FLUID MECHANICS FUNDAMENTALS+APPS
4th Edition
ISBN: 2810022150991
Author: CENGEL
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 4, Problem 92P
Consider the general form of the Reynolds transport theorem (RTT) given by
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A Newtonian fluid flows in the annular space created by a concentric pipe and rod moving to the
right at a constant velocity V (this could be the configuration of a wire coating process). The
flow is the result of the shear stress created by the moving rod. The flow is steady and
incompressible. Assume u, is only a function of r, both u, and ue (as well as their derivatives)
are zero, the pipe is horizontal, and the pressure gradient in the z direction is constant. Derive
an expression for the velocity profile uz as a function of r. Note: R, is the inside radius of the
outer pipe and R; is the radius of the moving rod.
R.
R;
V
9- V(D1)^2=V1(D2)^2 mass
10 points
continuity equation
O true
O False
10-stream line is a line giving 10 points
direction of velocity at any
point.
O True
O False
In plane stagnation flow, an incompressible fluid occupying the space y>0 has one
velocity component given by Vx-x. The flow is two-dimensional and steady, such that
V₂=0 and nothing depends on z or time t.
(a)
Use the continuity equation to determine Vy(x,y), given that Vy(x,0) =0.
(This condition for Vy corresponds to the plane y=0 being an impenetrable boundary.)
(b)
is arbitrary, so you may set Y=0 at any convenient location.)
Determine the stream function for this flow, (x,y). (The absolute value of
Chapter 4 Solutions
FLUID MECHANICS FUNDAMENTALS+APPS
Ch. 4 - What does the word kinematics mean? Explain what...Ch. 4 - Briefly discuss the difference between derivative...Ch. 4 - Consider the following steady, two-dimensional...Ch. 4 - Consider the following steady, two-dimensional...Ch. 4 - -5 A steady, two-dimensional velocity field is...Ch. 4 - Consider steady flow of water through an...Ch. 4 - What is the Eulerian description of fluid motion?...Ch. 4 - Is the Lagrangian method of fluid flow analysis...Ch. 4 - A stationary probe is placed in a fluid flow and...Ch. 4 - A tiny neutrally buoyant electronic pressure probe...
Ch. 4 - Define a steady flow field in the Eulerian...Ch. 4 - Is the Eulerian method of fluid flow analysis more...Ch. 4 - A weather balloon is hunched into the atmosphere...Ch. 4 - A Pilot-stalk probe can often be seen protruding...Ch. 4 - List at least three oiler names for the material...Ch. 4 - Consider steady, incompressible, two-dimensional...Ch. 4 - Converging duct flow is modeled by the steady,...Ch. 4 - A steady, incompressible, two-dimensional velocity...Ch. 4 - A steady, incompressible, two-dimensional velocity...Ch. 4 - For the velocity field of Prob. 4-6, calculate the...Ch. 4 - Consider steady flow of air through the diffuser...Ch. 4 - For the velocity field of Prob. 4-21, calculate...Ch. 4 - A steady, incompressible, two-dimensional (in the...Ch. 4 - The velocity field for a flow is given by...Ch. 4 - Prob. 25CPCh. 4 - What is the definition of a timeline? How can...Ch. 4 - What is the definition of a streamline? What do...Ch. 4 - Prob. 28CPCh. 4 - Consider the visualization of flow over a 15°...Ch. 4 - Consider the visualization of ground vortex flow...Ch. 4 - Consider the visualization of flow over a sphere...Ch. 4 - Prob. 32CPCh. 4 - Consider a cross-sectional slice through an array...Ch. 4 - A bird is flying in a room with a velocity field...Ch. 4 - Conversing duct flow is modeled by the steady,...Ch. 4 - The velocity field of a flow is described by...Ch. 4 - Consider the following steady, incompressible,...Ch. 4 - Consider the steady, incompressible,...Ch. 4 - A steady, incompressible, two-dimensional velocity...Ch. 4 - Prob. 41PCh. 4 - Prob. 42PCh. 4 - The velocity field for a line some in the r plane...Ch. 4 - A very small circular cylinder of radius Rtis...Ch. 4 - Consider the same two concentric cylinders of...Ch. 4 - The velocity held for a line vartex in the r...Ch. 4 - Prob. 47PCh. 4 - Name and briefly describe the four fundamental...Ch. 4 - Prob. 49CPCh. 4 - Prob. 50PCh. 4 - Prob. 51PCh. 4 - Prob. 52PCh. 4 - Prob. 53PCh. 4 - Converging duct