Question 2 Air flow at a constant speed (Us = 10 m/s) is forming a two-dimensional incompressible laminar boundary layer along a flat plate The velocity profile inside the boundary layer is given by: = 2²-² (Equation 1) At x = 1.00 m, the boundary layer thickness is given as 6.6094 mm. At this location: a) Determine the shear stress at the wall, at y = 3 mm and y = 10 mm. b) Calculate the boundary layer displacement thickness. c) Calculate the mass flow rate through the boundary layer per unit width. d) Calculate the mass flow rate per unit width of an ideal flow going through the same height as the boundary layer thickness. e) Through calculation relate the difference between the mass flow rates in parts (c) and (d) to the local boundary layer displacement thickness. In not more than 60 word justify your answer. Use sketch(s) to illustrate your justification. f) Does the assumed velocity profile satisfy the pressure boundary condition? In not more than 30-40 words and including the use of an appropriate equation justify your answer. U-30 m/s Question 2 continued g) A wind tunnel designer plans to build a two dimensional test section for a low speed wind tunnel. The design specification requires that in the test section the free stream flow must be equal to the air velocity at the entrance of the test section. (Figure Q2). h₁ ⒸX-0.0 9 Question 2 continues on the next page (WI Top wall Bottom wall X-300 mm ₂-300 mm Figure Q2 Assuming the same velocity profile as in equation 1, and by using the momentum integral equation determine how much the bottom and top walls should be displaced at point 2 (x2 = 300 mm) in order to achieve the design requirement as was stated above. In not more than 30-40 words justify your solution. you.

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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Transcribed Image Text:Question 2 Air flow at a constant speed (Us = 10 m/s) is forming a two-dimensional incompressible laminar boundary layer along a flat plate The velocity profile inside the boundary layer is given by: = 2²-² (Equation 1) At x = 1.00 m, the boundary layer thickness is given as 6.6094 mm. At this location: a) Determine the shear stress at the wall, at y = 3 mm and y = 10 mm. b) Calculate the boundary layer displacement thickness. c) Calculate the mass flow rate through the boundary layer per unit width. d) Calculate the mass flow rate per unit width of an ideal flow going through the same height as the boundary layer thickness. e) Through calculation relate the difference between the mass flow rates in parts (c) and (d) to the local boundary layer displacement thickness. In not more than 60 word justify your answer. Use sketch(s) to illustrate your justification. f) Does the assumed velocity profile satisfy the pressure boundary condition? In not more than 30-40 words and including the use of an appropriate equation justify your answer. U-30 m/s Question 2 continued g) A wind tunnel designer plans to build a two dimensional test section for a low speed wind tunnel. The design specification requires that in the test section the free stream flow must be equal to the air velocity at the entrance of the test section. (Figure Q2). h₁ 2 X-0.0 Question 2 continues on the next page (1) Top wall Bottom wall X-300 mm 3-300 mm Figure Q2 Assuming the same velocity profile as in equation 1, and by using the momentum integral equation determine how much the bottom and top walls should be displaced at point 2 (x₂ = 300 mm) in order to achieve the design requirement as was stated above. In not more than 30-40 words justify your solution. you.

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