This calculator works out the pressure drop and head loss for a fluid flowing through a pipe, using the Darcy-Weisbach equation, the standard method in fluid mechanics and plumbing design. As a liquid or gas flows along a pipe, friction against the pipe wall and turbulence within the fluid steadily sap its energy, showing up as a drop in pressure from one end to the other. Knowing this pressure drop is essential for sizing pipes and pumps, designing water, heating and process systems, and ensuring adequate flow and pressure at the far end. The Darcy-Weisbach equation relates the pressure drop to the pipe's length and diameter, the fluid's density and velocity, and a friction factor that accounts for the pipe's roughness and the flow conditions. This tool computes it. You enter the friction factor, the pipe length, the internal diameter, the fluid density, and the flow velocity, and the calculator returns the pressure drop in kilopascals, along with the value in pascals, the equivalent head loss in metres, and the velocity head. The results update as you type, so you can see how a longer or narrower pipe, or a faster flow, increases the loss. Use it for plumbing and pipe design, for pump selection, or for fluid mechanics study. The relationship is the pressure drop equals the friction factor times the length over the diameter, times the density times velocity squared over two. A few insights it makes clear: pressure drop rises with the square of the velocity, so doubling the flow speed quadruples the loss; it is inversely proportional to diameter, so a slightly wider pipe cuts the loss substantially; and it grows directly with length. Converting the pressure drop to head loss, by dividing by density times gravity, gives the equivalent height of fluid, which is how pump duties are often specified.
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40 kPa
pressure drop
In pascals40,000 Pa
Head loss4.077 m
Velocity head0.204 m
Darcy-Weisbach: pressure drop = f x (L/D) x (density x velocity² / 2). Pressure drop rises with velocity squared and falls with diameter. Head loss = drop / (density x g).
How it works
The Darcy-Weisbach equation multiplies the friction factor by the ratio of pipe length to diameter, and by the dynamic pressure, which is half the fluid density times the velocity squared. This gives the pressure drop. Dividing the pressure drop by the fluid density times gravity converts it to a head loss in metres of fluid.
Worked example
For water flowing at 2 metres per second through a 50 metre pipe of 0.05 metre diameter, with a friction factor of 0.02, the pressure drop is 0.02 times 50 over 0.05, times 1,000 times 2 squared over 2. That is 0.02 times 1,000 times 2,000, which is 40,000 pascals, or 40 kilopascals, equivalent to about 4.08 metres of head loss.
