Calculation of centrifugal pump power and efficiency

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I. Formula for calculating the shaft power of a centrifugal pump:
P = Flow rate × Head × 9.81 × Specific gravity of the fluid ÷ 3600 ÷ Pump efficiency
The unit of flow rate is cubic meters per hour; the unit of head is meters.
P = 2.73HQ/η, where H represents the head in meters, Q represents the flow rate in m3/h, and η represents the pump efficiency. P represents the shaft power in KW. In other words, the shaft power of the pump is given by P = ρgQH/1000η (kW), where ρ = 1000 Kg/m3, g = 9.8. The unit of specific gravity is Kg/m3, the unit of flow rate is m3/h, and the unit of head is meters. 1 Kg equals 9.8 Newtons.
Therefore, P = Specific gravity × Flow rate × Head × 9.8 Newtons/Kg = Kg/m3 × m3/h × m × 9.8 Newtons/Kg = 9.8 Newtons × m / 3600 seconds = Newtons × m / 367 seconds = Watts / 367. The above explanation clarifies the origins of the units. This formula is used to calculate the power required for water transfer; the shaft power is then divided by the efficiency to obtain the actual power needed.
Let Ne be the shaft power, P be the motor power, and K be a coefficient (the reciprocal of efficiency).
Motor power P = Ne × K (K takes different values depending on Ne; see the table below):
Ne ≤ 22: K = 1.25
22 < Ne ≤ 55: …

II. Formula for calculating the shaft power of a slurry pump:
Flow rate Q: m3/h
Head H: meters of water
Efficiency n: %
Density of the slurry A: Kg/m3
Shaft power N: KW
N = H × Q × A × g / (n × 3600)
The motor power also needs to take into account the transmission efficiency and safety factors. Generally, 1 is used for direct connection, 0.96 for belt drive, with a safety factor of 1.2. III. Pump efficiency and its calculation formula: It refers to the ratio of the pump’s effective power to its shaft power. η=Pe/P The power of a pump generally refers to the input power, that is, the power transmitted from the prime mover to the pump shaft; hence it is also known as shaft power, denoted by P. 　　Effective power is equal to the product of the pump’s head, mass flow rate, and gravitational acceleration. 　　Pe=ρg QH (W) or Pe=γQH/1000 (KW). ρ: the density of the liquid pumped by the pump (kg/m3); γ: the specific weight of the liquid pumped by the pump, γ=ρg (N/m3); g: the acceleration due to gravity (m/s). Mass flow rate: Qm=ρQ (t/h or kg/s). IV. Introduction to the efficiency of water pumps. What is pump efficiency? What is the formula for it? Answer: It refers to the ratio of the effective power of the pump to its shaft power. η=Pe/P The power of a pump generally refers to the input power, that is, the power transmitted from the prime mover to the pump shaft; hence it is also known as shaft power, denoted by P. 　　Effective power is equal to the product of the pump’s head, mass flow rate, and gravitational acceleration. 　　Pe=ρg QH W or Pe=γQH/1000 (KW) 　　ρ: Density of the liquid pumped by the pump (kg/m3) 　　γ: Specific weight of the liquid pumped by the pump; γ=ρg (N/m3) 　　g: Acceleration due to gravity (m/s) 　　Mass flow rate: Qm=ρQ t/h or kg/s