Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 9, Problem 22P
Repeat Example 9-1(gas compressed in a cylinder by a piston), but without using the continuity equation. Instead, consider the fundamental definition as mass divided by volume. Verify that Eq.5 of Example 9-1 is correct.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Engine oil at 60°C rotates as a rigid body about the z-axis in a spinning cylindrical container. There are no viscous stresses since the water moves as a solid body; thus the Euler equation is appropriate. (We neglect viscous stresses caused by air acting on the water surface.) Integrate the Euler equation to generate an expression for pressure as a function of r and z everywhere in the water. Write an equation for the shape of the free surface (zsurface as a function of r). (Hint: P = Patm everywhere on the free surface. The flow is rotationally symmetric about the z-axis.)
1. For a soap bubble, the inside pressure must be greater than that outside, and the surface tension acts
like a skin to support this pressure difference Ap. The pressure difference is then a function of surface
tension σ and bubble radius R, i.e., Ap = f(o, R). Using Buckingham Pi theorem, find the II group(s)
associated with this problem and express them in the form II₁ = (II2, ..., II-r). (Ans: ApR = constant)
σ
(b)
One form of fluid movement is rotation and deform angularly.
Figure Q1(b) shows the rotation and angular deformation caused by
velocity variation about z-axis. Based on Table 1 and setting given to you,
derive an equation of rotation.
ди
Sy St
ây
> B'
ĉu
B
B
ôy
dy
A'
↑ Sa
v+.
ôx
A
ôx
Figure Q1(b) : Rotation and Angular Deformation
Table 1: Axis of Rotation
Setting
Axis of Rotation
2
у-ахis
Chapter 9 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 9 - Explain the fundamental differences between a flow...Ch. 9 - What does it mean when we say that two more...Ch. 9 - The divergence theorem is v.cdv=A c . n dACh. 9 - Prob. 4CPCh. 9 - Prob. 5CPCh. 9 - Prob. 6CPCh. 9 - Prob. 7PCh. 9 - Prob. 8PCh. 9 - Let vector G=2xzi12x2jz2kk . Calculate the...Ch. 9 - Prob. 10P
Ch. 9 - Prob. 11PCh. 9 - Prob. 12PCh. 9 - Prob. 13PCh. 9 - Alex is measuring the time-averaged velocity...Ch. 9 - Let vector c be given G=4xziy2i+yzkand let V be...Ch. 9 - The product rule can be applied to the divergence...Ch. 9 - Prob. 18PCh. 9 - Prob. 19PCh. 9 - Prob. 20CPCh. 9 - In this chapter we derive the continuity equation...Ch. 9 - Repeat Example 9-1(gas compressed in a cylinder by...Ch. 9 - Consider the steady, two-dimensional velocity...Ch. 9 - The compressible from of the continuity equation...Ch. 9 - In Example 9-6 we derive the equation for...Ch. 9 - Consider a spiraling line vortex/sink flow in the...Ch. 9 - Verify that the steady; two-dimensional,...Ch. 9 - Consider steady flow of water through an...Ch. 9 - Consider the following steady, three-dimensional...Ch. 9 - Consider the following steady, three-dimensional...Ch. 9 - Two velocity components of a steady,...Ch. 9 - Imagine a steady, two-dimensional, incompressible...Ch. 9 - The u velocity component of a steady,...Ch. 9 - Imagine a steady, two-dimensional, incompressible...Ch. 9 - The u velocity component of a steady,...Ch. 9 - What is significant about curves of constant...Ch. 9 - In CFD lingo, the stream function is often called...Ch. 9 - Prob. 39CPCh. 9 - Prob. 40CPCh. 9 - Prob. 41PCh. 9 - Prob. 42PCh. 9 - Prob. 44PCh. 9 - Prob. 45PCh. 9 - As a follow-up to Prob. 9-45, calculate the volume...Ch. 9 - Consider the Couette flow of Fig.9-45. For the...Ch. 9 - Prob. 48PCh. 9 - AS a follow-up to Prob. 9-48, calculate the volume...Ch. 9 - Consider the channel flow of Fig. 9-45. The fluid...Ch. 9 - In the field of air pollution control, one often...Ch. 9 - Suppose the suction applied to the sampling...Ch. 9 - Prob. 53PCh. 9 - Flow separates at a shap corner along a wall and...Ch. 9 - Prob. 55PCh. 9 - Prob. 56PCh. 9 - Prob. 58PCh. 9 - Prob. 59PCh. 9 - Prob. 60PCh. 9 - Prob. 61PCh. 9 - Prob. 62PCh. 9 - Prob. 63EPCh. 9 - Prob. 64PCh. 9 - Prob. 65EPCh. 9 - Prob. 66PCh. 9 - Prob. 68EPCh. 9 - Prob. 69PCh. 9 - Prob. 71PCh. 9 - Prob. 72PCh. 9 - Prob. 73PCh. 9 - Prob. 74PCh. 9 - Prob. 75PCh. 9 - Wht in the main distionction between Newtormine...Ch. 9 - Prob. 77CPCh. 9 - What are constitutive equations, and to the fluid...Ch. 9 - An airplane flies at constant velocity Vairplane...Ch. 9 - Define or describe each type of fluid: (a)...Ch. 9 - The general cool volume from of linearmomentum...Ch. 9 - Consider the steady, two-dimensional,...Ch. 9 - Consider the following steady, two-dimensional,...Ch. 9 - Consider the following steady, two-dimensional,...Ch. 9 - Consider liquid in a cylindrical tank. Both the...Ch. 9 - Engine oil at T=60C is forced to flow between two...Ch. 9 - Consider steady, two-dimensional, incompressible...Ch. 9 - Consider steady, incompressible, parallel, laminar...Ch. 9 - Prob. 89PCh. 9 - Prob. 90PCh. 9 - Prob. 91PCh. 9 - The first viscous terms in -comonent of the...Ch. 9 - An incompressible Newtonian