FE Environmental Water and Wastewater Practice Problems

The current FE Environmental specification assigns 12-18 of the 110 exam questions to Water and Wastewater. Form A contains 14 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A granular media filter with a $20$ ft by $24$ ft plan area operates at a filtration rate of $4.0$ gpm/ft $^{2}$ for a $60$ h run, then is backwashed at $18$ gpm/ft $^{2}$ for $10$ min. The backwash water expressed as a percentage of the water filtered during the run is most nearly:

(A)0.062 %
(B)1.25 %
(C)3.1 %
(D)12.5 %

Show worked solution

Answer: (B)

Backwash consumes about $1.25$ percent of production: the wash rate is 4.5 times the filtration rate, but the run lasts 360 times as long as the wash.

Plan area cancels from both volumes, leaving a ratio of rate times duration in gallons per square foot.

\frac{V _{b w}}{V _{f}} = \frac{( 18 ) ( 10 )}{( 4.0 ) ( 60 \times 60 )}

Run length in minutes is $3, 600$ , so $180$ gal/ft $^{2}$ of wash water stands against $14, 400$ gal/ft $^{2}$ filtered.

\frac{180}{14 , 400} = 0.0125 = 1.25%

FE Reference Handbook — Water and Wastewater: Granular Media Filtration, Filtration and Backwash Rates

Why the other choices appear

(A)Inverts the rate ratio, computing (4.0/18)(10/3,600) = 6.2 x 10^-4 = 0.062%.
(C)Takes the run as 24 h, comparing 86,400 gal of backwash with 2,764,800 gal filtered.
(D)Reads the run length as 6 h, a decimal slip that inflates the ratio tenfold to 12.5%.