A flow of 68°F air develops in a flat horizontal duct following a well-rounded entrance section. The duct height is H = 1 ft. Turbulent boundary layers grow on the duct walls, but the flow is not yet fully developed. Assume that the velocity profile in each boundary layer is u / U = ( y / δ ) 1/7 . The inlet flow is uniform at V = 40 ft/s at section ①. At section ②, the boundary-layer thickness on each wall of the channel is δ 2 = 4 in. Show that, for this flow, δ * = δ /8. Evaluate the static gage pressure at section ①. Find the average wall shear stress between the entrance and section ②, located at L = 20 ft.
A flow of 68°F air develops in a flat horizontal duct following a well-rounded entrance section. The duct height is H = 1 ft. Turbulent boundary layers grow on the duct walls, but the flow is not yet fully developed. Assume that the velocity profile in each boundary layer is u / U = ( y / δ ) 1/7 . The inlet flow is uniform at V = 40 ft/s at section ①. At section ②, the boundary-layer thickness on each wall of the channel is δ 2 = 4 in. Show that, for this flow, δ * = δ /8. Evaluate the static gage pressure at section ①. Find the average wall shear stress between the entrance and section ②, located at L = 20 ft.
A flow of 68°F air develops in a flat horizontal duct following a well-rounded entrance section. The duct height is H = 1 ft. Turbulent boundary layers grow on the duct walls, but the flow is not yet fully developed. Assume that the velocity profile in each boundary layer is u/U = (y/δ)1/7. The inlet flow is uniform at V = 40 ft/s at section ①. At section ②, the boundary-layer thickness on each wall of the channel is δ2 = 4 in. Show that, for this flow, δ* = δ/8. Evaluate the static gage pressure at section ①. Find the average wall shear stress between the entrance and section ②, located at L = 20 ft.
The design of the gear-and-shaft system shown requires that steel shafts of the
same diameter be used for both AB and CD. It is further required that the angle
D through which end D of shaft CD rotates not exceed 1.5°. Knowing that G =
77.2 GPa, determine the required diameter of the shafts.
40 mm
400 mm
100 mm
600 mm
T-1000 N-m
D
Assume a Space Launch System (Figure 1(a)) that is approximated as a cantilever undamped single degree of freedom (SDOF) system with a mass at its free end (Figure 1(b)). The cantilever is assumed to be massless. Assume a wind load that is approximated with a concentrated harmonic forcing function p(t) = posin(ωt) acting on the mass. The known properties of the SDOF and the applied forcing function are given below. • Mass of SDOF: m =120 kip/g • Acceleration of gravity: g = 386 in/sec2 • Bending sectional stiffness of SDOF: EI = 1015 lbf×in2 • Height of SDOF: h = 2000 inches • Amplitude of forcing function: po = 6 kip • Forcing frequency: f = 8 Hz
13.44 The end of a cylindrical liquid cryogenic propellant
tank in free space is to be protected from external
(solar) radiation by placing a thin metallic shield in
front of the tank. Assume the view factor Fts between
the tank and the shield is unity; all surfaces are diffuse
and gray, and the surroundings are at 0 K.
Tank
T₁
Shield, T
T₁ = 100 K
E1
Solar
irradiation
Gs
ε₁ = ε₂ = 0.05
ε₁ = 0.10
Gs = 1250 W/m²
E2
Find the temperature of the shield T, and the heat flux
(W/m²) to the end of the tank.
Chapter 9 Solutions
Fox And Mcdonald's Introduction To Fluid Mechanics
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