FE Civil Water Resources and Environmental Engineering Practice Problems

The current FE Civil specification assigns 10-15 of the 110 exam questions to Water Resources and Environmental Engineering. Form A contains 11 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A rectangular concrete-lined drainage channel has a bottom width of 8 ft and carries uniform flow at a depth of 3 ft. The Manning roughness coefficient is 0.013, and the bed slope is 0.002 ft/ft. The discharge is most nearly:

(A)118 ft³/s
(B)176 ft³/s
(C)255 ft³/s
(D)275 ft³/s

Show worked solution

Answer: (B)

With $A = 24$ ft² and $R = 1.714$ ft, the USCS Manning equation gives 176 ft³/s.

Only the bed and the two side walls are wetted.

A = b y = (8) (3) = 24 ft^{2}

R = \frac{A}{b + 2 y} = \frac{24}{14} = 1.714 ft

Manning's equation governs uniform flow; in USCS units the 1.486 factor is mandatory.

Q = \frac{1.486}{n} A R^{2/3} S^{1/2}

Q = \frac{1.486}{0.013} (24) (1.714)^{2/3} (0.002)^{1/2} = 175.7 ft^{3} / s

FE Reference Handbook — Water Resources and Environmental Engineering: Manning Equation

Why the other choices appear

(A)Omitting the USCS conversion factor 1.486 (using the SI form with n = 0.013) gives 118 ft³/s.
(C)Using the flow depth 3 ft as the hydraulic radius instead of A/P gives 255 ft³/s.
(D)Raising R to the 3/2 power instead of the 2/3 power gives 275 ft³/s.