Pump Total Dynamic Head (TDH) Calculation

What is Pump Head?

In the world of centrifugal pumps, engineers rarely talk about "pressure." Instead, they talk almost exclusively about Head.

Head is a measure of energy expressed as a height of a fluid column. If a pump has a Total Dynamic Head (TDH) of 50 meters, it means the pump imparts exactly enough kinetic energy into the fluid to shoot a column of that specific fluid straight up into the air to a height of exactly 50 meters.

Why use Head instead of Pressure?
A centrifugal pump is a kinetic machine. It accelerates fluid outward using a spinning impeller. The velocity it imparts to the fluid is independent of the fluid's density. Therefore, a pump running at 3000 RPM might generate exactly 50 meters of head, regardless of whether it is pumping water, heavy crude oil, or light gasoline. However, the pressure at the pump discharge will be vastly different for each fluid because pressure depends on density!

The Total Dynamic Head (TDH) Formula

The Total Dynamic Head is the total equivalent height that a fluid is to be pumped, taking into account friction losses in the pipe. It is calculated using the modified Bernoulli equation:

$$ TDH = (h_{d} - h_{s}) + (Z_{d} - Z_{s}) + (h_{fd} + h_{fs}) $$

Let's break down the three primary components:

1. Static Pressure Head $(h_d - h_s)$

This is the difference in absolute pressure between the destination vessel ($P_d$) and the suction vessel ($P_s$), converted into meters of fluid.

$$ h = \frac{P \cdot 10^5}{\rho \cdot g} \text{ (for P in bar, } \rho \text{ in } kg/m^3 \text{)} $$

If you are pumping from a tank at atmospheric pressure (1.013 bar a) into a pressurized reactor at 10 bar a, the pump must overcome this massive pressure differential.

2. Elevation Head $(Z_d - Z_s)$

This is simply the physical change in elevation (in meters) from the liquid level in the suction tank to the highest liquid level in the discharge tank. If you are pumping water up to a cooling tower basin 25 meters in the air, the elevation head is 25 m.

3. Friction Head $(h_{fd} + h_{fs})$

As the fluid moves through the suction and discharge pipes, it loses energy due to friction against the pipe walls and turbulence through elbows, valves, and strainers. This is calculated using the Darcy-Weisbach equation:

$$ h_f = f \cdot \frac{L}{D} \cdot \frac{v^2}{2g} $$

Where $f$ is the Darcy friction factor, $L$ is equivalent pipe length, $D$ is internal diameter, and $v$ is fluid velocity.

Worked Example

Scenario: Pumping water ($\rho = 998 \ kg/m^3$) from an atmospheric tank ($Z_s = 2 \text{ m}$) to a pressurized boiler ($P_d = 5 \text{ bar a}$, $Z_d = 15 \text{ m}$). The friction losses are calculated as $h_{fs} = 0.5 \text{ m}$ and $h_{fd} = 4.0 \text{ m}$.

Step 1: Calculate Pressure Head

Suction is atmospheric (1.013 bar a). Discharge is 5.0 bar a. The difference is 3.987 bar.

$$ h_{press} = \frac{3.987 \times 10^5}{998 \times 9.81} = 40.7 \text{ m} $$

Step 2: Calculate Elevation Head

$$ h_{elev} = 15 - 2 = 13.0 \text{ m} $$

Step 3: Sum the TDH

$$ TDH = 40.7 + 13.0 + 4.5 = 58.2 \text{ m} $$

The pump must be selected to deliver a Total Dynamic Head of exactly 58.2 meters at the required flow rate.