flow is modeled by the steady,...Ch. 4 - Converging duct flow is modeled by the steady,...Ch. 4 - Using the results of Prob. 4—57 and the...Ch. 4 - Converging duct flow (Fig. P4—16) is modeled by...Ch. 4 - Prob. 60PCh. 4 - For the velocity field of Prob. 4—60, what...Ch. 4 - For the velocity field of Prob. 4—60, calculate...Ch. 4 - For the velocity field of Prob. 4—60, calculate...Ch. 4 - Prob. 64PCh. 4 - Prob. 65PCh. 4 - Consider steady, incompressible, two-dimensional...Ch. 4 - Prob. 67PCh. 4 - Consider the steady, incompressible,...Ch. 4 - Prob. 69PCh. 4 - Prob. 70PCh. 4 - Prob. 71PCh. 4 - Prob. 72PCh. 4 - Prob. 73PCh. 4 - A cylindrical lank of water rotates in solid-body...Ch. 4 - Prob. 75PCh. 4 - A cylindrical tank of radius rrim= 0.354 m rotates...Ch. 4 - Prob. 77PCh. 4 - Prob. 78PCh. 4 - Prob. 79PCh. 4 - For the Couette flow of Fig. P4—79, calculate the...Ch. 4 - Combine your results from Prob. 4—80 to form the...Ch. 4 - Consider a steady, two-dimensional, incompressible...Ch. 4 - A steady, three-dimensional velocity field is...Ch. 4 - Consider the following steady, three-dimensional...Ch. 4 - Prob. 85PCh. 4 - A steady, three-dimensional velocity field is...Ch. 4 - Briefly explain the purpose of the Reynolds...Ch. 4 - Prob. 88CPCh. 4 - True or false: For each statement, choose whether...Ch. 4 - Consider the integral ddtt2tx2. Solve it two ways:...Ch. 4 - Prob. 91PCh. 4 - Consider the general form of the Reynolds...Ch. 4 - Consider the general form of the Reynolds...Ch. 4 - Prob. 94PCh. 4 - Prob. 95PCh. 4 - Prob. 96PCh. 4 - Prob. 97PCh. 4 - The velocity field for an incompressible flow is...Ch. 4 - Consider fully developed two-dimensional...Ch. 4 - For the two-dimensional Poiseuille flow of Prob....Ch. 4 - Combine your results from Prob. 4—100 to form the...Ch. 4 - Prob. 103PCh. 4 - Prob. 107PCh. 4 - Prob. 108PCh. 4 - Prob. 109PCh. 4 - Prob. 110PCh. 4 - Prob. 112PCh. 4 - Prob. 113PCh. 4 - Prob. 114PCh. 4 - Prob. 116PCh. 4 - Based on your results of Prob. 4—116, discuss the...Ch. 4 - Prob. 118PCh. 4 - In a steady, two-dimensional flow field in the...Ch. 4 - A steady, two-dimensional velocity field in the...Ch. 4 - A velocity field is given by u=5y2,v=3x,w=0 . (Do...Ch. 4 - The actual path traveled by an individual fluid...Ch. 4 - Prob. 123PCh. 4 - Prob. 124PCh. 4 - Prob. 125PCh. 4 - Water is flowing in a 3-cm-diameter garden hose at...Ch. 4 - Prob. 127PCh. 4 - Prob. 128PCh. 4 - Prob. 129PCh. 4 - Prob. 130PCh. 4 - Prob. 131PCh. 4 - An array of arrows indicating the magnitude and...Ch. 4 - Prob. 133PCh. 4 - Prob. 134PCh. 4 - Prob. 135PCh. 4 - A steady, two-dimensional velocity field is given...Ch. 4 - Prob. 137PCh. 4 - Prob. 138PCh. 4 - Prob. 139PCh. 4 - Prob. 140PCh. 4 - Prob. 141P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Consider the general form of the Reynolds transport theorem (RTT) given by dBsys / dt = d/dt ∫CV ρb dV +∫CS ρbV-› r·n-› dAwhere V-›r is the velocity of the fluid relative to the control surface. Let Bsys be the mass m of a closed system of fluid particles. We know that for a system, dm/dt = 0 since no mass can enter or leave the system by definition. Use the given equation to derive the equation of conservation of mass for a control volume.arrow_forwardA stream function is given by = 4x – 3y. The resultant velocity at any point isarrow_forwardYou are given the velocity profile within a thin layer of liquid, draining from an inclined plane as vx = v0 (ay/h − y2/h2), where v0 is the surface velocity and a is a constant that needs to be determined. The height of the liquid film h = 2 cm and the flow rate is 1.8liters/minute. The plane has width 10 cm into the paper.(i). Determine the constant a by applying a suitable boundary condition at y = h.arrow_forward
