Air flows in a cylindrical duct of diameter D = 6 in. At section ①, the turbulent boundary layer is of thickness δ 1 = 0.4 in. and the velocity in the inviscid central core is U 1 = 80 ft/s. Further downstream, at section ②, the boundary layer is of thickness δ 2 = 1.2 in. The velocity profile in the boundary layer is approximated well by the 1 7 -power expression. Find the velocity, U 2 , in the inviscid central core at the second section, and the pressure drop between the two sections. Does the magnitude of the pressure drop indicate that we are justified in approximating the flow between sections ① and ② as one with zero pressure gradient? Estimate the length of duct between sections ① and ②. Estimate the distance downstream from section ① at which the boundary layer thickness is δ = 0.6 in. Assume standard air.
Air flows in a cylindrical duct of diameter D = 6 in. At section ①, the turbulent boundary layer is of thickness δ 1 = 0.4 in. and the velocity in the inviscid central core is U 1 = 80 ft/s. Further downstream, at section ②, the boundary layer is of thickness δ 2 = 1.2 in. The velocity profile in the boundary layer is approximated well by the 1 7 -power expression. Find the velocity, U 2 , in the inviscid central core at the second section, and the pressure drop between the two sections. Does the magnitude of the pressure drop indicate that we are justified in approximating the flow between sections ① and ② as one with zero pressure gradient? Estimate the length of duct between sections ① and ②. Estimate the distance downstream from section ① at which the boundary layer thickness is δ = 0.6 in. Assume standard air.
Air flows in a cylindrical duct of diameter D = 6 in. At section ①, the turbulent boundary layer is of thickness δ1 = 0.4 in. and the velocity in the inviscid central core is U1 = 80 ft/s. Further downstream, at section ②, the boundary layer is of thickness δ2 = 1.2 in. The velocity profile in the boundary layer is approximated well by the
1
7
-power expression. Find the velocity, U2, in the inviscid central core at the second section, and the pressure drop between the two sections. Does the magnitude of the pressure drop indicate that we are justified in approximating the flow between sections ① and ② as one with zero pressure gradient? Estimate the length of duct between sections ① and ②. Estimate the distance downstream from section ① at which the boundary layer thickness is δ = 0.6 in. Assume standard air.
Air flows through the test section of a small wind tunnel at speed V = 7.5 ft/s. The temperature of the air is 80°F, and the length of the wind tunnel test section is 1.5 ft. Assume that the boundary layer thickness is negligible prior to the start of the test section. Is the boundary layer along the test section wall laminar or turbulent or transitional?
The air with temperature T. 20°C, speed U. = 20 m/s flows over the plate with length L = 1 m, width b = 1.5 m, surface temperature T = 60°C. a) Calculate the drag force acting on the plate.
Consider two different flows over geometrically similar airfoil shapes,one airfoil being twice the size of the other. The flow over the smallerairfoil has freestream properties given by T∞ = 200 K, ρ∞ = 1.23 kg/m3,and V∞ = 100 m/s. The flow over the larger airfoil is described byT∞ = 800 K, ρ∞ = 1.739 kg/m3, and V∞ = 200 m/s. Assume thatboth μ and a are proportional to T 1/2. Are the two flows dynamicallysimilar?
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