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.
Flow straighteners consist of arrays of narrow ducts placed in a flow to remove swirl and other transverse
(secondary) velocities. One element can be idealised as a square box with thin sides as shown below.
Calculate the pressure drop across a box with L=22 cm and a= 2.7 cm, if air with free-stream velocity of
Uo = 11 m/s flows though the straightener. Use laminar flat-plate theory and take u = 1.85 x 10-5 Pa.s
and p = 1.177kg/m³ .
%3D
%3D
a
Uo
Figure 1: Flow across straighteners.
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?
The wing of a tactical support aircraft is approximately rectangular with a wingspan (the length
perpendicular to the flow direction) of 16.5 m and a chord (the length parallel to the flow
direction) of 2.75 m. The airplane is flying at standard sea level with a velocity of 250 ms¯¹.
Assume the wing is approximated by a flat plate. Assume incompressible flow. Use μ =
1.789 x 10-5 kg/ms
(a) If the flow is considered to be completely laminar, calculate the boundary layer
thickness at the trailing edge and the total skin friction drag.
Chapter 9 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
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