How to Calculate Total Dynamic Head (TDH) Step by Step

Key Formula / Key Facts Box

Overview — What It Is and Why It Matters

Total Dynamic Head (TDH) is the sum of all energy terms a pump must supply to move a fluid from the suction side to the discharge side at a specified flow rate. It combines static elevation, pressure differentials, friction losses in the piping, and the fluid’s velocity head, while subtracting any beneficial suction head. Accurate TDH calculation is the cornerstone of pump selection, motor sizing, and system efficiency. Under‑estimating TDH can cause cavitation, premature wear, or failure to meet flow requirements; over‑estimating leads to oversized equipment, higher capital cost, and wasted energy.

The Method — Derivation and Variants

The Bernoulli equation, augmented with a head‑loss term, provides the theoretical basis. For a steady incompressible flow between point 1 (suction) and point 2 (discharge):

[ frac{p_1}{rho g}+frac{v_1^2}{2g}+z_1 + h_p = frac{p_2}{rho g}+frac{v_2^2}{2g}+z_2 + h_f ]
where (h_p) is the head added by the pump, (h_f) is the friction loss, (z) are elevations, and the velocity terms are (v^2/2g). Rearranging yields the TDH expression shown above.

Two common variants exist:

• SI version – uses metres for all head terms and the pressure head is expressed as (Delta p / (rho g)).
• US‑customary version – head is in feet; pressure head is derived from pressure difference (psi) using the conversion (1,text{psi}=2.31,text{ft of water}) for water at 4 °C.

Constants such as (g = 9.80665,text{m/s}^2) (SI) or (32.174,text{ft/s}^2) (US) ensure dimensional consistency. The velocity head is often negligible for low‑velocity, large‑diameter lines and may be omitted in preliminary sizing.

Worked Example

Scenario (US): A water‑cooling system draws from a tank 10 ft below the pump (suction head = 10 ft). The pump discharges to a storage tank 30 ft above the pump. Pipe length = 150 ft of 2‑in. schedule 40 steel (Darcy friction factor ≈ 0.019). Flow rate = 500 gpm. Desired discharge pressure = 50 psi.

1. Static head: 30 ft (elevation) – 10 ft (suction) = 20 ft.
2. Pressure head: (50,text{psi}times2.31 = 115.5,text{ft}).
3. Velocity head: (v = Q/A = 500,text{gpm} ÷ (pi D^2/4)). Convert 500 gpm → 1.11 ft³/s. Pipe ID ≈ 0.067 ft, area = 0.0035 ft², so (v≈317,text{ft/s}). Velocity head = (v^2/(2g) = 317^2/(2×32.174)≈1560,text{ft}). In practice, this high value indicates the line is undersized; designers usually include a reducer or increase diameter. For illustration we keep it.
4. Friction head (Darcy‑Weisbach): (h_f = ffrac{L}{D}frac{v^2}{2g}). (L=150,ft, D=0.067,ft, f=0.019). (h_f =0.019×(150/0.067)×(317^2/(2×32.174))≈4,300,ft).
5. TDH = static + pressure + velocity + friction = 20 + 115.5 + 1560 + 4300 ≈ 5,996 ft.

Result: The pump must be capable of ~6,000 ft of head at 500 gpm – a clear sign the pipe diameter is too small for this application.

Scenario (SI): Same system, but expressed in metres. Tank 3 m below pump, discharge 9 m above pump, pipe 45 m of DN 50 PVC (roughness 0.0015 mm, (f≈0.022)). Flow = 31 L/s (≈ 0.031 m³/s). Desired discharge pressure = 345 kPa.

1. Static head: 9 m – 3 m = 6 m.
2. Pressure head: (Delta p/(rho g) = 345,000,text{Pa}/(1000,text{kg/m³}×9.80665)≈35.2,text{m}).
3. Velocity: Area = (π(0.05)^2/4 = 0.00196,text{m}^2). (v = 0.031/0.00196 ≈ 15.8,text{m/s}). Velocity head = (v^2/(2g) = 15.8^2/(2×9.80665)≈12.7,text{m}).
4. Friction head: (h_f = ffrac{L}{D}frac{v^2}{2g}=0.022×(45/0.05)×12.7≈ 251,text{m}).
5. TDH = 6 + 35.2 + 12.7 + 251 ≈ 305 m.

The SI example shows a more realistic head (≈ 305 m) for a properly sized pipe, confirming the pump selection process.

Calculator

For quick on‑line computation, use the free tool at http://pumpcalcs.com/calculators/total-dynamic-head/.

Reference Values & Typical Ranges

• Domestic water supply: 30–80 ft (9–25 m) TDH.
• Industrial cooling towers: 100–300 ft (30–90 m) TDH.
• High‑rise fire‑suppression systems: up to 1,200 ft (366 m) TDH.
• Typical pipe‑friction factor for steel (new) at turbulent flow: 0.015–0.025.
• Velocity head becomes <10 % of total head when (v < 5,text{ft/s}) (1.5 m/s) in large ducts.

Sources: ANSI/HI 9.6‑1‑2014, ISO 9906:2012, and Munson et al., “Fundamentals of Fluid Mechanics.”

Application Guidance

When sizing a pump, start with a conservative TDH estimate; add 10‑15 % margin for future flow increases or fouling. Verify that the selected pump’s NPSH available exceeds the required NPSH by at least 1 m (3 ft) to avoid cavitation. In looped systems, consider the effect of parallel branches on friction loss – use the equivalent length method or hydraulic software for complex networks.

Common Mistakes, Limits & Safety Notes

1. Unit mix‑up: Plugging psi directly into a feet‑based formula without conversion yields a 2.31× error.
2. Ignoring suction head: Treating suction elevation as zero can underestimate cavitation risk.
3. Neglecting velocity head in high‑speed lines: For diameters  10 ft/s, the velocity head may exceed 5 % of total head.
4. Using a single‑value friction factor: Roughness and Reynolds number vary with temperature and flow; recompute (f) for each case.
5. Assuming laminar flow in large pipes: Most industrial systems operate turbulent; laminar formulas underestimate loss.
6. Over‑sizing pump: Leads to low operating point, reduced efficiency, higher energy cost, and possible thermal overload.
7. Exceeding pump’s rated TDH: Can cause motor over‑current, seal failure, and premature bearing wear.
8. Safety oversight: Always verify that the pump’s maximum allowable suction lift does not exceed the system’s static lift, especially for vertical installations.