Question

An 80cm plate of 500g mass is hinged along one side. If air is blown over the upper surface only, what speed must the air have to hold the plate horizontal?

Answer 1

Apply Bernoulli's Principle to the top (1) and bottom (2) of the plate. These two values must be equal.p1 + dV12/2 + dgy1 = p2 + dV22/2 + dgy2(1)Simplify since h(top) = h(under) for all practical purposes.p1 + dV12/2  = p2 + dgy2(2)Since v(under) = 0 and v(top) = v,p2 - p1 = dV2/2(3)Force = pressure * area.F = A * dV2/2 = Weight(4)Plugging in:Weight = mg = (0.5)(9.8) = 4.9 N (5)1/2 (1.2)v2(80 * 10-4) = 4.9 (6)v = 32.0 m/s.(5)