2R Z 2RL L Task 1. Applying the lubrication approximation, derive the following result for the relation between mass flow rate and pressure drop for a power-law fluid flow in a slightly tapered tube: 79/ W= PAR RAP 1 [3n(2-1)] n-1 +32mL 1-2-3n (CAD)" where w = mass flow rate p= density min = parameters of the power-law fluid model Ro = tube radius at the inlet, neglecting ends effect 1 = R/R = Tapper ratio, where RL = tube radius at the outlet AP/L = Pressure drop per unit length from the inlet to the outlet Notice that the last term on the right-hand side of the above equation may be viewed as a taper correction to the mass flow rate vs. pressure drop (w vs. AP/L) relationship for a power-law fluid in a circular tube of constant radius Ro