A single-acting reciprocating pump has a 15 cm piston with a crank radius of 15 cm. The delivery pipe is 10 cm in diameter. At a speed of 60 rpm, 310 litres /minute of water is lifted to a height of 15 cm. Find the coefficient of discharge.

Explanation:

Theoretical discharge from a single-acting reciprocating pump:

\(Q_{th}={LAN\over 60}\)

Where L = Stroke length = 2 × crank radius

A = Area of Piston

N = Pump rotation in rpm

Calculation:

Given data:

Piston diameter (d) =15 cm or 0.15 m

Crank radius (r) = 15 cm or 0.15 m

Diameter of delivery pipe (D) = 10 cm

L = 0.30 m

Pump rotation (N) = 60 rpm

Actual discharge (Q_act) = 310 liters/minute

Lifting height (h) = 15 cm

Coefficient of discharge (C_d) =?

\(Q_{th}={0.30× 60×({\pi \over 4})× 0.15^2\over 60}\)

\(Q_{th}=0.00530\, m^3/s\)

given, \(Q_{act}=310\, liters/minute\)

1000 liters = 1 m³

\(Q_{act}={310\over 1000× 60}\, m^3/s\)

\(Q_{act}=0.00516\, m^3/s\)

\(Coefficient\, of\, discharge\,(C_d)={Actual\, discharge\,(Q_{act})\over Theoretical\, discharge\,(Q_{th})}\)

\(C_d={0.00516\over 0.00530}=0.9735\approx 0.974\)

\(C_{d}=0.974\)

Hence, the most appropriate answer is option 4.