In the regeneration of a packed bed of ion-exchange resin, hydrochloric acid (SG = 1.2, μ = 0.002 kg/m³s) flows upward through a bed of resin particles (particle density of 2500 kg/m³). The bed is 40 cm in diameter, and the particles are spherical with a diameter of 2 mm and a bed void fraction of 0.4. The bed is 2 m deep, and the bottom of the bed is 2 m off the ground.

The acid is pumped at a rate of 2 ×10^-5 m³s from an atmospheric pressure, ground-level storage tank through the packed bed and into another atmospheric pressure, ground-level storage tank, in which the filled height is 2 m. The complete piping system consists of 75 equivalent meters of 4-in, schedule-40, commercial-steel pipe.

Determine the required power of a 75% efficient pump for this duty. Remember that a pump must be sized for the maximum duty needed.

What do you learn from the numbers in Part (a) regarding the relative magnitudes of the maximum duty and the steady-state duty?

What is the pressure rise needed for the pump?