An algal sludge is to be clarified by filtering. A lab test is run on the sludge using an area A of the filter medium. At a constant pressure drop of 40 kN/m2 , a plot of the time required to collect...

An algal sludge is to be clarified by filtering. A lab test is run on the sludge using an area A of the filter medium. At a constant pressure drop of 40 kN/m2 , a plot of the time required to collect a volume V~ of the filtrate times P=ðV~ =A) vs. V~ =A gives a straight line with a slope of 1:2  106 kN s/m4 and an intercept of 6:0  104 kN s/m3 . A repeat of the data at a pressure drop of 200 kN/m2 also gave a straight line on the same type of plot, with the same intercept but with a slope of 2:1  106 kN s/m4 . When a filter aid was added to the sludge in an amount equal to 20% of the algae by weight, the lab test gave a straight line with the same intercept but with a slope of 1:4  106 kN s/m4 .

(a) What does this tell you about the sludge?

(b) The sludge is to be filtered using a rotary drum filter, with a diameter of 4 ft and a length of 6 ft, operating at a vacuum of 700 mmHg with 35% of the drum submerged. If the drum is rotated at a rate of 2 rpm, how many gallons of filtrate will be collected in a day, (1) with and (2) without the filter aid?

(c) What would the answer to (b) be if the drum speed was 4 rpm?