Question 15.6: The piston diameter and the stroke length of a single acting......
The piston diameter and the stroke length of a single acting reciprocating pump are 20 cm and 40 cm respectively. The sump level is 4 m below the centre of the pump cylinder. The length of the suction pipe is 6.5 m. The speed of the pump is 60 rpm. Find the minimum diameter of the suction pipe. The separation pressure head is 2.4 m of water, and the atmospheric pressure is 10.3 m of water.
Given: D = 20 cm = 0.2 m, L = 40 cm = 0.4 m, H_{s} = 4 m, l_{s} = 6.5 m, N = 60 rpm, H_{sep} = 2.4 m of water, and H_{at}= 10.3 m of water
{\mathrm{Crank~radius~}}r={\frac{L}{2}}={\frac{0.4}{2}}Crank angular velocity \omega={\frac{2\pi N}{60}}
Now, the condition for occurrence of separation at the beginning of stroke is:
H_{a t}-H_{s}-h_{a s}=H_{sep}10.3 – 4 – h_{as} = 2.4
∴ h_{as} = 3.9
or \frac{l_{s}}{g}\frac{A}{a_{s}}r\omega^{2}=3.9
or {\frac{6.5}{9.81}}\times{\frac{(\pi/4)\times0.2^{2}}{(\pi/4)\times d_{s}^{2}}}\times0.2\times{\left({\frac{2\pi N}{60}}\right)}^{2}=3.9
or {\frac{0.2093263}{d_{s}^{2}}}=3.9
∴ d_{s}=0.23164{\mathrm{~m}}=23.164{\mathrm{~cm}}