a. What is a favorable pressure gradient? What is an adverse pressure gradient? b. What is boundary layer separation? Explain underlying physics. d. The turbulent boundary layer has greater momentum near the wall than the laminar boundary layer. Briefly explain why. What is the implication of this greater momentum on boundary layer separation?

a. What is a favorable pressure gradient? What is an adverse pressure gradient? b. What is boundary layer separation? Explain underlying physics. d. The turbulent boundary layer has greater momentum near the wall than the laminar boundary layer. Briefly explain why. What is the implication of this greater momentum on boundary layer separation?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Q1) Briefly explain laminar, transition and turbulent flow based on boundary layer separation.
(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 = 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/S)/2 – (y/8)³/2
(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?/2
Air at T = 25 C° and p = 1 atm flows past a long flat plate, at the end of which is placed a narrow scoop, as shown in the figure below. (a) Determine if the boundary layer is laminar or turbulent at the position of the scoop assuming Re,trans = 5 x 10°; (b) estimate the height h of the scoop if it is to extract 4 kg/s per meter of width b into the paper. (c) Find the drag on the plate per meter of width, D/b up to the inlet of the scoop.
Q4) Define the boundary layer, then find the thickness of boundary layer, shear stress, drag force and coefficiet of drag in terms of Re for the velocity profile of laminar boundary layer u/U=4(y/8)-6(y/8)5. Calcate the boundary layer thickness and drag force if the air flows over a sharp edged flat plate 1m long and 0.5m wide at a velocity 0.9m/s, the air density 1.23 kg/m³ and the kinematic viscosity is 1.46*10-5 m/s².
2) Discuss the importance of boundary layer approximation in finding the solution of fluid flow problems.
Q4 (a) What is drag? What cause it and why do we usually try to minimize it? Explain your answer.
Engine oil at 40 C flows over a 5-m-long flat plate with a free-stream velocity of 2 m/s. Determine the drag force acting on the top side of the plate per unit width. The density and kinematic viscosity of oil at 40 C are 876 kg/m^3 and 2.458 x 10 m^-4/s respectively.
Using von Karman momentum integral, derive boundary layer height 8, boundary layer displacement thickness d, boundary layer momentum thickness 0, wall shear stress To, local skin friction coefficient c, and total drag coefficient C, for turbulent boundary layer flow with power law constant, n = 5. Discuss by comparing your answers to turbulent boundary layer flow with power law constant, n = 7. Take the empirical wall shear stress: To = 0.0204pU 2 %3D SU 1/4
Q5. A deep pool of oil having kinematic viscosity 3.45x10 m²/s is resting over a flat plate. The plate is suddenly set into motion with velocity 5 cm/s at time t-0. What will be the boundary layer thickness after 10s when the plate was set in motion?
The momentum thickness OM for laminar flow over a flat plate is (115/1134) 6. Find the following: a) Boundary layer thickness (6) divided by x. Compare this answer to the Blasius Solution. Answer should be 6/x = 5.733/sqrt(Rex). b) Local skin friction coefficient (cf). Answer hould be 0.5814/sqrt(Rex). c) Friction Drag Coefficient. Answer should be 1.1628/sqrt(Rex).
We 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.