Chapter 6, Problem 21P

Heavy weights can be moved with relative ease on air cushions by using a load pallet as shown. Air is supplied from the plenum through porous surface AB. It enters the gap vertically at uniform speed, q. Once in the gap, all air flows in the positive x direction (there is no flow across the plane at x = 0). Assume air flow in the gap is incompressible and uniform at each cross section, with speed u(x), as shown in the enlarged view. Although the gap is narrow (h << L), neglect frictional effects as a first approximation. Use a suitably chosen control volume to show that u(x) = qx/h in the gap. Calculate the acceleration of a fluid particle in the gap. Evaluate the pressure gradient, ∂p/∂x, and sketch the pressure distribution within the gap. Be sure to indicate the pressure at x = L.

P6.21