Two gauge readings, a tape measure, and the trade size are enough. The room solves Hazen-Williams backward for the flow the line can deliver; every quantity can explain its own relationship.
Model 08 · Open to everyone
Head budget11.6 ftPressure difference minus the climb
Velocity7.7 ft/sWithin the erosion guideline
Friction gradient5.0 psi/100ftSpending rate along the run
Head budget and deliveryLive
Diagram controlsInspect a live quantity
Supporting readoutsLine quantitiesOpen
Actual inner diameter1.985in
Hazen-Williams C140
Straight run100ft
Fittings equivalent0.0ft
Effective run100.0ft
Operating curveCapacity versus diameter1.985 in selected
Deliverable flow vs inner diameter
Drag the plot to set the bore. Capacity climbs with the 2.63 power of diameter, which is why one trade size up ends most arguments.
Reference
How the pipe flow model works
A pipe's capacity is a budget question. The pressure difference between two gauges converts to feet of head, any climb takes its share, and whatever remains is spendable on friction. Hazen-Williams solved backward gives the largest flow that budget can carry, which is the deliverable capacity of the line.
The instrument above solves the line live. The governing relationships are written out below.
Available head
ha=2.31(Pin−Pout)−Δz
The head budget. Pressure difference converts to feet of water (2.31 ft per psi), less the climb. Whatever remains is spendable on pipe friction; zero or less means the line cannot deliver the required outlet pressure at any flow.
P inlet
Inlet gauge pressure (psig)
P outlet
Required outlet gauge pressure (psig)
Elevation gain
Rise from inlet to outlet; negative when the run drops (ft)
Assumes
Water near 60°F (2.31 ft of water per psi)
Gauge pressures read against the same reference state
Capacity
Q=(0.002083L(100/C)1.852had4.8655)1/1.852
Hazen-Williams solved for flow: the largest Q whose friction over the run exactly spends the available head. This is the deliverable capacity of the line, the number that sizes the equipment downstream.
0.002083 handbook coefficient (the 4.52 psi-basis form differs about 1%)
C reflects the pipe's in-service condition
Velocity
V=d20.4085Q
Bulk velocity at capacity flow. Above about 8 ft/s, erosion and noise risk climbs (copper guidance runs 5 to 8 ft/s). A warning to size up, not a hard stop.
Q
Flow through the pipe (gpm)
Inner diameter
Actual inner diameter (in)
Assumes
One 8 ft/s warning threshold across materials in v1
Worked example
Take the room's default case: a 2 inch line (1.985 inch inner diameter) running 100 ft on level ground, 60 psi at the inlet gauge, 55 psi required at the outlet, and a Hazen-Williams C of 140.
Available head
11.6 ft
Deliverable flow
74 gpm
Velocity at that flow
7.7 ft/s
Friction gradient
5.0 psi per 100 ft
Add elevation gain in the instrument and watch the climb eat the head budget before friction gets a turn. A line that cannot pay the climb delivers nothing.
Common questions
How much water can a pipe deliver?
As much as its head budget can pay for. The gauge pressure difference converts to feet of water at 2.31 ft per psi, the elevation gain is subtracted, and the capacity is the largest flow whose friction over the run spends exactly what remains.
What does the Hazen-Williams C value mean?
C grades the pipe's interior condition. Smooth new pipe runs high, old rough pipe runs low, and the model uses the in service value directly in the friction fit, so the same trade size can carry very different flows at different ages.
When is velocity too high?
Above about 8 ft/s the risk of erosion and noise climbs, with copper guidance running 5 to 8 ft/s. The room treats it as a warning to size up, not a hard stop.