Centrifugal Pump Head and Power Calculation for an Overhead Tank
Choosing a pump means answering two questions: how much water per second (discharge) and against how much resistance (head). Too small a pump never fills the tank; too large a pump wastes power and may run far from its best efficiency point. This article walks through a complete calculation for a typical building setup, a centrifugal pump lifting water from an underground sump to an overhead tank, and then checks suction conditions with NPSH.
What Makes Up Total Head
Head is energy per unit weight of liquid, expressed in metres. The pump must supply enough head to overcome everything between the sump surface and the tank inlet.
| Component | Meaning | How to find it |
|---|---|---|
| Static suction lift | Height from sump water level up to pump centreline | Measure on site |
| Static delivery head | Height from pump centreline to the outlet in the tank | Measure on site |
| Major (friction) loss | Friction along straight pipe | Darcy-Weisbach equation |
| Minor losses | Foot valve, bends, tees, valves, entry and exit | Sum of K times velocity head |
Total head H = H_static + h_f + h_minor Velocity V = Q / A Velocity head V^2 / (2g) Major loss h_f = f * (L / D) * V^2 / (2g) (f = Darcy friction factor) Minor loss h_m = (sum of K) * V^2 / (2g) Hydraulic power P_h = rho * g * Q * H Shaft power P_s = P_h / eta_pump Motor input P_in = P_s / eta_motor
Worked Example: Sump to Overhead Tank
Data: required flow 1.5 L/s (5.4 m^3/h), suction lift 3 m, delivery height 15 m above the pump, pipe inside diameter 40 mm, total pipe length 30 m, Darcy friction factor 0.02, sum of minor loss coefficients 5 (including the foot valve, elbows, a gate valve and the exit). Pump efficiency 60 percent, motor efficiency 85 percent.
Step 1: Velocity and velocity head
A = pi/4 * 0.04^2 = 1.2566e-3 m^2 V = 0.0015 / 1.2566e-3 = 1.194 m/s V^2 / 2g = 1.194^2 / 19.62 = 0.0726 m
Step 2: Losses
h_f = 0.02 * (30 / 0.04) * 0.0726 = 15 * 0.0726 = 1.09 m h_m = 5 * 0.0726 = 0.36 m
Step 3: Total head
H = (3 + 15) + 1.09 + 0.36 = 19.45 m (design for about 20 m)
Step 4: Power
P_h = 1000 * 9.81 * 0.0015 * 19.45 = 286 W P_s = 286 / 0.60 = 477 W P_in = 477 / 0.85 = 561 W
A 0.75 kW (1 HP) pump set covers this duty with a reasonable margin. When you look at a catalogue, pick a model whose head-discharge curve passes through about 20 m at 5.4 m^3/h, preferably near its best efficiency point.
Checking Suction with NPSH
If pressure at the pump inlet falls below the vapour pressure of water, bubbles form and collapse violently on the impeller. This is cavitation, and it causes noise, vibration, loss of head and pitting. To avoid it, the net positive suction head available (NPSHa) must exceed the value the pump requires (NPSHr), given in the manufacturer's curve.
NPSHa = p_atm/(rho g) - suction lift - suction losses - p_vapour/(rho g) At sea level, water at about 30 C: p_atm/(rho g) = 10.33 m p_vapour/(rho g) = about 0.43 m suction lift = 3.0 m suction losses = 0.5 m (assumed) NPSHa = 10.33 - 3.0 - 0.5 - 0.43 = 6.4 m
Most small domestic pumps need well under this, so the installation is safe. At higher altitudes, with hot water or with long, narrow suction pipes, NPSHa drops quickly. This is why suction pipes are kept short, straight and often one size larger than the delivery pipe.
Changing Speed: The Affinity Laws
For the same centrifugal pump running at a different speed, discharge, head and power scale as shown. They are used when pumps are driven by variable frequency drives.
| Quantity | Proportional to | Speed doubled from 1440 to 2880 rpm |
|---|---|---|
| Discharge Q | N | 2 times |
| Head H | N^2 | 4 times |
| Power P | N^3 | 8 times |
The cube law for power is why reducing pump speed by just 20 percent can cut power by nearly half (0.8 cubed is 0.512).
Common Mistakes
- Using only the vertical height and ignoring friction, which leads to undersized pumps in long pipe runs.
- Mixing Darcy and Fanning friction factors; the Fanning value is one quarter of Darcy.
- Sizing the motor on hydraulic power without dividing by pump and motor efficiency.
- Placing the pump too high above the sump so that suction lift exceeds what NPSH allows.
- Leaving a large safety margin on head, which pushes the pump to run far right of its best efficiency point.
Summary
Total head is static lift plus pipe friction plus fitting losses. Multiply it by rho g Q to get hydraulic power, then divide by efficiencies to size the motor. Always check NPSH on the suction side and use the affinity laws when speed changes. The same method scales from a 1 HP domestic pump to large municipal pumping stations.