Pump Head (TDH) and Pump Power Calculator
How the formula works
Total dynamic head (TDH) is the total height of water that a pump must overcome. It includes the vertical lift, the friction in the pipes and fittings, the velocity of the water, and any pressure needed at the outlet. The pump you select must deliver the required flow at this head. This calculator finds the TDH from the pipe and the levels, and it can also find the pump power and the motor size.
Total dynamic head
TDH = Static head + Pipe friction loss + Fittings loss + Velocity head + Residual pressure head
Pipe friction loss (Hazen-Williams, SI units)
hf = 10.67 × L × Q1.852 ÷ (C1.852 × D4.87)
Other terms
Velocity v = Q ÷ (π ÷ 4 × D²)
Velocity head = v² ÷ (2 × 9.81)
Fittings loss = Pipe friction loss × Allowance %
Residual pressure head (m) = Pressure (bar) × 10.197
Design head = TDH × (1 + Safety margin %)
Pump power
Hydraulic power (kW) = 9.81 × Q × H
Pump shaft power = Hydraulic power ÷ Pump efficiency
Motor input power = Pump shaft power ÷ Motor efficiency
Suggested motor = next standard size above 1.15 × Pump shaft power
Where
- hf = friction head loss in metres
- L = total pipe length in metres
- Q = flow rate in m³/s
- C = Hazen-Williams roughness coefficient of the pipe
- D = pipe inside diameter in metres
- H = design head in metres
- Static head = vertical height from the suction water level to the discharge point or the water level in the delivery tank
Typical Hazen-Williams C values
- PVC, CPVC or HDPE: about 150
- Copper or new stainless steel: about 140
- Ductile iron, cement lined: about 130
- Steel, new: about 120
- GI or old steel: about 100
Typical efficiencies
Small pumps often have an efficiency of 50 to 65 %, and larger pumps 70 to 80 %. Motor efficiency is commonly 85 to 96 %. Use the pump curve and the motor data sheet for the actual values.
How to use the calculator
- For head, select Find pump head (TDH) and enter the flow, pipe diameter, static head, pipe length, material, fittings loss and safety margin.
- Enter the residual pressure only if the outlet needs pressure, such as a spray, a hydrant or a pressurised system. Leave it empty for an open tank.
- For power, select the pump efficiency and the motor efficiency. In the second mode, enter the flow and the head directly.
- Click Calculate. You can then download the result as a PDF.
Important notes
- The formula is for clean water in full pipes. It is not for other liquids or for partly filled pipes.
- Check the pump curve and make sure the duty point (flow and head) lies near the best efficiency point.
- For suction lift, also check the NPSH available against the NPSH required by the pump.
Worked example
Example 1: Water supply pump with TDH and motor size
A pump delivers 25 m³/h through an 80 mm PVC pipe, 100 m long (C = 150). The static head is 20 m. Use a fittings allowance of 20 %, a safety margin of 10 %, no residual pressure (open tank), a pump efficiency of 70 % and a motor efficiency of 92 %.
Step 1: Flow and velocity
Q = 25 ÷ 3600 = 0.006944 m³/s
v = 0.006944 ÷ (π ÷ 4 × 0.08²) = 1.38 m/s
Step 2: Pipe friction loss
hf = 10.67 × 100 × 0.0069441.852 ÷ (1501.852 × 0.084.87) = 2.20 m
Step 3: Other heads
Fittings loss = 2.20 × 0.20 = 0.44 m
Velocity head = 1.38² ÷ 19.62 = 0.10 m
Step 4: TDH
TDH = 20 + 2.20 + 0.44 + 0.10 = 22.74 m
Design head with 10 % margin = 22.74 × 1.10 = 25.01 m (82.1 ft, 2.45 bar)
Step 5: Power
Hydraulic power = 9.81 × 0.006944 × 25.01 = 1.70 kW
Pump shaft power = 1.70 ÷ 0.70 = 2.43 kW
Motor input power = 2.43 ÷ 0.92 = 2.65 kW
Suggested motor: 1.15 × 2.43 = 2.80 kW, so the next standard size is 3 kW (4.0 HP)
Example 2: Pump with residual pressure
A pump delivers 50 m³/h through a 100 mm new steel pipe, 150 m long (C = 120). The static head is 30 m, the fittings allowance is 30 %, the outlet needs 2 bar, and the safety margin is 10 %.
