Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 10, Problem 122P
To determine
The approximate Navier-Strokes equation in dimensional form for creeping flow.
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Exercise 1
At a certain point of a body, the components of the cauchy stress tensor are
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[2 5 3
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5 1 4
3 4 3
a) Find the components of cauchy traction vector tn at the point on the
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b) Find the normal and shear commponents of tn on that point.
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IN FLUID MECHANICS, THE DIVERGENCE OF VELOCITY EXPRESSES
In fluid mechanics, the divergence of velocity expresses
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A volume dilatation rate
A particular eigen value of the Navier-Stokes equation.
An elongational rate in the direction of motion
Viscous effects
Chapter 10 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 10 - Discuss how nondimensalizsionalization of the...Ch. 10 - Prob. 2CPCh. 10 - Expalain the difference between an “exact”...Ch. 10 - Prob. 4CPCh. 10 - Prob. 5CPCh. 10 - Prob. 6CPCh. 10 - Prob. 7CPCh. 10 - A box fan sits on the floor of a very large room...Ch. 10 - Prob. 9PCh. 10 - Prob. 10P
Ch. 10 - Prob. 11PCh. 10 - In Example 9-18 we solved the Navier-Stekes...Ch. 10 - Prob. 13PCh. 10 - A flow field is simulated by a computational fluid...Ch. 10 - In Chap. 9(Example 9-15), we generated an “exact”...Ch. 10 - Prob. 16CPCh. 10 - Prob. 17CPCh. 10 - A person drops 3 aluminum balls of diameters 2 mm,...Ch. 10 - Prob. 19PCh. 10 - Prob. 20PCh. 10 - Prob. 21PCh. 10 - Prob. 22PCh. 10 - Prob. 23PCh. 10 - Prob. 24PCh. 10 - Prob. 25PCh. 10 - Prob. 26PCh. 10 - Prob. 27PCh. 10 - Consider again the slipper-pad bearing of Prob....Ch. 10 - Consider again the slipper the slipper-pad bearing...Ch. 10 - Prob. 30PCh. 10 - Prob. 31PCh. 10 - Prob. 32PCh. 10 - Prob. 33PCh. 10 - Prob. 34EPCh. 10 - Discuss what happens when oil temperature...Ch. 10 - Prob. 36PCh. 10 - Prob. 38PCh. 10 - Prob. 39CPCh. 10 - Prob. 40CPCh. 10 - Prob. 41PCh. 10 - Prob. 42PCh. 10 - Prob. 43PCh. 10 - Prob. 44PCh. 10 - Prob. 45PCh. 10 - Prob. 46PCh. 10 - Prob. 47PCh. 10 - Prob. 48PCh. 10 -
Ch. 10 - Prob. 50CPCh. 10 - Consider the flow field produced by a hair dayer...Ch. 10 - In an irrotational region of flow, the velocity...Ch. 10 -
Ch. 10 - Prob. 54CPCh. 10 - Prob. 55PCh. 10 - Prob. 56PCh. 10 - Consider the following steady, two-dimensional,...Ch. 10 - Prob. 58PCh. 10 - Consider the following steady, two-dimensional,...Ch. 10 - Prob. 60PCh. 10 - Consider a steady, two-dimensional,...Ch. 10 -
Ch. 10 - Prob. 63PCh. 10 - Prob. 64PCh. 10 - Prob. 65PCh. 10 - In an irrotational region of flow, we wtite the...Ch. 10 - Prob. 67PCh. 10 - Prob. 68PCh. 10 - Water at atmospheric pressure and temperature...Ch. 10 - The stream function for steady, incompressible,...Ch. 10 -
Ch. 10 - We usually think of boundary layers as occurring...Ch. 10 - Prob. 73CPCh. 10 - Prob. 74CPCh. 10 - Prob. 75CPCh. 10 - Prob. 76CPCh. 10 - Prob. 77CPCh. 10 - Prob. 78CPCh. 10 - Prob. 79CPCh. 10 - Prob. 80CPCh. 10 - Prob. 81CPCh. 10 -
Ch. 10 - On a hot day (T=30C) , a truck moves along the...Ch. 10 - A boat moves through water (T=40F) .18.0 mi/h. A...Ch. 10 - Air flows parallel to a speed limit sign along the...Ch. 10 - Air flows through the test section of a small wind...Ch. 10 - Prob. 87EPCh. 10 - Consider the Blasius solution for a laminar flat...Ch. 10 - Prob. 89PCh. 10 - A laminar flow wind tunnel has a test is 30cm in...Ch. 10 - Repeat the calculation of Prob. 10-90, except for...Ch. 10 - Prob. 92PCh. 10 - Prob. 93EPCh. 10 - Prob. 94EPCh. 10 - In order to avoid boundary laver interference,...Ch. 10 - The stramwise velocity component of steady,...Ch. 10 - For the linear approximation of Prob. 10-97, use...Ch. 10 - Prob. 99PCh. 10 - One dimension of a rectangular fiat place is twice...Ch. 10 - Prob. 101PCh. 10 - Prob. 102PCh. 10 - Prob. 103PCh. 10 - Static pressure P is measured at two locations...Ch. 10 - Prob. 