FE Environmental Fluid Mechanics and Hydraulics Practice Problems

The current FE Environmental specification assigns 12-18 of the 110 exam questions to Fluid Mechanics and Hydraulics. Form A contains 13 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A centrifugal pump handles 0.075 $m^{3} / s$ of water. The 250 mm suction line carries a gauge reading of $- 25$ kPa; the 150 mm discharge line carries a gauge reading of $+ 310$ kPa at a point 0.60 m above the suction gauge. Head loss between the two gauges is negligible. The total dynamic head developed by the pump is most nearly:

(A)30.5 m
(B)33.9 m
(C)34.7 m
(D)35.5 m

Show worked solution

Answer: (D)

Total dynamic head reaches 35.5 m, with the suction vacuum and the contraction to 150 mm both adding to the head rise.

Continuity fixes both velocities from the single discharge, and the reduced discharge bore nearly triples the velocity.

V_{s} = \frac{0.075}{\frac{π}{4} ( 0.250 ) ^{2}} = 1.53 m/s

V_{d} = \frac{0.075}{\frac{π}{4} ( 0.150 ) ^{2}} = 4.24 m/s

Pump head is the total head rise across the flanges, so the pressure, velocity, and elevation terms all enter.

h_{p} = \frac{p _{d} - p _{s}}{γ} + \frac{V _{d}^{2} - V _{s}^{2}}{2 g} + Δ z

A 25 kPa vacuum on the suction side enlarges the pressure difference to 335 kPa rather than shrinking it.

h_{p} = \frac{335}{9.81} + \frac{18.01 - 2.33}{19.62} + 0.60

h_{p} = 34.15 + 0.80 + 0.60 = 35.5 m

FE Reference Handbook — Fluid Mechanics: Energy Equation with Pump Head; Continuity Equation

Why the other choices appear

(A)Reading the suction gauge as +25 kPa instead of a vacuum gives (310 − 25)/9.81 + 0.80 + 0.60 = 30.5 m.
(B)Reversing the sign of the velocity-head difference gives 34.15 − 0.80 + 0.60 = 33.9 m.
(C)Dropping the velocity-head difference leaves 34.15 + 0.60 = 34.7 m.