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Fluid Mechanics

Pipe friction and fitting losses

Head lost to straight-pipe friction and fittings in a pipe run.

Ref: FLU-04
Rev: v1
Field: Fluid Mechanics
Result: h_L [m]

h_{f} = f_{D} \frac{L}{D} \frac{V^{2}}{2 g}, h_{m} = Σ K_{i} \frac{{V_{i}}^{2}}{2 g}

The Darcy friction factor f_D is four times the Fanning factor. Use the mean speed specified for each fitting. Add the straight-pipe and fitting losses. The calculator gives total head loss and the pressure drop for water.

Water loses energy to rubbing along the pipe wall and to bends and valves; both losses grow with the square of the speed.

Calculator

Solve for

h_LTotal head lossComputed

f_DDarcy friction factor

0.0080.1

LPipe length

11,000

DPipe diameter

10500

VMean speed

m/s

0.110

ΣKFitting loss coefficients

020

Friction loss hf0.8158 m
Pressure drop for water8 kPa

What drives the result

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

Total head loss (m) current value 0.8158 m

LPipe lengthKey driver

0.081681.6

VMean speed

0.0020420.4

ΣKFitting loss coefficients

4.89

DPipe diameter

0.08164.08

f_DDarcy friction factor

0.3264.08

Water at 2 m/s in 10 m of 50 mm pipe loses about 0.82 m of head, an 8 kPa pressure drop.
Halving the diameter at the same flow rate raises the speed fourfold and the loss by about 32 times.

Chart data as tables

Ranked variables

Variable	Typical range	Lowest result	Highest result	Swing (m)	Local step	Change in result
L Pipe length	1 to 1,000 m	0.08158	81.58	81.5	+10%	+10 %
V Mean speed	0.1 to 10 m/s	0.002039	20.39	20.39	+10%	+21 %
ΣK Fitting loss coefficients	0 to 20	0.8158	4.895	4.079	+10%	0 %
D Pipe diameter	10 to 500 mm	0.08158	4.079	3.997	+10%	−9.09 %
f_D Darcy friction factor	0.008 to 0.1	0.3263	4.079	3.753	+10%	+10 %

Sweep of Mean speed

Mean speed (m/s)	Total head loss (m)
0.1	0.002039
0.1778	0.006449
0.3162	0.02039
0.5623	0.06449
1	0.2039
1.778	0.6449
3.162	2.039
5.623	6.449
10	20.39

Sweep one variable

Vary

Total head loss (m)Hover, touch, or use the arrow keys on the chart

Variables and how each one contributes

h_L

Total head loss

Result · m

What the equation gives you. Everything else feeds it.

f_D

Darcy friction factor

· typical 0.008 to 0.1

Darcy friction factor. Directly proportional to friction loss.

Pipe length

m · typical 1 to 1,000

Straight pipe length. Directly proportional to friction loss.

Pipe diameter

mm · typical 10 to 500

Internal diameter. A wider pipe cuts friction loss sharply.

Mean speed

m/s · typical 0.1 to 10

Mean flow speed. Squared: the strongest driver.

ΣK

Fitting loss coefficients

· typical 0 to 20

Sum of fitting loss coefficients (elbows, valves, entries). Adds K V²/2g.

Worked example with the values above

Velocity head: V²/2g = 2² / 19.61 = 0.2039 m.
Loss coefficient: f_DL/D + ΣK = 0.02 × 200 + 0 = 4.
h_L = 0.8158 m (about 8 kPa for water).

Assumptions and limits

Fully developed flow in a round pipe.
Constant friction factor.

Common mistakes

Using Fanning in place of Darcy.
Using the wrong diameter units.

Statistics and uncertainty

Friction factors from roughness charts are uncertain by ±10–20%, which carries straight into the loss.

Where it is used

Pump and piping-system design.
Water-cooling and fuel-line checks.

Maths you need

Reynolds number: Re = ρVD/μ
Velocity head: V²/2g

Related formulas

Practise this formula