2011 Case Afternoon 25

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25. A centrifugal pump is used to transfer the 75°C fluid medium from an underground open tank to a tank at a higher elevation of 10 m. It is known that the flow rate Q = 18 m3/h, the pipe specification is φ57×3.5 mm, the length of the suction side pipeline is 12 m (including the equivalent lengths of various pipe fittings), and the resistance coefficient of the pipeline is λ = 0.03. The local atmospheric pressure is 97 kPa. If the safety margin for the pump’s installation height is not taken into account, which of the following values represents the calculated installation height (in meters) for this pump? It is known that the saturated vapor pressure Pv of this medium at 75°C is 49 kPa, and its density is 890 kg/m3. The net positive suction head available (NPSHa) for this pump system is 3.0 m. (A) 1.0 (B) 0.5 (C) 0 (D) -0.5
Answer from HaiChuan: u = Q / 0.785d² = 18 / (0.785 × 0.052 × 3600) = 2.548 m/s
∑hf = λ(l/d)u²/2g = 0.03 × (12/0.05) × 2.548² / (2 × 9.81) = 2.382 Hg
= (P1 – PV) / (ρg) – NPSHa – ∑hf = (97 – 49) × 10³ / (890 × 9.81) – 3 – 2.382 = 0.116 m
Answer: C

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I have 2 questions: 1. Is there a mistake in the question? Should NPSHa be replaced with NPSHr? 2. Hg = (P1 – PV) / ρg – (NPSHa + 0.5) – ∑hf (Generally, NPSHr needs to be multiplied by a safety factor; if the safety factor is not specified, +0.5 should be used). This 0.5 value was omitted here, so the calculated result should be D, right?