Find the number of pumps required to take water from a deep well under a total head of 120 m

Question: Find the number of pumps required to take water from a deep well under a total head of 120 m. All the pumps are identical and are running at 800 rpm. The specific speed of each pump is given as 25 while the rated capacity of each pump is 0.16 m3/s

Solution: Given: total head h = 120 m
Speed, N = 800 rpm
Specific speed at each pump, Ns = 25
Rated capacity of each Pump, Q = 0.16 m^3/s
Let us assume, head developed by each pump is Hm
Specific speed, Ns = N (Q)^(1/2)/ (Hm)^(3/4)
25 = 800(0.16)^(1/2)/(Hm)^(3/4)
(Hm)^(3/4) = 800 (0.16)^(1/2)/25
(Hm)^(3/4) = 12.8
Hm = (12.8)^(4/3)
head developed by each pump
Hm = 29.94 m

Number of pumps required
= total head/head developed by each pump
= 120/29.94 = 4.008 = 4
4 numbers of pumps are required to lift water from deep well under a total of 120m

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