How to use this calculator
- Measure the static lift. Pump-off liquid level up to the highest point before the discharge turns down.
- Build the equivalent length. Straight discharge run plus the equivalent length of every elbow, check valve and gate valve.
- Read TDH and the scour check. The calculator adds friction and any discharge pressure, and flags discharge velocity below 2 ft/s.
- Read the pump curve at TDH. The flow at that head is what the pump delivers — carry it to the sump-pump-capacity screen.
How it works
A pump moves liquid against three things: the height it must lift it, the friction of the pipe, and any pressure it discharges into. Add them and you have the head to size against —
TDH = H_static + H_friction + H_pressure · H_friction = 10.67·L·Q^1.852 / (C^1.852·d^4.87) · v = Q/A ≥ 2 ft/s
The friction term is Hazen-Williams, the plumbing-standard relation for water and sewage; the velocity check is the scour floor that keeps solids moving. The general pipe-run version (Darcy, Reynolds, pressure drop) is the pipe flow pressure drop calculator, the basin-cycling side is the sump pump capacity calculator (which takes this TDH's flow-at-head as its input), and the suction-side margin is the pump NPSH calculator.
Worked example
Verified against the live calculator
A sewage ejector pumping 40 GPM up 12 ft
through 100 ft equivalent length of 2 in
pipe, C = 120, open discharge:
H_f ≈ 4.0 ft · TDH = 12 + 4.0 = 16.0 ft · v = 3.8 ft/s (≥ 2 ft/s scour) ✓
Read the pump curve at 16 ft, not 12 — the friction is
a third of the lift again. And the discharge holds 3.8 ft/s, well
above the scour floor: solids stay suspended. Move that same 40 GPM
to a 3 in pipe "to be safe" and velocity drops to
0.9 ft/s — below scour, and the line silts up. Bigger
is not safer here.
Frequently asked questions
How do you calculate total dynamic head for a pump?
TDH = static lift + friction head + discharge pressure head. For 40 GPM lifted 12 ft through 100 ft of 2 in pipe (Hazen-Williams C = 120), friction adds about 4 ft, so TDH ≈ 16 ft. You then read the pump curve at 16 ft to find the flow that pump actually delivers.
What is the minimum velocity in a sewage or sump discharge pipe?
2 ft/s (0.61 m/s) — the scouring velocity. Below it, solids settle out and the pipe clogs. 40 GPM in 2 in pipe runs about 3.8 ft/s, comfortably above; the same flow in 3 in pipe drops below 2 ft/s, which is why oversizing the discharge causes blockages.
Why use TDH instead of just the static lift?
Because a pump fights friction as well as gravity. A 12 ft lift can need a 16 ft pump once pipe and fitting friction are counted — and on a long or small-bore run, friction can exceed the static lift entirely. Sizing on static lift alone undersizes the pump and starves the flow.
How do I account for elbows and check valves?
Add their equivalent length to the straight run. Each fitting behaves like so many feet of straight pipe (from a fitting-equivalent chart) — a check valve and a couple of elbows on a short lift can double the effective length, so they belong in the friction calculation, not as an afterthought.
Method & assumptions
- TDH = static + Hazen-Williams friction + discharge pressure head. Velocity head is small for these systems and folded into the friction allowance, not added separately (standard plumbing-engineer practice).
- Equivalent length is user-entered and must already include fitting allowances; the calculator does not embed a fitting-equivalent table.
- The 2 ft/s scour floor is the widely-adopted minimum for pumped sewage/sump discharge; the adopted plumbing code and the pump manufacturer govern the final design.
- Hazen-Williams suits water and domestic sewage near ambient temperature; high-viscosity or high-solids slurries need their own method. Pump curve, NPSH and basin cycling are separate checks.