How it works — TDH in four steps
Total dynamic head is the net head the pump must add: everything upstream and downstream that is not the pump itself. Build it once, in order — elevation difference, surface pressure difference, then every friction and minor loss between the two liquid surfaces — and the pump duty is fixed.
1 · Total dynamic head — two equivalent formulations
Gauge-difference method — take pressures at the two liquid surfaces (gauge, so atmospheric cancels):
$$TH=\frac{p_{d}-p_{s}}{\rho g}\;+\;(Z_{d}-Z_{s})\;+\;\frac{V_{d}^{2}-V_{s}^{2}}{2g}\;+\;\Sigma h_{f}$$Arbitrary-point method — write the total head at any one section, \(H=p/\rho g+Z+V^{2}/2g\); then \(TH=H_{\text{discharge}}-H_{\text{supply}}\). Both routes give the same number when applied consistently — a useful cross-check on real drawings.
US shortcut for a gauge pressure: \(H(\text{ft}) = 2.31\,p(\text{psi})/SG\). The velocity-head term is zero when both surfaces are large and open, as in most tank-to-tank systems — this tool omits it and lets you fold it into the friction terms when it matters.
2 · From TDH to shaft power
\(Q\) is the design flow, \(\eta\) the pump efficiency at that duty (not the BEP maximum), and \(SG\) the specific gravity at pumping temperature. Power scales directly with gravity — a 0.8 SG crude needs 20% less shaft power than water at the same Q·TH.
3 · Motor selection — service factor by power band
The motor target is \(BHP\times SF\), snapped up to the nearest standard rating. Recommended service factor by continuous shaft-power band (1.0–1.5 range):
$$\begin{array}{lccc} \text{BHP band} & <1 & 1\text{–}5 & 5\text{–}20 \; (20\text{–}150,\; >150)\\[2pt] \text{SF} & 1.50 & 1.25 & 1.20\;(1.15,\;1.10) \end{array}$$A motor may briefly deliver its service-factor power, but at higher winding temperature — size for continuous duty at nameplate, never planning to live on the service factor.
4 · Margin verdict (🟢🟡🔴)
With \(\text{margin}=\dfrac{\text{motor rating}}{BHP}-1\):
- 🔴 margin < 10% — motor rides at or above nameplate at design duty; any head or viscosity excursion overloads it. Go one rating up.
- 🟢 margin 10–25% — the healthy band: covers head scatter, wear and SG drift without wasting capacity.
- 🟢 margin 25–50% — acceptable, usually the price of the next standard rating up; fine, just not free.
- 🟡 margin > 50% — oversized selection: motors lose efficiency and power factor well below nameplate load; check if a smaller frame fits.
Worked example
Suction-liquid level −5 ft, discharge-liquid level +50 ft (so 55 ft of static lift), receiving-vessel gauge pressure 100 psi, SG 0.8, design flow 1,000 gpm, suction friction 3 ft, discharge friction 25 ft. Pressure head: \(2.31\times100/0.8=288.8\) ft. Then \(TH = 55 + 288.8 + 3 + 25 = \mathbf{372\ ft}\). At \(\eta=70\%\): \(BHP = 1000\times372\times0.8/(3960\times0.70) = \mathbf{107.3\ hp}\). Service-factor band 20–100 hp gives SF 1.15 → target 123.4 hp → snap to the 125 hp standard rating → margin 16.5% 🟢.
Symbol table
| Symbol | Meaning | Units |
|---|---|---|
| \(Q\) | design flow rate | gpm / m³/h |
| \(TH\) | total dynamic head | ft / m |
| \(Z_s,\,Z_d\) | suction / discharge liquid-surface elevation | ft / m |
| \(p_s,\,p_d\) | surface gauge pressure, suction / discharge vessel | psi / kPa |
| \(\Sigma h_f\) | sum of friction & minor losses (suction + discharge) | ft / m |
| \(SG\) | specific gravity at pumping temperature | — |
| \(\eta\) | pump efficiency at duty | % |
| \(BHP\) | shaft (brake) power | hp / kW |
| \(SF\) | motor service factor | — |
Engineering criteria applied
- Static + pressure head is flow-independent — it forms the system-curve floor; friction grows with \(Q^{2}\) around the design point.
- Service factor is not spare capacity — continuous load above nameplate is not permitted; the margin verdict turns red below 10%.
- Standard ratings only — the tool snaps the motor target up to a standard NEMA/IEC frame power; ratings between standard frames round up, never down.
- Gravity check — if computed TH ≤ 0 the system flows by gravity; a pump adds nothing (and a throttle or siphon breaker may be needed).