What is the cumulative volume of filtrate collected when

Question

Question 1

Water is to be cooled from 50^oC to 20^oC in a cooling tower. Under the operational conditions and the type of the fill used in the tower, the height of a transfer unit (HG) is 3.5 ft. Air enters the bottom of the tower at 20oC with a wet-bulb temperature of 14^oC. The tower is operated at 1.7 times the minimum air flowrate.

a) Estimate the tower height required if 500,000 lb of water is to be cooled per minute?

b) Estimate the tower diameter if the "packing factor", Fp, for the fill in the tower is 20 ft2/ft3, and the design pressure drop per foot of the fill in the tower (i.e. "packing") is 0.5 inch of water column.

Question 2

A slurry solution was filtered at a constant rate of 10 L of filtrate/s, using a filter press. The data obtained were used to plot (-ΔP) versus V (cumulative filtrate volume collected at a specific pressure drop ΔP), and the filtration model for constant rate operation was obtained as:
(-ΔP) = 1.2x10^-2 V
where -ΔP is in psia, V is in (L). This model indicates that the filter cloth resistance to the filtrate flow is negligible (RM = 0) compared to that of the filter cake.

Given data and properties of the filtrate, the slurry and the cake:

Viscosity of the filtrate: 6.72x10^-4 lb/ft.s

The specific cake resistance (independent of pressure), α: 2.10x10¹¹ ft/lb

The solid concentration, Cs: 14.6 lb/ft³ filtrate

The gravitational acceleration, gc: 32.2 ft. lb/s².lbf

Also, note that the model equation can be expressed generally as below (with gc in the denominators of the terms on the right-hand side of the equation):

ΔP = [(μ ∝ C_s)/g_cA²] V + [(μR_M/g_c.A dV/dt] = K_R V + F_R

a) What is the cumulative volume of filtrate collected when -ΔP reaches 60 psia?

b) What is the cloth area in the filter?

c) If the filter is operated under a constant pressure mode at -ΔP = 30 psia with the same slurry, estimate the filtrate volume collected after 10 minutes of filtration.