The classic Poiseuille flow (Eq. 8.12), is for no-slip conditions at the walls. If the fluid is a gas, and when the mean free path, l (the average distance a molecule travels before collision with another molecule), is comparable to the length-scale L of the flow, slip will occur at the walls, and the flow rate and velocity will be increased for a given pressure gradient. In Eq. 8.11, c1 will still be zero, but c2 must satisfy the slip condition u=l ∂u=∂r at r =R. Derive the velocity profile and flow rate of gas flow in a micro- or nanotube which has such a slip velocity on the wall. Calculate the flow rate when R=10 μm, μ=1:84 × 10−5 N s=m2, the mean free path l =68 nm, and −∂p=∂x=1:0×106 Pa=m