FE Civil Fluid Mechanics Practice Problems

The current FE Civil specification assigns 6-9 of the 110 exam questions to Fluid Mechanics. Form A contains 7 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A vertical rectangular gate in a reservoir retaining wall is 4 ft wide and 6 ft tall. The top edge of the gate is 8 ft below the free water surface. The specific weight of water is 62.4 lbf/ft $^{3}$ . The magnitude of the resultant hydrostatic force on the gate is most nearly:

(A)12,000 lbf
(B)16,500 lbf
(C)21,000 lbf
(D)24,500 lbf

Show worked solution

Answer: (B)

Pressure at the centroid governs: $\overset{ˉ}{h} = 11$ ft over $A = 24$ ft $^{2}$ gives $F_{R} = γ \overset{ˉ}{h} A \approx 16, 500$ lbf.

Depth to the gate centroid, and the wetted area.

\overset{ˉ}{h} = 8 + \frac{6}{2} = 11 ft

A = 4 \times 6 = 24 ft^{2}

Centroid pressure times area gives the resultant on any plane surface.

F_{R} = γ \overset{ˉ}{h} A

F_{R} = 62.4 \times 11 \times 24 = 16, 474 lbf

FE Reference Handbook — Fluid Mechanics: Forces on Submerged Surfaces (Resultant Force on a Plane Surface)

Why the other choices appear

(A)Using the depth to the top edge (8 ft) instead of the centroid gives 62.4 x 8 x 24 = 11,981 lbf.
(C)Using the depth to the bottom edge (14 ft) instead of the centroid gives 62.4 x 14 x 24 = 20,966 lbf.
(D)Integrating the pressure prism from the free surface to the bottom edge over the gate width, (1/2)(62.4)(14^2)(4), gives 24,461 lbf.