Question 15.5: 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 0.12 m and 0.24 m respectively. The diameter and length of suction pipe are 8 cm and 4 m, respectively. The centre of the pump is 3.5 m above the sump water level. Find the maximum speed at which the pump can run. Assume atmospheric and separation pressure heads to be 10.35 m and 2.55 m respectively.
Given: D = 0.12 m, L = 0.24 m, d_{s} = 8 cm = 0.08 m, L_{S} = 4 m, H_{S} = 3.5 m, H_{at} = 10.35 m, H_{sep} = 2.55 m, r = 0.24/2 = 0.12 m
Now, at maximum speed, separation occurs at the beginning of the suction stroke.
For this condition, Pressure head in the cylinder = H_{a t}-H_{s}-h_{s max}=H_{\mathrm{sep}}
or 10.35\,-\,3.5\,-\,h_{\mathrm{smax}}=2.55
or h_{s\mathrm{max}}=10.35-3.5-2.55=4.3~{\mathrm{m}}^{2}
or 4.3={\frac{l_{s}}{g}}{\frac{A}{a_{s}}}r\omega^{2}
Now, a_{s}={\frac{\pi}{4}}\,(0.08)^{2}=0.005026\,\mathrm{m}^{2}
A={\frac{\pi}{4}}\,(0.12)^{2}=0.01131\,\mathrm{m^{2}}and \omega={\frac{2\pi N}{60}}
Substituting the values of all parameters in Eq. (i), we get
4.3={\frac{4}{9.81}}\times{\frac{0.01131}{0.005026}}\times0.12\times{\left\lgroup{\frac{2\pi N}{60}}\right\rgroup }^{2}Solving for N, we get
N = 59.613 rpm