Exercise Problems  -  Chapter 10

1.Estimate the power required to move a flat plate, 15 m. long and 4 m. wide, in oil at 4m/sec, under the following cases:

a) The boundary layer is assumed laminar over the entire surface of the plate. (Ans. 1665.5 N-m/sec)

b) Transition to turbulence occurs at and plate is smooth.(Ans. 9486 N-m/sec)

c) The boundary layer is turbulent over the entire plate which is smooth.(Ans. 10023.94 N-m/sec)

d) The boundary layer is turbulent over the entire rough plate with .(Ans. 17200 N-m/sec)

2. Water is transported through a horizontal pipeline, 800 m. long, with a maximum velocity of 3m/sec. If the Reynolds number is , find the diameter of the pipe (with and without the use of Moody Diagram ).

Also calculate the thickness of laminar sub-layer and the buffer layer, and find the power required to maintain the flow. Calculate your results for a fully rough pipe with .

(Ans. Diameter of the pipe 0.8 m., laminar sub-layer thickness 0.1 mm, buffer layer thickness 1.3 mm, power required 50250 W)

3. Find the frictional drag on the top and sides of a box-shaped moving van 2.4 m wide, 3.0 m high, and 10.5 m long traveling at 100km/h through air ( ). Assume that the vehicle has a rounded nose so that the flow does not seperate from the top and side. also assume that a turbulent boundary layer starts immediately at the leading edge.

Also, find the thickness of the boundary layer and the shear stress at the trailing edge.

(Ans. Drag = 105.9 N, B.L. = 0.136m, Shear stress = 0.904 Pa)