Physics
Pipe pressure loss calculator
Enter flow, diameter, length and roughness: you get the velocity, the Reynolds number, the friction factor solved from Colebrook–White, and the loss in metres of head, pascals and bar.
How pressure loss is worked out
Friction loss along a pipe comes from Darcy–Weisbach: h = f·(L/D)·v²/(2g). The three factors say everything. Length enters linearly, diameter appears in the denominator and again inside the velocity, and the upshot is that loss grows as the fifth power of the inverse diameter: halving the pipe at the same flow multiplies the loss about thirtyfold. That is why an undersized pipe cannot be fixed with a bigger pump.
The friction factor depends on the regime. Below a Reynolds number of about 2300 the flow is laminar and f is exactly 64/Re, with roughness playing no part: the fluid moves in layers and never sees the wall. Above 4000 the flow is turbulent and f comes from Colebrook–White, which ties f to the Reynolds number and to the relative roughness. Between the two lies a transition zone where no formula is dependable.
Colebrook is implicit — f appears on both sides — which is why explicit approximations such as Swamee–Jain are common. Here the equation is actually solved, by Newton's method, which converges in three or four steps: the approximations are out by about a percent in the middle of the range and more at its edges, an error not worth accepting when solving it properly costs nothing. Fitting losses are added to the friction loss, each expressed as a multiple of the velocity head v²/2g.
Common mistakes
- Using the nominal diameter instead of the internal one. A DN50 steel pipe is about 53 mm inside; a 63 mm outside-diameter plastic pipe is about 51. The difference enters to the fifth power.
- Applying 64/Re in turbulent flow, or Colebrook in laminar flow. They are two laws for two different phenomena, and using the wrong one is out by a factor, not by a few percent.
- Confusing kinematic with dynamic viscosity. The Reynolds number wants the kinematic one, in mm²/s: water at 20 °C is 1.004 mm²/s, while the dynamic viscosity is about 1.002 mPa·s. The numbers look alike only because water's density is close to 1000.
Frequently asked questions
What velocity should a pipe run at?
Building water services usually sit between 1 and 2 m/s. Above 3 m/s noise and erosion become a problem and losses climb steeply; below 0.5 m/s the pipe is oversized and sediment tends to settle.
What is the Reynolds number?
The ratio of inertial to viscous forces, Re = v·D/ν. Below 2300 the flow is laminar, above 4000 turbulent, with a transition zone between. It is the number that decides which friction-factor law applies.
What roughness do common pipes have?
Commercial steel about 0.045 mm, galvanised steel 0.15 mm, cast iron 0.26 mm, PVC and polyethylene 0.0015 mm, copper 0.0015 mm, concrete 0.3 to 3 mm. In turbulent flow roughness weighs as much as the Reynolds number.
How are fitting losses counted?
Each bend, valve or sudden change of section has a K coefficient, and the loss is K·v²/2g. Enter the sum of the K values: a 90° bend is about 0.9, an open ball valve 0.05, an open gate valve 0.2, an exit into a tank 1.
What pump power does it take?
The hydraulic power is Δp·Q — the loss in pascals times the flow in m³/s. The electrical power drawn is larger: divide by the efficiency of pump and motor together, often between 0.5 and 0.75.
How this calculation works
Velocity: v = Q/A, with A = πD²/4. Reynolds number: Re = v·D/ν. Regime: laminar below Re 2300, turbulent above 4000, transitional between. Friction factor: in laminar flow f = 64/Re, exact and independent of roughness; in turbulent flow from Colebrook–White, 1/√f = −2·log₁₀(ε/(3.7·D) + 2.51/(Re·√f)), which is implicit and is solved by Newton's method on x = 1/√f, in which it is nearly linear, started from the explicit Swamee–Jain estimate. Friction loss, Darcy–Weisbach: h = f·(L/D)·v²/(2g). Fitting losses: h = ΣK·v²/(2g). Converted to pressure: Δp = ρ·g·h. Hydraulic power: P = Δp·Q. Units are converted internally to SI: millimetres of diameter and roughness to metres, mm²/s of viscosity to m²/s, m³/h of flow to m³/s.