A rectangular computer chip floats on a thin layer of air, \(h=0.5 \mathrm{~mm}\) thick, above a porous surface. The chip width is \(b=40 \mathrm{~mm}\), as shown. Its length, \(L\), is very long in the direction perpendicular to the diagram. There is no flow in the \(z\) direction. Assume flow in the \(x\) direction in the gap under the chip is uniform. Flow is incompressible, and frictional effects may be neglected. Use a suitably chosen control volume to show that \(U(x)=q x / h\) in the gap. Find a general expression for the (2D) acceleration of a fluid particle in the gap in terms of \(q, h, x\), and \(y\). Obtain an expression for the pressure gradient \(\partial p / \partial x\). Assuming atmospheric pressure on the chip upper surface, find an expression for the net pressure force on the chip; is it directed upward or downward? Explain. Find the required flow rate \(q\left(\mathrm{~m}^{3} / \mathrm{s} / \mathrm{m}^{2}\right)\) and the maximum velocity, if the mass per unit length of the chip is \(0.005 \mathrm{~kg} / \mathrm{m}\). Plot the pressure distribution as part of your explanation of the direction of the net force.

"Chip" 1 1 11111 Uniform flow of air, q U (x) P6.20 Porous surface