i. The rate of growth of o as a function of r. ii. The displacement thickness, & as a function of r. iii. The total friction force on a flat plate of length, L and width b.
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- (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* 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
- (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)³/2An 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)(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
- Q.3 Air (density 1.2 kg/m3 and kinematic viscosity 15 centistokes) flows over a flat plate, at zero angle of incidence, at a velocity of 20 m/s. If Reynolds number at transition is taken as 2.5 x 105, maximum distance, from leading edge up to which the boundary layer remains laminar, isConduct thorough a research on Boundary layer and viscous sub layer, Shear stress in circular pipe as it relates to mechanics of fluidsUsing 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
- 2) Discuss the importance of boundary layer approximation in finding the solution of fluid flow problems.Consider laminar flow entering a tube. Before the fluid enters, the velocity profile is constant and equal to to. The tube diameter is D and radius R. You are interested in estimating how much distance the fluid must travel into the tube before the classic Poiseuille parabolic velocity profile is established - this distance is called the "entrance length" or Zent- Using boundary layer theory, which of the following would be a reasonable estimate? (Hint: assume as flow enters the tube, you can model the growing viscous boundary layer as laminar flow over a flat plate, and note that the De where v = Reynolds number for a tube is Rep %3D Zent = (Rep) Zent = D 2 (Rep) Zent = 2. Rep - Rep O Zent R-Rep %3D O None of the above.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