we have limited our consideration so far to flows for which density variations and thus compressibility effects are negligible. In this chapter we lift this

More information

Engineering Problem Solving as Model Building

Engineering Problem Solving as Model Building Engineering Problem Solving as Model Building Part 1. How professors think about problem solving. Part 2. Mech2 and Brain-Full Crisis Part 1 How experts think about problem solving When we solve a problem

More information

1. A belt pulley is 3 ft. in diameter and rotates at 250 rpm. The belt which is 5 ins. wide makes an angle of contact of 190 over the pulley.

1. A belt pulley is 3 ft. in diameter and rotates at 250 rpm. The belt which is 5 ins. wide makes an angle of contact of 190 over the pulley. Sample Questions REVISED FIRST CLASS PARTS A1, A2, AND A3 (NOTE: these questions are intended as representations of the style of questions that may appear on examinations. They are not intended as study

More information

Tennessee State University

Tennessee State University Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an F-grade. Other instructions will be given in the Hall. MULTIPLE CHOICE.

More information

Physics 1653 Exam 3 - Review Questions

Physics 1653 Exam 3 - Review Questions Physics 1653 Exam 3 - Review Questions 3.0 Two uncharged conducting spheres, A and B, are suspended from insulating threads so that they touch each other. While a negatively charged rod is held near, but

More information

Experiment (13): Flow channel

Experiment (13): Flow channel Introduction: An open channel is a duct in which the liquid flows with a free surface exposed to atmospheric pressure. Along the length of the duct, the pressure at the surface is therefore constant and

More information