A single acting reciprocating pump discharges 3.5 litres of water per second at 40 rpm. The pump has a piston diameter of 150 mm and a stroke of 300 mm. The percentage slip is
GATE AG - 2012,
Answer: A
The keyed slip is 0.85%.
The theoretical discharge of a single acting pump is swept volume per stroke times strokes per second:
\[ \begin{aligned} Q_{th} &= \tfrac{\pi}{4}(0.15)^{2}(0.3)\tfrac{40}{60} \\ &= 0.003534\ \text{m}^{3}/\text{s} \approx 3.53\ \text{L/s} \\ \text{slip} &= \frac{3.53 - 3.5}{3.53} \times 100 \\ &\approx 0.85\% \end{aligned} \]
The key rounds the theoretical discharge to 3.53 L/s before taking the difference; carrying more digits (3.534 L/s) gives about 0.97%, which is still nearest to 0.85 among the options. 3.53 is the theoretical discharge in L/s, not the slip, and 1.97 and 6.05 do not come from this data.
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