liquid is confined...Ch. 9 - Prob. 94PCh. 9 - Prob. 95PCh. 9 - Prob. 96PCh. 9 - Prob. 97PCh. 9 - Consider steady, incompressible, laminar flow of a...Ch. 9 - Consider again the pipe annulus sketched in Fig...Ch. 9 - Repeat Prob. 9-99 except swap the stationary and...Ch. 9 - Consider a modified form of Couette flow in which...Ch. 9 - Consider dimensionless velocity distribution in...Ch. 9 - Consider steady, incompressible, laminar flow of a...Ch. 9 - Prob. 104PCh. 9 - Prob. 105PCh. 9 - Prob. 106PCh. 9 - Prob. 107CPCh. 9 - Prob. 108CPCh. 9 - Discuss the relationship between volumetric strain...Ch. 9 - Prob. 110CPCh. 9 - Prob. 111CPCh. 9 - Prob. 112PCh. 9 - Prob. 113PCh. 9 - Look up the definition of Poisson’s equation in...Ch. 9 - Prob. 115PCh. 9 - Prob. 116PCh. 9 - Prob. 117PCh. 9 - For each of the listed equation, write down the...Ch. 9 - Prob. 119PCh. 9 - Prob. 120PCh. 9 - A block slides down along, straight inclined wall...Ch. 9 - Water flows down a long, straight, inclined pipe...Ch. 9 - Prob. 124PCh. 9 - Prob. 125PCh. 9 - Prob. 126PCh. 9 - Prob. 128PCh. 9 - The Navier-Stokes equation is also known as (a)...Ch. 9 - Which choice is not correct regarding the...Ch. 9 - In thud flow analyses, which boundary condition...Ch. 9 - Which choice is the genera1 differential equation...Ch. 9 - Which choice is the differential , incompressible,...Ch. 9 - A steady, two-dimensional, incompressible flow...Ch. 9 - A steady, two-dimensional, incompressible flow...Ch. 9 - A steady velocity field is given by...Ch. 9 - Prob. 137P
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
- Bernoulli’s principle and the continuity equation. Give alsoan example of their real-life application.arrow_forwardAn idealized incompressible fl ow has the proposed threedimensionalvelocity distributionV = 4xy2i + f (y)j - zy2k Find the appropriate form of the function f ( y ) that satisfi esthe continuity relation.arrow_forwardvolumetric strain rate as the rate of increase of volume of a fluid element per unit volume. In Cartesian coordinates we write the volumetric strain rate as 1/ V DV/Dt = ∂u/∂x + ∂?/∂y + ∂w/∂zWrite the primary dimensions of each additive term, and verify that the equation is dimensionally homogeneous. Show all your work.arrow_forward
- 1ODiem # The side thrust F, for a smooth spinning ball in a fluid is a function of the ball diameter D, the free-stream velocity V, the densityp, the viscosityu, and the angular velocity of spino. F= f( D, ρ, μ, V, ω) Using the Buckingham Pi theorem to express this relation in dimensionless form. Farrow_forward2- Obtain a General Conservation of Mass Equation (the Continuity Equation) in 3-D Cylindrical Coordinates.arrow_forwardLet's say that the semiempirical binding energy formula is Eb= aA-bA^2/3 - s(N-Z)^2/A -dZ^2/A^1/3 where a,b,s,d are constants. Imagine that you are in a different universe where there are 3 types of nucleons with spin equal to 1/2 and electric charges equal to +1, -1 and 0. Mass similar to that of a proton. Forces are similar to those of our universe. i) How do equations change for A and Z as a function of N+, N-, No and what is the semiempirical equation for the binding energy as a function of A, Z, and No? ii) At what Z and No do we have the maximum and minimum binding energy for every A? iii) When do we have stable nuclei under beta (β) decay? If "alpha particle" in this situation has N+ = N- = No = 2, what does apply for alpha (α) decay? iv) What does apply for nuclear fission and finally, how would life be in this situation?arrow_forward
- EGMN 301 - Fluid Mechanicsarrow_forwardConsider the equations of ideal gas dynamics (3.4)-(3.5) from Roberts (see the extracts from the book of Roberts on the Study Desk). Take y = 7/5 (suitable for air) and find the distribution of density of an atmosphere in equilibrium when it is acted on by a uniform gravitational field F=-gp (assume p = po at x = 0). Sketch a graph of the density as a function of height z.arrow_forwardThis question is related to Fluid Mechanics.arrow_forward
- 3. Problem 4-31C: Consider the visualization of flow over a sphere in Fig. P4-31C. Are we seeing streamlines, streaklines, pathlines, or timelines? Explain. FIGURE P4-31c Visualization of flow over a sphere at a Reynolds number of 15,000. The visualization is produced by a time expo- sure of air bubbles in water. Courtesy of ONERA. Photo by Werle.arrow_forwardQ1:: Explain all the terms of the Continuity Equation and their physical meanings with the help of examples.arrow_forward3- Consider laminar flow over a flat plate. The boundary layer thickness & grows with distance x down the plate and is also a function of free-stream velocity U, fluid viscosity u, and fluid density p. Find the dimensionless parameters for this problem, being sure to rearrange if necessary to agree with the standard dimensionless groups in fluid mechanics.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 PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering 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