FE Mechanical Fluid Mechanics Practice Problems

The current FE Mechanical specification assigns 10-15 of the 110 exam questions to Fluid Mechanics. Form A contains 10 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A horizontal venturi meter in a chilled-water line has an inlet diameter of $150$ mm and a throat diameter of $75$ mm. The measured pressure drop from inlet to throat is $28$ kPa, the meter coefficient is $0.98$ , and the water density is $1, 000$ kg/m $^{3}$ . The volumetric flow rate is most nearly:

(A)32.4 L/s
(B)33.5 L/s
(C)34.1 L/s
(D)37.4 L/s

Show worked solution

Answer: (B)

With a diameter ratio of $0.5$ the velocity-of-approach factor is $0.9375$ , yielding a throat velocity of $7.57$ m/s and about $33.5$ L/s.

Continuity locks the inlet speed to the throat speed through the area ratio, and the horizontal energy balance converts the measured pressure drop into a single throat velocity.

β = \frac{75}{150} = 0.5

V_{2} = C_{v} \frac{2Δ p}{ρ ( 1 - β ^{4} )}

Retaining the $1 - β^{4}$ term keeps the upstream kinetic energy in the balance, which at $β = 0.5$ raises the velocity by about $3$ percent.

V_{2} = 0.98 \frac{2 ( 28 , 000 )}{( 1000 ) ( 0.9375 )} = 7.57 m/s

Throat area converts that velocity into discharge.

Q = V_{2} A_{2} = (7.57) \frac{π ( 0.075 ) ^{2}}{4} = 0.0335 m^{3} / s

FE Reference Handbook — Fluid Mechanics: Flow Measurement, Venturi Meters (with the Continuity Equation)

Why the other choices appear

(A)Drops the velocity-of-approach factor and uses $V_{2} = C_{v} 2Δ p / ρ = 7.33$ m/s, giving $32.4$ L/s.
(C)Omits the meter coefficient $0.98$ , using the ideal throat velocity $7.73$ m/s to obtain $34.1$ L/s.
(D)Writes the correction as $1 - β^{2} = 0.75$ instead of $1 - β^{4}$ , raising the velocity to $8.47$ m/s and the flow to $37.4$ L/s.