Question

A single-acting reciprocating ram pump, while running at 120 rpm, delivers water at a rate of 10 litres per second. Considering the ram diameter is 150 mm and stroke length is 300 mm, the volumetric efficiency of the pump, in percent, is \(\underline{\hspace{1cm}}\). (round off to one decimal place)

Hint:

Volumetric efficiency is the ratio of the actual discharge to the theoretical discharge.

Answer 1

Correct Answer: 92

First, calculate the theoretical discharge:
The area of the ram is:
\[ A = \pi \left(\frac{d}{2}\right)^2 = \pi \left(\frac{150}{2}\right)^2 = 17671.46 \, \text{mm}^2 \] The displacement per stroke is:
\[ \text{Displacement} = A \times \text{Stroke length} = 17671.46 \times 300 = 5301438 \, \text{mm}^3 = 5.30 \, \text{litres} \] The theoretical discharge is:
\[ Q_{\text{theoretical}} = \text{Displacement} \times \text{RPM} = 5.30 \times 120 = 636 \, \text{litres/min} \] Now, actual discharge is given as 10 litres per second, which is equivalent to:
\[ Q_{\text{actual}} = 10 \times 60 = 600 \, \text{litres/min} \] Finally, the volumetric efficiency \( \eta \) is:
\[ \eta = \frac{Q_{\text{actual}}}{Q_{\text{theoretical}}} \times 100 = \frac{600}{636} \times 100 = 94.34% \] Thus, the volumetric efficiency of the pump is \( \boxed{94.3%} \).