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 130P
To determine
The incorrect statement regarding the boundary layer approximation.
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Which nondimensional parameter in the nondimensionalized Navier–Stokes equation is eliminated by use of modified pressure instead of actual pressure? Explain.
Consider a boundary layer growing along a thin flat plate. This problem involves the following parameters: boundary layer thickness ? , downstream distance x, freestream velocity V, fluid density ? , and fluid viscosity ? . The number of expected nondimensional parameters Πs for this problem is (a) 5 (b) 4 (c) 3 (d ) 2 (e) 1
Question A2 continued
a) By using appropriate assumptions simplify the conservation of mass and
momentum of the incompressible Navier-Stokes equations. All the assumptions
and the simplified equations should be written;
[10 marks]
b) By using appropriate boundary conditions find the velocity distribution in the two
layers.
[15 marks]
Question A3
In the usual notations the velocity distribution in a laminar boundary layer forming on a thin
equilateral triangle plate (Figure Q-A3) is approximated as: U=Asin()+B
xy
28'
12 m
Air at 27 C
and 1 atm
2m
2m
1-cos(2a)
2
2 m
Figure Q-A3
a) By using appropriate boundary conditions determine A and B in terms of Us:
[2 marks]
b) For the above velocity distribution, compute 8/8;
[5 marks]
c) Using the momentum integral equation, find an expression for the wall shear stress
as a function of fluid properties, Usand x;
[8 marks]
d) If this plate is immersed parallel to a 12 m/s stream of air at 1 atm and 27° C, as is
shown in Figure Q-A3, assuming…
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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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
- please answer quicklyarrow_forwardThe Navier–Stokes equation is also known as (a) Newton’s first law (b) Newton’s second law (c) Newton’s third law (d ) Continuity equation (e) Energy equationarrow_forwardWhat criteria can you use to determine whether an approximation of the Navier–Stokes equation is appropriate or not? Explain.arrow_forward
- not only tell correct answer but also provide proper explanationarrow_forwardWe usually think of boundary layers as occurring along solid walls. However, there are other flow situations in which the boundary layer approximation is also appropriate. Name three such flows, and explain why the boundary layer approximation is appropriate.arrow_forwardNeed help figuring this outarrow_forward
- (b) In two-dimensional boundary layer, shear stress was changed linearly from the solid surface toward y-axis until it reaches the value of zero at y = 8. Based on Table 2 and setting given to you; (i) Derive the equation of displacement thickness and momentum thickness using Von Karman Approximation Method; and (ii) Determine the accuracy of this method in determining the value of displacement thickness and momentum thickness. Table 2: Equation of Velocity Profile Equation u/U = 3(y/8)/2 – (y/8)³/2 Setting 2arrow_forwardConsider a boundary layer growing along a thin flat plate. This problem involves the following parameters: boundary layer thickness ? , downstream distance x, free-stream velocity V, fluid density ? , and fluid viscosity ? . The number of primary dimensions represented in this problem is (a) 1 (b) 2 (c) 3 (d ) 4 (e) 5arrow_forward(b) In two dimensional boundary layer, shear stress was changed linearly from the solid surface toward y-axis until it reach the value of zero at y = 6. Based on Table 2 and setting given to you; () Derive the equation of displacement thickness and momentum thickness using Von Karman Approximation Method ; and (ii) Determine the accuracy of this method in determining the value of displacement thickness and momentum thickness. Table 2 : Equation of Velocity Profile Setting Equation wU = 3(y/8)/2 – (y/8j?/2arrow_forward
- Discuss how nondimensionalization of the Navier– Stokes equation is helpful in obtaining approximate solutions. Give an example.arrow_forwardHow could the fluid flow variable be introduced into the following simplified Navier-Stokes equation? If you consider: -The fluid is incompressible P dv at µAv + VP = 0 (Ctrl) -arrow_forwardPlease do both parts and correctly I will rate your solution but pls follow what I have said other wise skip plsarrow_forward
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