Velocity = 1.77 m/s
Pipe friction = 6.08 m, fittings loss = 1.82 m, velocity head = 0.16 m
Residual pressure head = 2 × 10.197 = 20.39 m
TDH = 30 + 6.08 + 1.82 + 0.16 + 20.39 = 58.46 m
Design head = 58.46 × 1.10 = 64.30 m (211.0 ft, 6.31 bar)
Example 3: Pump power from flow and head
A pump delivers 30 m³/h at a head of 40 m. The pump efficiency is 70 % and the motor efficiency is 92 %.
Hydraulic power = 9.81 × (30 ÷ 3600) × 40 = 3.27 kW
Pump shaft power = 3.27 ÷ 0.70 = 4.67 kW
Motor input power = 4.67 ÷ 0.92 = 5.08 kW
Suggested motor: 1.15 × 4.67 = 5.37 kW, so the next standard size is 5.5 kW (7.4 HP)
Common mistakes
- Using only the static head. TDH must also include the friction loss, the fittings loss, the velocity head and the residual pressure.
- Using the pipe nominal size instead of the inside diameter. The inside diameter is smaller than the nominal size, and friction rises sharply when the diameter falls.
- Forgetting the full pipe length. Add the suction pipe and the delivery pipe, not only the delivery side.
- Ignoring fittings and valves. Bends, valves and strainers add real loss. A 20 to 30 % allowance is common for a simple layout, more for a complex one.
- Mixing pressure and head. 1 bar is about 10.2 m of water head. Convert the pressure before adding it to the head.
- Using a very high flow velocity. Velocity above about 3 m/s causes noise, wear and high friction loss. Choose a larger pipe.
- Selecting the motor at exactly the shaft power. Leave a margin for the motor service factor. This calculator suggests the next standard size above 1.15 times the shaft power.
- Not checking the pump curve. The pump must give the required flow at the calculated head, near its best efficiency point.
- Ignoring NPSH on suction lift. If the pump is above the water level, check that the NPSH available is higher than the NPSH required.
Frequently asked questions
What is total dynamic head (TDH)?
It is the total head a pump must produce to move water at the required flow. It is the sum of the static head, the pipe and fittings friction loss, the velocity head and the residual pressure head.
How do I calculate pump head?
Add the static head (the vertical lift), the friction loss in the pipe and fittings, the velocity head, and the pressure needed at the outlet in metres. The calculator does this for you from the flow, pipe size, length and material.
What is static head?
It is the vertical distance from the water level on the suction side to the discharge point or to the water level in the delivery tank.
What is the Hazen-Williams formula?
It is a common formula for friction loss of water flowing in a full pipe. It uses the flow, the pipe length and diameter, and a roughness coefficient C that depends on the pipe material.
What C value should I use?
Use about 150 for PVC, CPVC and HDPE, 140 for copper, 130 for cement lined ductile iron, 120 for new steel, and 100 for GI or old steel. Older pipes have lower values.
How do I calculate pump power in kW?
Hydraulic power (kW) = 9.81 × flow (m³/s) × head (m). Divide by the pump efficiency for the shaft power, and by the motor efficiency for the electrical input power.
How do I choose the motor size?
Take the pump shaft power, add about 15 % margin, and select the next standard motor size. For example, a shaft power of 4.67 kW needs 5.37 kW, so a 5.5 kW motor is selected.
How do I convert bar to metres of head?
1 bar equals about 10.197 m of water. So a pressure of 2 bar equals about 20.4 m of head.
What safety margin should I add?
A margin of 5 to 15 % is common to cover pipe ageing and calculation uncertainty. Follow your project specification.
Can I use this for liquids other than water?
No. The formula and the power values are for clean water. Other liquids need their own density and viscosity data.
Does this replace pump selection?
No. It gives the duty point (flow and TDH). You must still select a pump from its curve, check the efficiency and the NPSH, and follow the manufacturer data.