A laboratory wind tunnel has a flexible upper wall that can be adjusted to compensate for boundary-layer growth, giving zero pressure gradient along the test section. The wall boundary layers are well represented by the 1 7 -power-velocity profile. At the inlet the tunnel cross section is square, with height H 1 and width W 1 , each equal to 1 ft. With freestream speed U 1 = 90 ft/s, measurements show that δ 1 = 0.5 in. and downstream δ 6 = 0.65 in. Calculate the height of the tunnel walls at ⑥. Determine the equivalent length of a flat plate that would produce the inlet boundary layer thickness. Estimate the streamwise distance between sections ① and ⑥ in the tunnel. Assume standard air.
A laboratory wind tunnel has a flexible upper wall that can be adjusted to compensate for boundary-layer growth, giving zero pressure gradient along the test section. The wall boundary layers are well represented by the 1 7 -power-velocity profile. At the inlet the tunnel cross section is square, with height H 1 and width W 1 , each equal to 1 ft. With freestream speed U 1 = 90 ft/s, measurements show that δ 1 = 0.5 in. and downstream δ 6 = 0.65 in. Calculate the height of the tunnel walls at ⑥. Determine the equivalent length of a flat plate that would produce the inlet boundary layer thickness. Estimate the streamwise distance between sections ① and ⑥ in the tunnel. Assume standard air.
A laboratory wind tunnel has a flexible upper wall that can be adjusted to compensate for boundary-layer growth, giving zero pressure gradient along the test section. The wall boundary layers are well represented by the
1
7
-power-velocity profile. At the inlet the tunnel cross section is square, with height H1 and width W1, each equal to 1 ft. With freestream speed U1 = 90 ft/s, measurements show that δ1 = 0.5 in. and downstream δ6 = 0.65 in. Calculate the height of the tunnel walls at ⑥. Determine the equivalent length of a flat plate that would produce the inlet boundary layer thickness. Estimate the streamwise distance between sections ① and ⑥ in the tunnel. Assume standard air.
Local boundary layer effects, such as shear stress and heattransfer, are best correlated with local variables, rather usingdistance x from the leading edge. The momentum thicknessθ is often used as a length scale. Use the analysis of turbulentflat-plate flow to write local wall shear stress τw in terms ofdimensionless θ and compare with the formula recommendedby Schlichting: Cf ≈ 0.033 Reθ -0.268.
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.
A two-dimensional diverging duct is being designed to diffuse the high-speed air exiting a wind tunnel. The x-axis is the centerline of the duct (it is symmetric about the x-axis), and the top and bottom walls are to be curved in such a way that the axial wind speed u decreases approximately linearly from u1 = 300 m/s at section 1 to u2 = 100 m/s at section 2 . Meanwhile, the air density ? is to increase approximately linearly from ?1 = 0.85 kg/m3 at section 1 to ?2 = 1.2 kg/m3 at section 2. The diverging duct is 2.0 m long and is 1.60 m high at section 1 (only the upper half is sketched in Fig. P9–36; the halfheight at section 1 is 0.80 m). (a) Predict the y-component of velocity, ?(x, y), in the duct. (b) Plot the approximate shape of the duct, ignoring friction on the walls. (c) What should be the half-height of the duct at section 2?
Chapter 9 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
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