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Minimum volume of sump volume for pumps
Maximum pumping rate = QP
Volume of sump = V
Inflow Rate = Qi
Cycle Time Tc= t1 + t2
t1 = V / QP - Qi
t2 = V / Qi
Tc = Minimum Cycle Time
V = Tc / {1/ (QP - Qi) + 1 / Qi}
For Minimum Volume,
δV / δQi = δ/δQi[Tc / {1/ (QP - Qi) + 1/ Qi}]
Minimum Volume occurs when Qi = 0.5Qp
Hence, Minimum Volume of sump = Tc / {1/ (QP - 0.5Qp) + 1/0.5Qp}
= Tc QP / 4
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