Head Loss Calculator Formula

Understand the math behind the head loss calculator. Each variable explained with a worked example.

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Formulas Used

Friction Head Loss

head_loss = friction_f * pipe_length / d_m * pow(velocity, 2) / (2 * 9.81)

Pressure Drop

pressure_loss = friction_f * pipe_length / d_m * pow(velocity, 2) / (2 * 9.81) * 1000 * 9.81 / 1000

Variables

VariableDescriptionDefault
friction_fDarcy Friction Factor (f)0.02
pipe_lengthPipe Length (L)(m)100
diameterPipe Diameter (D)(mm)100
velocityFlow Velocity (V)(m/s)2
d_mDerived value= diameter / 1000calculated

How It Works

Darcy-Weisbach Head Loss

Friction between the fluid and the pipe wall converts kinetic energy into heat, causing a pressure drop along the pipe.

Formula

h_f = f (L/D) (V^2 / 2g)

where f is the Darcy friction factor (from Moody chart or Colebrook equation), L is pipe length, D is pipe diameter, V is flow velocity, and g is gravitational acceleration (9.81 m/s^2).

Worked Example

Water at 2 m/s in a 100 mm pipe, 100 m long, with f = 0.02.

friction_f = 0.02pipe_length = 100diameter = 100velocity = 2
  1. 01D = 0.1 m
  2. 02V^2 / 2g = 4 / 19.62 = 0.2039 m
  3. 03h_f = 0.02 x (100/0.1) x 0.2039 = 0.02 x 1000 x 0.2039 = 4.08 m
  4. 04Pressure drop = 1000 x 9.81 x 4.08 / 1000 = 40.0 kPa

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