FLUID MECHANICS FUNDAMENTALS+APPS
4th Edition
ISBN: 2810022150991
Author: CENGEL
Publisher: MCG
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Textbook Question
Chapter 9, Problem 129P
The Navier-Stokes equation is also known as
(a) Newton’s first law
(b) Newton’s second law
(c) Newton’s third Law
(d) Coutinuity equation
(e) Energy equation
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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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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
- Which nondimensional parameter in the nondimensionalized Navier–Stokes equation is eliminated by use of modified pressure instead of actual pressure? Explain.arrow_forwardQ2:: Discuss the usefulness of Navier-Stokes equation with the help of practical examples.arrow_forwardDiscuss how nondimensionalization of the Navier– Stokes equation is helpful in obtaining approximate solutions. Give an example.arrow_forward
- Which dimensionless parameter does not appear in the nondimensionalized Navier–Stokes equation? (a) Reynolds number (b) Prandtl number (c) Strouhal number (d ) Euler number (e) Froude numberarrow_forwardDerive the Navier stokes equation in detail.If you copy from other source I will give you thumbs down.arrow_forwardRederive Pouiseuelle’s Law for flow in a tube using the Navier-Stokes strategy. What are the boundary conditions you will use? (you can use a horizontal tube with no gravity at play and just small p, not script p)arrow_forward
- Which choice is not correct regarding the Navier– Stokes equation? (a) Nonlinear equation (b) Unsteady equation (c) Second-order equation (d ) Partial differential equation (e) None of thesearrow_forwardDarrow_forwarda) Can we use the incompressible Navier-Stokes equations: Conservation of mass: du, dv, dw ду dz Conservation of momentum: du dt Fu u Pu du du du + W + V- az dy =pgx + dx dx? ay? dz? dv dv + u dt dv dv pgyay +v- +w- dy dy? az? aw w w ay? dz? dw dw +w- dw dw +w ду = p9z + dx? for the flow defined by the following velocity field? (2a – y)t U = v = -(x + 2y)t b) What other assumptions are inherent to this velocity field? Rewrite the simplified set of equations (using assumptions) for this flow. c) Find an expression for the pressure. d) What might the boundary conditions be? e) How would you solve the set of equations numerically by finite differences? f) Can we use the potential equations instead? g) Sketch the flow.arrow_forward
- 5. (a) (1) What are the assumptions made in deriving the Navier-Stokes equations? (ii) From the general form of the Navier-Stokes equations, derive Euler's equations. (b) Consider an incompressible flow, which oscillates at a frequency w, through a long square channel with a channel height h and length L. The coordinate is defined such that the centroid of the square cross section is at (0, 0). O Derive the mass and momentum balances of this problem. Write down a form of oscillatory pressure. (ii) State the boundary conditions. (iii) If the range of the pressure does not oscillate about 0 mPa, but instead about 10 mPa. Please modify the form of oscillating pressure. (iv) The Bessel function is used in solving oscillatory flow in cylindrical geometry. State the similarity and differences between Bessel function of the first kind of the zeroth order, Jo(x), and a cosine function, cos x.arrow_forwardYour textbook shows that the Navier-Stokes Equation for v, in cylindrical coordinates is: Our + Uodur 1/2 + 0₂ 037) ve aur - Uz r de r² az ар Ər P aur at + Ur ar plour +uror P ar at while Bird, Stewart, and Lightfoot show this equation to be: our un aur ur - 2) მს + Uz az + r de = + pgr + μ 10² 2 dve, a²u₁] + 14 = 3² (²00²) - 1/² + 1/²2 30 2² 1² 30 + 3z² - * 12 ар Ər Prove that these are the same. /1 2 -H [ 2 (-²-3, (ru) + ²1 200² - ² 000 +02 Ər r2 + pgr + μarrow_forwardWrite out the three components of the Navier–Stokes equation in Cartesian coordinates in terms of modified pressure. Insert the definition of modified pressure and show that the x-, y-, and z-components are identical to those in terms of regular pressure. What is the advantage of using modified pressure?arrow_forward
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