105PCh. 10 - For each statement, choose whether the statement...Ch. 10 - Prob. 107PCh. 10 - Calculate the nine components of the viscous...Ch. 10 - In this chapter, we discuss the line vortex (Fig....Ch. 10 - Calculate the nine components of the viscous...Ch. 10 - Prob. 111PCh. 10 - The streamwise velocity component of a steady...Ch. 10 - For the sine wave approximation of Prob. 10-112,...Ch. 10 - Prob. 115PCh. 10 - Suppose the vertical pipe of prob. 10-115 is now...Ch. 10 - Which choice is not a scaling parameter used to o...Ch. 10 - Prob. 118PCh. 10 - Which dimensionless parameter does not appear m...Ch. 10 - Prob. 120PCh. 10 - Prob. 121PCh. 10 - Prob. 122PCh. 10 - Prob. 123PCh. 10 - Prob. 124PCh. 10 - Prob. 125PCh. 10 - Prob. 126PCh. 10 - Prob. 127PCh. 10 - Prob. 128PCh. 10 - Prob. 129PCh. 10 - Prob. 130PCh. 10 - Prob. 131PCh. 10 - Prob. 132PCh. 10 - Prob. 133PCh. 10 - Prob. 134PCh. 10 - Prob. 135PCh. 10 - Prob. 136PCh. 10 - Prob. 137PCh. 10 - Prob. 138P
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- An Eulerian velocity vector field is described by V = i + 2zj − 3x2k, where i, j and k are unit vectors in the x-, y- and z-directions, respectively. (i) Is the flow incompressible or compressible? (ii) Find the rate of change of velocity following a fluid particle. (iii) Find the viscous force per unit volume (that is, the viscous term in the Navier-Stokes equation).arrow_forwardConsider a steady, two-dimensional, incompressible flow field in the xy-plane. The linear strain rate in the x-direction is 1.75 s−1. Calculate the linear strain rate in the y-direction.arrow_forward4. The velocity vectors of three flow fileds are given as V, = axĩ + bx(1+1)}+ tk , V, = axyi + bx(1+t)j , and V3 = axyi – bzy(1+t)k where coefficients a and b have constant values. Is it correct to say that flow field 1 is one-, flow filed 2 is two-, and flow filed 3 is three-dimensional? Are these flow fields steady or unsteady?arrow_forward
- b) Derive the Navier-Stokes of continuity Equation If the fluid is incompressible, p = constant, independent of space and time, so that dp/ờt = 0. The continuity equation then reduces to v-v = 0.arrow_forwardX=1 X=7 2. A fluid flow is described by the velocity vector; U = 5x³i - 15x²yj (a) Determine the shear strain rate. (b) Find the stream function of the flow. (c) Find the velocity potential of the flow.arrow_forwardA simple parallel flow with constant velocity shear σ is given byu = σy v = w = 0 Evaluate the five components of motion (e.g. translation, divergence, vorticity,shearing and stretching deformation.)arrow_forward
- Derive the Eulerian acceleration of a fluid particle in a flow field given by 1 V = xy²i -y'j + xykarrow_forwardGiven the Eulerian velocity vector field: V = 3ti + xzj + ty²k Find the total acceleration of a particle av av av W дх' ду' ду Hint: u Varrow_forwardAn equation for the velocity for a 2D planar converging nozzle is Uy u =U1+ w=0 L Where U is the speed of the flow entering into the nozzle, and L is the length. Determine if these satisfy the continuity equation. Write the Navier-Stokes equations in x and y directions, simplify them appropriately, and integrate to determine the pressure distribution P(x.y) in the nozzle. Assume that at x = 0, y = 0, the pressure is a known value, P.arrow_forward
- The flow field about a rotating cylinder with the radius a can be modelled by superimposing the velocity potentials of a uniform flow filed, a doublet and a potential vortex: p = Ux[1+ (a/r)²] – (TO)/(2x) Does this velocity potential satisfy the Laplace equation? True Falsearrow_forward4. For a parallel plate arrangement of the type shown in Figure Q4, it is found that when the distance between plates is 2 mm, a shearing stress of 150 Pa develops at the upper plate when it is pulled at a velocity of 1 m/s. Assume the velocity distribution is linear between the plates, Determine: (i) the dynamic viscosity of the fluid between the plates. (2 marks) (a)0.3 N.S/m² (b) 3.3 N.S/m² (c) 0.3 kg S/m² '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_forward
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