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Total Dynamic Head Calculator

Pump-selection TDH from the three components: static lift, Hazen-Williams pipe friction, and fitting minor losses. Enter flow, pipe geometry, C-factor, and ΣK; the calculator returns each component, the total, and a velocity check against the 2–8 ft/s force-main range.

gpm
ft
ft
in
— (PVC 150, lined DI 140, old CI 100)
— (itemize fittings here)
—ft/s
——
—ft
—ft
—ft
—hp

Static head is the elevation difference between the pumping water level and the discharge point (use the wet-well low level for the conservative TDH case). Hazen-Williams applies to water at ordinary temperatures in turbulent flow; for other fluids use Darcy-Weisbach. In SI, friction uses hf = 10.67·L·Q1.852/(C1.852·D4.87) with Q in m³/s and D in m.

$$ TDH = H_s + \frac{10.44\,L\,Q^{1.852}}{C^{1.852}\,d^{4.87}} + \Sigma K \frac{V^2}{2g} $$
Hs static lift · L pipe length (ft) · Q flow (gpm) · C Hazen-Williams coefficient · d inside diameter (in) · ΣK summed fitting coefficients · V velocity.

Hazen-Williams C for common force-main materials

Design C-factors
Pipe materialC (new)C (design/aged)
PVC / HDPE150–155150
Ductile iron, cement-mortar lined140–150140
Steel, new welded140–145130
Cast iron, unlined, 20+ yr—80–110
Concrete / cylinder pipe135–140130

Worked example

Example — sewage force main

Given: Q = 800 gpm, static lift 45 ft, 2,400 ft of 8-inch lined DI (C = 140), ΣK = 5.0 from station piping.
V = (800/448.8) / (π/4·(8/12)²) = 1.78 / 0.349 = 5.1 ft/s ✓ (within 2–8 ft/s)
hf = 10.44 × 2400 × 8001.852 / (1401.852 × 84.87) ≈ 25.4 ft (≈ 10.6 ft per 1,000 ft)
hm = 5.0 × 5.1²/64.4 = 2.0 ft
TDH = 45 + 25.4 + 2.0 ≈ 72 ft · WHP = 800 × 72/3960 = 14.6 hp → at 75% pump efficiency, BHP ≈ 19.4 hp

References: Hazen, A. & Williams, G.S. (1920). Hydraulic Tables, 3rd ed. GLUMRB (2014). Recommended Standards for Wastewater Facilities (Ten-State Standards), §48. Sanks, R.L. et al., Pumping Station Design, 3rd ed., Butterworth-Heinemann.

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