FLUID MECHANICS FUNDAMENTALS+APPS
4th Edition
ISBN: 2810022150991
Author: CENGEL
Publisher: MCG
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Chapter 9, Problem 32P
Imagine a steady, two-dimensional, incompressible flow that is purely circular in the xy-or
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An incompressible velocity field is given by u=a(x°y²-y), v unknown, w=bxyz where a and b are constants.
(a)What is the form of the velocity component for that the flow conserves mass?
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Ay j. Is this a possible case of incompres-
3.9 A velocity field is given by V= Axyi --
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sible flow? If yes, obtain the stream function and find the value of constant A for
which the flow rate between the streamlines passing through the points (3, 3) and
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Axy
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Chapter 9 Solutions
FLUID MECHANICS FUNDAMENTALS+APPS
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
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- (d) Consider the following steady, three dimensional velocity field in Cartesian coordinates. V= (axy? – b)i – (2cy'j +(dxy)k where a, b, c and d are constants. Under what conditions is this flow field incompressible?arrow_forwardConsider fully developed Couette flow between two infinite parallel plates separated by distance h, with the top plate moving and the bottom plate stationary, as illustrated in the figure below. The flow is steady, incompressible, and two-dimensional in the XY plane. The velocity field is given by V }i = (u, v) = (v² )i +0j = V (a) Find out the acceleration field of this flow. (b) Is this flow steady? What are the u and v components of velocity? u= V² harrow_forwardImagine a steady, two-dimensional, incompressible flow that is purely radial in the xy- or r?-plane. In other words, velocity component ur is nonzero, but u? is zero everywhere. What is the most general form of velocity component ur that does not violate conservation of mass?arrow_forward
- [2] Consider the following stedy, incompressible, two-dimensional velocity field: V=(u,v)=(0.5+1.2x) 7+ (-2.0-1.2y) Generate an analytical expression for the flow streamlines and draw several streamlines in the upper-right quadrant from x=0 to 5 and y=0 to 6. (Here use the relation: dy/dx=v/u in the streamlines.)arrow_forwardConsider steady, two-dimensional, incompressible flow due to a spiraling line vortex/sink flow centered on the z-axis. Streamlines and velocity components are shown in Fig. The velocity field is ur = C/r and u? = K/r, where C and K are constants. Calculate the pressure as a function of r and ?.arrow_forward(d) Consider the following steady, three dimensional velocity field in Cartesian coordinates. V = (axy² – b)i – (2cy)³j +(dxy)k where a, b, c and d are constants. Under what conditions is this flow field incompressible?arrow_forward
- The velocity field for a line vortex in the r?-plane is given byur = 0 u? = K / rwhere K is the line vortex strength. For the case with K = 1.5 m/s2, plot a contour plot of velocity magnitude (speed). Specifically, draw curves of constant speed V = 0.5, 1.0, 1.5, 2.0, and 2.5 m/s. Be sure to label these speeds on your plot.arrow_forwardpls answer question with steparrow_forwardPLS SHOW ME FULL STEPS SIR PLS ANSWER WITHIN 30 MIN SIR SUBJECT (FLUID MECH 2)arrow_forward
- V u-v Question 4: Consider fully developed Couette flow - flow between two infinite parallel plates separated by distance h, with the top plate moving and the bottom plate stationary as illustrated. The flow is steady, incompressible, and two dimensional in the xy-plane. The velocity field is given by V = (u,v) = (V y/h)ỉ + 0ỷ, Generate an expression for stream function Yalong the vertical dashed line in the figure. For convenience, 4= 0 along the bottom wall of the channel. What is the value of Y along the top wall?arrow_forward(a) In a variety of environmental problems, it is common to find fluid motions that have a cellular character; i.e. the fluid streamlines form closed loops in the form of a cell. An example of a 2D cellular flow is ū = sin(rx) cos(ry)î – cos(rx) sin(ry)j (i) Is this flow incompressible? (Justify you answer.) (ii) Calculate the vorticity. (iii) Where is the magnitude of the vorticity highest, and where does it vanish?arrow_forwardKindly solve Question 2 complete only this is complete Question 2 nothing more information is provided for this questionarrow_forward
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