FE Other Disciplines Fluid Mechanics Practice Problems

The current FE Other Disciplines specification assigns 12-18 of the 110 exam questions to Fluid Mechanics. Form A contains 12 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 sluice gate 4 ft wide and 6 ft high is set in the side wall of a reservoir. The top edge of the gate lies 8 ft below the free water surface, which is open to the atmosphere. Water has a specific weight of 62.4 lbf/ft $^{3}$ . The resultant hydrostatic force on the gate is most nearly:

(A)12,000 lbf
(B)16,500 lbf
(C)16,900 lbf
(D)21,000 lbf

Show worked solution

Answer: (B)

The gate's centroid lies 11 ft below the surface, and pressure at that depth acting over the whole gate gives a resultant near 16,500 lbf.

Hydrostatic pressure grows linearly with depth, so the resultant on a plane area is the centroidal pressure acting over the whole area.

h_{c} = 8 + \frac{6}{2} = 11 ft

A = 4 (6) = 24 ft^{2}

The second moment of area shifts the line of action below the centroid but leaves the magnitude untouched.

F = γ h_{c} A = 62.4 (11) (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)Takes the top-edge depth of 8 ft as the centroidal depth: $62.4 (8) (24) = 11, 980$ lbf.
(C)Uses the center-of-pressure depth $11.27$ ft in the force equation: $62.4 (11.27) (24) = 16, 880$ lbf.
(D)Takes the bottom-edge depth of 14 ft as the centroidal depth: $62.4 (14) (24) = 20, 970$ lbf.