Worked problem

Pipe Pressure Loss: Straight Pipe Plus Fittings

Use Darcy–Weisbach and fitting K values to find the water pressure loss in a short DN100 line and see whether pipe or fittings dominate.

Mechanical, HVAC & Fluids · Last reviewed October 17, 2026

Given

Water (density 998 kg/m³) flows at 10 L/s through a 4 in. Schedule 40 steel line with an inside diameter of 102.3 mm. Straight length 25 m. Supplied Darcy friction factor f = 0.022. Fittings: 4 elbows with K = 0.9 each, one open gate valve K = 0.2, one strainer K = 3.0, a pipe entrance K = 0.5 and an exit K = 1.0.

Find

The total pressure loss, and whether the straight pipe or the fittings contribute more.

Solution

Flow area = π ÷ 4 × 0.1023² = 0.008219 m². Velocity V = 0.010 ÷ 0.008219 = 1.217 m/s.
Dynamic pressure = ½ × ρ × V² = 0.5 × 998 × 1.217² = 739 Pa.
Straight pipe: Δp = f × (L ÷ D) × dynamic pressure = 0.022 × (25 ÷ 0.1023) × 739 = 3,971 Pa.
Fittings: sum of K = 4 × 0.9 + 0.2 + 3.0 + 0.5 + 1.0 = 8.3, so Δp = 8.3 × 739 = 6,131 Pa.
Total = 3,971 + 6,131 = 10,102 Pa, about 10.1 kPa, or 1.03 m of water.

Answer

about 10.1 kPa (1.03 m of water)  |  fittings are 61% of the total

Which part dominates depends on length

The fittings add a loss equal to a length of straight pipe of K × D ÷ f = 8.3 × 0.1023 ÷ 0.022 = 38.6 m. On a 25 m run that is more than the pipe itself, so the fittings dominate. On a long run the pipe takes over.

Straight length	Straight pipe	Fittings	Total
25 m (this problem)	3.97 kPa	6.13 kPa	10.10 kPa
60 m	9.53 kPa	6.13 kPa	15.66 kPa

Common mistakes

Ignoring the fittings in a short line, such as a pump room or a skid, where they often exceed the pipe loss.
Using a K value written for a different velocity basis or a different pipe size.
Using the nominal diameter (100 mm) instead of the inside diameter. The velocity and loss depend on it strongly.
Treating f as constant when the flow or pipe roughness changes. Here f is supplied.

Related tools and labs

Calculators, labs and simulators are part of the All-Access Pass.

Questions

Where does the friction factor come from?

From the Moody chart or the Colebrook equation, using the Reynolds number and the relative roughness of the pipe. Here it is supplied so that the focus stays on the method.

How is the loss converted to head?

Divide the pressure loss by ρg: 10,102 ÷ (998 × 9.81) = 1.03 m.

Does this include elevation change?

No. Elevation adds ρgΔz to the pressure budget separately.

Educational material. Examples use simplified, hypothetical inputs and are not a design, a construction document or professional engineering advice. Confirm requirements with the codes and standards adopted where the work is built and with a licensed engineer.

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