Hydraulics
How much head your discharge line actually costs you
Total dynamic head is the whole reason a pump underperforms its box. It has two parts and they behave completely differently. The first is static lift — the vertical distance from the water in the basin to the point where the discharge finally releases. You cannot negotiate with it; it is set by where your basement is relative to where the water has to end up. The second is friction: the head the pump burns pushing water through pipe, elbows and the check valve. That part is entirely a function of choices somebody made, and it is frequently the cheapest improvement available anywhere in the system.
Break your discharge down
Total dynamic head at that flow
15.24 feet
7.0 ft of lift you cannot change, plus 8.24 ft of friction you probably can.
Biggest swing factor Pipe diameter. Head loss varies with roughly the inverse 4.87 power of the bore, so one nominal size up is not a marginal improvement — it is a different problem.
- Friction is 54% of your total head. That is pipe, not lift, and pipe is the cheap thing to change: stepping up one nominal size cuts friction by roughly two-thirds at the same flow.
Not included in this head figure
- Entrance and exit losses at the pit and the outlet, which are small next to lift and pipe friction.
- Any head added by a freeze plug, a partially blocked outlet, or ice at the termination — all of which can exceed the entire friction figure during the storm you care about.
- Head added by a backwater or anti-siphon device you have not told us about.
- The pressure needed to open the check valve itself, which manufacturers publish per valve and which we do not model.
Why one pipe size changes everything
At the 25 gallons per minute above, the same flow through three different pipe sizes loses head at wildly different rates. This is the whole argument for not reducing the discharge below the size of the pump's own outlet, which installers do surprisingly often because the smaller fitting was on the van.
| Nominal size | Actual bore | Friction per 100 ft | Relative to 1 1/4 in |
|---|---|---|---|
| 1 1/4 inch | 1.380 in | 7.96 ft | 1.00x |
| 1 1/2 inch | 1.610 in | 3.76 ft | 0.47x |
| 2 inch | 2.067 in | 1.11 ft | 0.14x |
Read the right-hand column carefully. Moving from a one-and-a-quarter inch line to a two inch line cuts friction to about 14 percent of what it was — not by a fifth, by a factor of several. On a long run that can be worth more delivered gallons than the next horsepower band up, at a fraction of the cost and with no increase in electricity or in cycling.
Elbows are pipe you did not know you had
A fitting is modelled as an equivalent length of straight pipe, because that is the tractable way to account for the head it costs. A 90-degree elbow behaves roughly like 30 pipe diameters of straight run; a 45 like 16; a swing check valve like 100; a spring-loaded check valve like 135, which is the price paid for the quiet.
Your 5 ninety-degree elbows, 2 forty-five-degree elbows and the spring check valve together add 36.5 feet of equivalent pipe to a 60-foot run. Put differently, the fittings are behaving like an extra 61 percent of pipe that nobody measured.
The practical consequence is not that elbows are bad — you cannot get out of a basement without turning — but that a route with two long sweeps beats a route with six tight turns, and that a pair of 45s costs less head than one 90 doing the same job.
The friction formula, written out
Friction here uses the Hazen-Williams equation in its United States customary form, which is the standard empirical relation for water in pipe at ordinary temperatures:
hf = 0.2083 × (100 / C)1.852 × Q1.852 / d4.8655
hf is head loss in feet per 100 feet of pipe, Q is flow in gallons per minute, d is the inside diameter in inches, and C is a roughness coefficient. The exponent on diameter is where the leverage lives: 4.8655 is why a modest increase in bore produces a dramatic reduction in loss.
We use C = 150. That is a value for new, smooth plastic pipe. Corrugated flexible discharge — the black ribbed hose sold for extending a sump line across a lawn — is very much rougher than this, and a long run of it can cost more head than the entire vertical lift of a typical basement.
Related tools
- Sizing calculator — combine this head with your measured inflow to get the full specification.
- Check valves and water hammer — why the 5.4 ft/s above matters at the moment the pump stops.
- Where the discharge may legally end — the constraint that often decides the route before hydraulics do.