Pipe Flow Calculator - Flow Rate & Pressure Drop

Darcy-Weisbach

Pressure Drop, Flow Rate and Pipe Diameter modes, with the Darcy-Weisbach method

ΔP

pressure drop from friction

f

Darcy friction factor (below)

L

pipe length

D

inside diameter

v

mean velocity: flow ÷ (π × D² ÷ 4)

ρ

fluid density

Flow Rate and Pipe Diameter solve the same equation for the unknown by iteration.

Source: Uses the Darcy-Weisbach formula as EPA's EPANET 2.2 manual gives it, in Table 3.1 [1]. EPANET calls it the most theoretically correct headloss formula, for all liquids and flow regimes.

Friction factor

Pressure Drop, Flow Rate and Pipe Diameter modes, with the Darcy-Weisbach method

Re

Reynolds number

f

Darcy friction factor

μ

dynamic viscosity

ε

pipe roughness

f = 64 ÷ Re below Re 2,300; the Colebrook line from there, solved by iteration. EPANET instead interpolates from Re 2,000 to 4,000, so here f steps up by 70% or more as Re crosses 2,300 and can put the drop 60% or more above EPANET's in that band.

Source: The turbulent line is Colebrook's equation (1939) [3]; f = 64/Re for laminar flow is as EPANET 2.2 gives it [2]. The 2,300 boundary is CalcTrail's own; no publisher.

Hazen-Williams

Pressure Drop, Flow Rate and Pipe Diameter modes, with the Hazen-Williams method

ΔP

pressure drop from friction

C

Hazen-Williams roughness coefficient

L

pipe length, in m

D

inside diameter, in m

Q

flow rate, in m³/s

For water only, and developed for turbulent flow. C falls as a pipe ages; new pipe runs from 110 to 150 in EPANET's Table 3.2. C is limited to 50 to 160; the default is 140.

Source: Based on the Hazen-Williams form in EPA's EPANET 2.2 manual, Table 3.1, in SI units with the diameter exponent rounded from 4.871 to 4.87 [1].

Minor losses

Pressure Drop mode, with fittings added

K

one fitting's loss coefficient, times how many

v

mean velocity

90° elbow (short radius)

0.9

45° elbow

0.4

Tee, through the run

0.6

Tee, through the branch

1.8

Gate valve, open

0.2

Globe valve, open

10

Swing check valve, open

2.5

A fitting row keeps the K saved with it; picking a type fills in the value above. Fittings count only when solving for pressure drop.

Source: Uses EPA's EPANET 2.2 minor-loss formula and its Table 3.3 coefficients [1]. For the reducer's 0.5, no primary source found.

Head loss and hydraulic power

Pressure Drop, Flow Rate and Pipe Diameter modes

h

head loss, in meters of the fluid

ΔP

total pressure drop

g

standard gravity, 9.80665 m/s²

The hydraulic gradient is h ÷ L, and the relative roughness ε ÷ D.

Source: Standard formulas; no single publisher. Standard gravity is the value the SI Brochure records from the 3rd CGPM (1901) [4].

Fluid and pipe presets

Every mode

Water, 20 °C

1,000 kg/m³, 0.001 Pa·s (NIST: 998.2, 0.0010016)

Water, 60 °C

983 kg/m³, 0.00047 Pa·s (NIST: 983.2, 0.000466)

Air, 20 °C, 1 atm

1.2 kg/m³, 1.8 × 10⁻⁵ Pa·s

Oil (SAE 30)

900 kg/m³, 0.3 Pa·s, at no stated temperature

Roughness

smooth 0.0015, steel 0.045, cast iron 0.26, concrete 0.3 mm (the low end of the 0.3 to 3 mm in EPANET Table 3.2)

Pick Custom to enter the density and viscosity of your own fluid at its temperature.

Source: Water checked against the NIST Chemistry WebBook [5]; roughness from EPANET 2.2, Table 3.2 [1]. The air and oil figures are CalcTrail's own; no publisher.

Velocity check (water)

For water

LOW

below 0.6 m/s

TYPICAL

0.6 to 2.4 m/s

HIGH

above 2.4, up to 3 m/s

EXCESSIVE

above 3 m/s

Source: CalcTrail's own guide values; no publisher (EPANET's manual sets none).