- b) A Newtonian fluid flows in an annular space created by a concentric pipe of radius R, and a rod of radius R;, as shown in Figure Q1(b). The rod is moving at a constant velocity V, while the pipe is stationary. The flow is steady, laminar and incompressible and there is no forced pressure gradient driving the flow. Assuming the velocity components in the radial and tangential directions are zero and ignoring the effects of gravity, derive an expression for the velocity field in the annular space. R. R: Figure Q1(b)arrow_forwardA fixed control volume has three one-dimensional boundary sections, as shown. The flow within the control volume is steady. The flow properties at each section are tabulated below. Find the rate of change of energy of the system which occupies the control volume at this instant. Section Туре P. kg/m V, m/s A, m? e, J/kg 1 Inlet 800 5.0 2.0 300 Inlet 800 8.0 3.0 100 3 Outlet 800 17.0 2.0 150 CVarrow_forwardThe flow between two horizontal infinite parallel plates is a two-dimension, steady-state, incompressible and fully- developed flow. The distance between the plates is h m. The bottom plate is stationary and the top plate velocity is U. m/s in the x-direction. The flow is driven by the top moving plate and there is, therefore, no pressure gradient in the direction of the flow. Velocity in the y-direction, v = 0. Note: Align the x-axis to the bottom wall. Use the x-momentum equation to show that the velocity profile equation is (a) u(y) = ay + b and find the values of a and b. Use the energy equation to derive the temperature distribution T(y) for the flow if the surface temperature and temperature gradient on the bottom plate are both zero. (b)arrow_forward
- Fluid Dynamics questionarrow_forward3. A circular cylinder of radius a is fitted with two pressure sensors to measure pressure at 0 = 180° and at 150°. The intent is to use this cylinder as a stream velocimeter, i.e. a device to determine the velocity of a stream by measuring the pressures at the two taps. The fluid is incompressible with a density of p. Figure for Part (a) U Figure for Part (b) 30 a) Using potential flow approximation, derive a formula for calculating U from the measured pressure difference at the two pressure taps. Note that for accurate measurement, the velocimeter must be aligned to have one of the taps exactly facing the stream as shown in the figure. (Ans: 2|Aptaps|/p ) b) Suppose the velocimeter has been misaligned by ổ degrees so that the two pressure taps are now at 180° + 8 and 150° + 8. Derive an expression for the percent error in stream velocity measurement. Then, calculate the error for 8 = 5°,10° and –10°. (Ans: [2/(sin2(150 + 8) – sin²(180 + 8) )– 1] × 100 )arrow_forwardnavier stokesarrow_forward
- An incompressible Newtonian fluid having a thickness of h, flows steadily in the x- direction along a fixed wall of infinite extent by the influence of the gravitational force (g=9.81 m/s²). There is no pressure change in the flow direction and air friction is negligible. Using the given parameter values; a determine the velocity function, b. calculate the shear stress that will occur along the wall. Z fixed wall air h 0 16.0 ↓arrow_forwardOne of the oldest equations in fluid mechanics deals with the flow of a liquid from a large reservoir. Using the Bernoulli equation along the streamline, (a) find out the velocity in m/s at the exit (location (2)) when h = 20 m and (b) find out the velocity in m/s at the location (5) for H = 4 m. Here the gravitational acceleration (g) can be approximated to be 10 m/s². h 147 H d (5) • (1) (3) (2) (4)arrow_forwardQ2/ Suppose you have crude oil flows through an annulus between two horizontal pipes with the same center, if the velocity distribution v, and the average velocity Vavg are expressed by: ΔΡ Rr²+ R² In (R₂/R₁) (¹) In 4μL ΔΡ Vavg = R₁ + R₂ R - R In (R₂/R₁ 8µL Where AP: is the pressure drop through the annulus, μ: is the fluid viscosity, L: is the pipe length, R₁ and R₂: are the inside radius of inner and outer pipes, respectively. Write a program in a script file that calculates the velocity distribution and the average velocity. When the script file is executed, it requests the user to input AP, μ, L, R₁ and R₂ where r has many values between R₁ and R₂. The program displays the inputted values and the calculated average velocity (using fprintf) followed by a table with the values r in the first column and the corresponding values of the velocity distribution in the second column.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Introduction to Kinematics; Author: LearnChemE;https://www.youtube.com/watch?v=bV0XPz-mg2s;License: Standard youtube license