A facilities engineer once specified a transfer pump from the static lift alone — the height the water had to climb — and ignored the long horizontal run feeding it. The pump arrived, the flow came up short, and the project lost a week. The missing piece was friction. Water does not slide through a pipe for free; every metre of wall drags energy out of the flow, and that loss has to be paid for by the pump.
This article explains how to predict that loss with the Darcy-Weisbach equation, works a full numerical example, and points out the assumptions that most often catch people out.
Why this calculation matters
Pressure drop is the quantity that connects a piping layout to the machine that has to push fluid through it. Size a pump or fan without it and you are guessing. Underestimate the loss and the flow falls short; overestimate it and you buy an oversized machine that runs inefficiently, throttled back, and cavitates at part load.
The same calculation governs more than pump selection. It sets the operating point where the pump curve meets the system curve. It decides pipe diameter — a slightly larger pipe can slash pumping cost over a plant's lifetime, because loss climbs steeply with velocity. It feeds energy budgets, control-valve authority, and network balancing. In short, pressure drop is where hydraulic design meets the electricity bill.
The core method
The standard tool is the Darcy-Weisbach equation, which gives the pressure loss for friction along a straight run of pipe:
dp = f * (L / D) * (rho * V^2 / 2)
Here f is the Darcy friction factor (dimensionless), L is the pipe length, D is the inside diameter, rho is the fluid density, and V is the mean velocity. The group rho*V^2/2 is the dynamic pressure — the same kinetic-energy term that appears in the Bernoulli equation.
The equation says three intuitive things. Loss grows linearly with length: twice the pipe, twice the loss. Loss grows inversely with diameter, and steeply, because a smaller bore both lengthens the L/D ratio and raises the velocity for a fixed flow rate. And loss grows with the square of velocity — the single most important sensitivity in the whole calculation.
The friction factor f is where the physics lives. It depends on the Reynolds number and on the relative wall roughness:
Laminar flow (Re < 2300): f = 64 / Re
Turbulent flow: f from the Colebrook equation or a Moody chart
In the laminar regime the formula is exact. In the turbulent regime f is read from a Moody chart or solved from the Colebrook correlation, using Re and the roughness ratio epsilon/D. Engineers often quote the result as a head loss rather than a pressure, by dividing by rho*g:
h_f = dp / (rho * g)
Head loss in metres is convenient because it can be added directly to the static lift to get the total head a pump must deliver.
A worked example
Take water flowing through a straight pipe. The fluid density is rho = 998 kg/m^3. The mean velocity is V = 2 m/s, the pipe length is L = 50 m, and the inside diameter is D = 0.05 m. For this flow the Darcy friction factor is f = 0.02.
Step 1 — assemble the geometric and dynamic terms.
L / D = 50 / 0.05 = 1000
rho * V^2 / 2 = 998 * 2^2 / 2 = 998 * 4 / 2 = 1996 Pa
Step 2 — apply Darcy-Weisbach.
dp = f * (L / D) * (rho * V^2 / 2)
dp = 0.02 * 1000 * 1996
dp = 39,920 Pa
So friction in this 50 m run costs about 39.9 kPa.
Step 3 — convert to head loss. Dividing by rho*g, with g = 9.81 m/s^2:
h_f = dp / (rho * g)
h_f = 39,920 / (998 * 9.81)
h_f = 39,920 / 9790
h_f = 4.08 m
The friction loss is equivalent to lifting the water about 4.08 m. If this pipe also climbs, say, 6 m vertically, the pump must supply roughly 10 m of head in total — and specifying it from the 6 m static lift alone, as in the opening story, would leave it 40 percent short.
It is worth noticing how the velocity term dominates. Because dp scales with V squared, raising the flow velocity from 2 m/s to 3 m/s would more than double this loss, all else equal. That single fact is the strongest argument for not undersizing pipe diameter.
Common mistakes
Counting only the straight pipe. Darcy-Weisbach gives the friction loss of straight runs. Elbows, tees, valves, expansions, and entries add minor losses — sometimes a large fraction of the total in a fitting-heavy layout. The full system loss is the sum of major and minor losses.
Using a guessed friction factor. f = 0.02 is a reasonable round number for moderately turbulent water flow, but it is not universal. It depends on the Reynolds number and the relative roughness. A clean plastic pipe and an old corroded steel one of the same size can differ by a factor of two.
Mixing up pressure and head. Pressure drop is in pascals; head loss is in metres. They are linked by dp = rho*g*h. Adding a pressure in kPa to a head in metres is a unit error that looks plausible until the pump underperforms.
Forgetting that velocity is set by flow rate and diameter. You rarely choose velocity directly. It follows from V = Q / A. Halving the diameter quadruples the velocity for the same flow, and since loss goes as velocity squared, the pressure drop rises sharply — diameter is a powerful and often underused design lever.
Applying the laminar formula in turbulent flow. f = 64/Re is exact only below Re of about 2300. Above the transition you must use the Colebrook equation or a Moody chart. Check the Reynolds number first.
Try the interactive NovaSolver calculator
Reading a Moody chart and iterating the Colebrook equation by hand is tedious, and it is exactly the kind of work worth automating. The Pipe Pressure Drop Calculator (Darcy-Weisbach) on NovaSolver lets you set the pipe diameter, length, flow rate, fluid, and wall roughness, and tick off the fittings in the line. It returns the Reynolds number, the friction factor, the velocity, the major and minor losses, and the total pressure drop, with a live Moody chart marking your operating point.
Related calculators
- Reynolds Number Calculator — establish the flow regime that decides which friction-factor relation applies.
- Minor loss (pipe fittings) calculator — quantify the losses from elbows, valves, and tees that Darcy-Weisbach leaves out.
- Pipe network calculator — extend the single-pipe result to branched and looped systems.
The full set lives in the fluid dynamics tools hub.
Closing note
Pipe pressure drop is a modest calculation with a direct line to cost and reliability. Remember the hierarchy that Darcy-Weisbach encodes: loss is linear in length, climbs hard as diameter shrinks, and rises with the square of velocity. Add the minor losses from fittings, check the Reynolds number before you trust a friction factor, and keep pressure and head in their own units. Do that, and the pump you specify will meet the system it was bought for — no lost week required.
