Air flows in a horizontal cylindrical duct of diameter D = 100 mm. At a section a few meters from the entrance, the turbulent boundary layer is of thickness δ 1 = 5.25 mm, and the velocity in the inviscid central core is U 1 = 12.5 m/s. Farther downstream the boundary layer is of thickness δ 2 = 24 mm. 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.
Air flows in a horizontal cylindrical duct of diameter D = 100 mm. At a section a few meters from the entrance, the turbulent boundary layer is of thickness δ 1 = 5.25 mm, and the velocity in the inviscid central core is U 1 = 12.5 m/s. Farther downstream the boundary layer is of thickness δ 2 = 24 mm. 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.
Air flows in a horizontal cylindrical duct of diameter D = 100 mm. At a section a few meters from the entrance, the turbulent boundary layer is of thickness δ1 = 5.25 mm, and the velocity in the inviscid central core is U1 = 12.5 m/s. Farther downstream the boundary layer is of thickness δ2 = 24 mm. 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.
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.
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.
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
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