A rudder is tested in a two-dimensional flow tunnel of height h = 1 m, as shown

Question

A rudder is tested in a two-dimensional flow tunnel of height h = 1 m, as shown in the following figure. After the flow has become steady, the horizontal velocity far ahead of the rudder is found to be uniform and given by u = U = 2 m/s. Some distance downstream, the velocity profile can be (very) roughly approximated by a region inside the wake with u = U/2 and an exterior region with u = 3U/2. You may assume that the total pressure at the downstream station is uniform across the tunnel and given by the value at the wall. Neglecting gravitational effects:
a. Determine the height of the wake region H.
b. Assuming ideal fluid flow (no shear stress), calculate the difference in pressure at point A and point B (i.e. pA – pB).
c. Calculate the drag force on the body.

Explanation / Answer

A rudder is tested in a two-dimensional °ow tunnel of height h = 1m, as shown: h U H A B After the °ow has become STEADY, the horizontal velocity far ahead of the rudder is found to be uniform and given by u = U = 2m/s. Some distance downstream, the velocity pro¯le can be (very) roughly approximated by a region inside the wake with u = U=2 and an exterior region with u = 3U=2. You may assume that the total pressure at the downstream station isuniform across the tunnel and given by the value at the wall. (a) Determine the height of the wake region H. (b) Assuming ideal °uid °ow (no shear stress), calculate the pressure di®erence PA ¡ PB. (c) Calculate the drag force D on the body

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