(a) Predict the effect of pressure drop on the permeate flux for the ultrafiltration of cheese whey in a 2-cm-diameter tubular membrane at a solution velocity of 3 m/s. Assume the membrane characteristics are the same as those in Example 29.3. 

(b) Calculate the frictional pressure drop if the tube length is 1.5 m.

Example 29.3 

A tubular membrane with a diameter of 2 cm and a water permeability of 250 L/m²-h-atm is being used for UF of cheese whey at 50°C. The whey proteins have an average diffusivity of 4 x 10^-7 cm²/s, and the osmotic pressure in atmospheres is given by Jonsson's equation π = 4.4 x 10^-3c - 1.7 x 10^-6c² + 7.9 x 10^-8c³ where c is the protein concentration in grams per liter.