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: -25-² 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). U-30 m/s X-0.0 Top wall Bottom wall X-300 mm X-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.

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: -25-² 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). U-30 m/s X-0.0 Top wall Bottom wall X-300 mm X-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.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.70P

See similar textbooks

Similar questions

2.0 m 7: 10.0 m = 2²-²² Us B 10.0 m Figure Q1-2 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: 2.0 m (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…
Consider liquid in a cylindrical tank. Both the tank and the liquid rotate as a rigid body. The free surface of the liquid is exposed to room air. Surface tension effects are negligible. Present the boundary conditions required to solve this problem. Specifically, what are the velocity boundary conditions in terms of cylindrical coordinates (r, 0, z) and velocity components (ur, uo, U:) at all surfaces, including the tank walls and the free surface? What pressure boundary conditions are appropriate for this flow field? Explain. Free surface Ps Paa Liquid
(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
(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 = ở. 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. C5 Table 2: Equation of Velocity Profile Setting Equation wU = 2y/8 - (y/S² 1
A wind tunnel has a cross-section of 1.0m at its inlet by 1.0m and length 10m. Wind at uniform velocity 15m/s enters the tunnel at 20°C. Assume, velocity distribution in turbulent 1/5 y boundary layer to follow the law U (Kinematic viscosity= 1.53x10°m² /s) Assuming the boundary layer to be turbulent from the beginning, then the value of 8(represents in law) is calculated as
(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 2
* ZAIN IQ liı. SuspendEA IN A ROom, Ana TS Subjected To Air Flow Parallel To I... A 2m by 3m flat plate is suspended in a room, and is subjected to air flow parallel to its surfaces along its 3m long side as shown in the figure. The free stream air temperature, T, is 20°C and the velocity is 7 m/s. The total drag force acting on the plate is measured to be 0.86 N. Determine the average convection heat transfer coefficient for the plate. Air 20°C, 7 m/s L= 3 m. This problem has been solved! See the answer
An approximation for the boundary-layer shape in is the formula u(y) - U sin 0 sys d where U is the stream velocity far from the wall and d is the boundary layer thickness, as in Fig. If the fluid is helium at 20°C and 1 atm, and if U = 10.8 m/s and 8= 3 cm, use the formula to (a) estimate the wall shear stress Tw in Pa, and (b) find the position in the boundary layer where t is one-half of Tw. -- y = 6 u(y)
Air at 20 °C forms a boundary layer near a solid wall, in which the velocity profile is sinusoidal (see Fig. 1-14). The boundary-layer thickness is 7 mm and the peak velocity is 9 m/s. Compute the shear stress in the boundary layer at y equal to (a) 0, (b) 3.5 mm, and (c) 7 mm. 7 mm Vmax = 9 m/s Peak Sine wave Fig. 1-14
We are testing a flat plate of length L = 1.125 m and width W = 0.225 m in a stream of air flowing with a velocity of 20 m/s. In test case 1, the air is flowing parallel to L and in test case 2 air is flowing parallel to W. Find: What portion of the boundary layer flow is laminar in each case? What is the highest laminar boundary layer thickness in each case? Assuming the flow is entirely turbulent over the plate, calculate the drag force in both test cases Take air density as 1.2 kg/m3 and its viscosity as μ=18×10−6μ=18×10−6 N.s/m2.
-5 2 Air stream k = 0.02439 W/m.K, v 1.426 x10 m /s, Pr = 0.7336) flows over a flat surface [L= 4.5 m, w = 2.5 m] with velocity of 97 km/hr, flow is parallel to L, What is the amount of heat transfer "kW" when the temperature difference is 84 °C?
An air whose cross-sections are visible in the figure on the side Channel 40 cm diameter and 60 cm tall test section references The air temperature is 200oC. At the entrance of the Test section A uniform airspeed of 2 m/s was measured.a) the number of Reynolds at the end of the test section (Rex)calculate.b) limit layer thickness at the end of the test sectioncalculate.c) air velocity test on centerlinewhat percentage increases by the end of the section,calculate.d) local surface friction at the end of the test sectioncalculate the coefficient. v = 1,516 . 10-5 m2/s.