Show that when a liquid 1ows through a narrow tube under pressure difference p between the ends, the total volume flowing through the tube in unit time is V (a4 8L)p, where is the viscosity L is the length a is the radius Assume that the flow is laminar and that the flow velocity at the walls of th...

Consider a cylindrical region with radius r a within the tube concentric with th ...

Show that when a liquid 1ows through a narrow tube under pressure difference p between the ends,

Question:

Show that when a liquid 1ows through a narrow tube under pressure difference p between the ends, the total volume flowing through the tube in unit time is

V = (πa4/8ηL)p,

where η is the viscosity; L is the length; a is the radius. Assume that the flow is laminar and that the flow velocity at the walls of the tube is zero.