Question

A single-acting reciprocating pump has a stroke of 25 cm, speed of 135 rpm, and a piston of 30 cm diameter. If its slip has been estimated as 4% at a particular operating condition, what is the corresponding realized discharge through a height of 14 m?
1. 33.2 lps
2. 35.6 lps
3. 37.0 lps
4. 38.2 lps

Answer 1

Correct Answer - Option 4 : 38.2 lps

Concept:

The theoretical discharge through piston is given by:

\({Q_{th}} = \frac{{ALN}}{{60}}\)

Where,

A = Cross –sectional area

L = Stroke length

N = Speed

D = Dia. Of piston

Calculation:

Given, L = 25 cm, N = 135 rpm, D = 30 cm

\({Q_{th}} = \frac{{\frac{\pi }{4} \times \left( {{{0.3}^2}} \right) \times 0.25 \times 135}}{{60}}\)

Q_th = 0.0397 m³/s or 39.7 l/s

We know that,

\({\rm{\% \;slip}} = 1 - {\rm{\;}}\frac{{{{\rm{Q}}_{{\rm{actual}}}}}}{{{{\rm{Q}}_{{\rm{th}}}}}}\)

\(0.04 = 1 - \frac{{{Q_{actual}}}}{{39.7}}\)

∴Q_actual = 38.11 l/s