Question 15.9: A single acting reciprocating pump has piston diameter 0.125......
A single acting reciprocating pump has piston diameter 0.125 m and stroke length 0.3 m. The centre of the cylinder is 4.5 m above the sump level. The diameter and the length of the suction pipe are 0.075 m and 5 m respectively. The separation occurs if the absolute pressure head during suction stroke falls below 2.3 m. Calculate the maximum speed at which the pump can run without separation. Take the atmospheric pressure head as 10.3 m of water.
Given: D = 0.125 m, L = 0.3 m, H_{s} = 4.5 m, d_{s}= 0.075 m, l_{s}= 5 m, H_{sep} = 2.3 m, and H_{at} = 10.3 m
Now, A_{s}={\frac{\pi}{4}}(125)^{2}
= 0.012271 m²
a_{s}={\frac{\pi}{4}}(0.075)^{2}= 0.004417 m²
r={\frac{L}{2}}={\frac{0.3}{2}}= 0.15 m
From Figure 15.7 of indicator diagram, the minimum pressure head occurs at the beginning of suction stroke. Hence, it may be written here, i.e.
H_{a t}=H_{s}+h_{a s}+H_{\mathrm{sep}}or H_{\mathrm{at}}-(H_{s}+h_{as})=H_{\mathrm{sep}}
or 10.3 – (4.5 + h_{as}) = 2.3
or h_{as} = 3.5
But maximum accelerating head h_{as} is given as:
h_{a s}=\frac{l_{s}}{g}\frac{A}{a_{s}}r\omega^{2}or h_{a s}={\frac{5}{9.81}}\times{\frac{0.012271}{0.004417}}\times0.15\times\left({\frac{2\pi N}{60}}\right)^{2}
or h_{a s} = 0.0023295 N²
Substituting the value of h_{a s} in Eq. (i), we have
0.0023295 N² =3.5
∴ N = 38.76 rpm
