5. Consider a pressure-driven fully-developed laminar flow of an incompressible Newtonian fluid of density p and viscosity # in a horizontal tube of diameter D and length L, referring to Figure 4. (24%)

(a) Derive the average fluid velocity, (v,), in terms of a function of pressure drop Ap across the tube by using the shell momentum balance method.

16

(b) Prove that the Fanning friction factor f; =.

Re

5. Consider a pressure-driven fully-developed laminar flow of an incompressible Newtonian fluid of density and viscosity in a horizontal tube of diameter D and length L, referring to Figure 4. (24\%) (a) Derive the average fluid velocity, vz, in terms of a function of pressure drop p across the tube by using the shell momentum balance method. (b) Prove that the Fanning friction factor fF=Re16, where Re=vzD. Figure 4