Head Loss Calculator Formula

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

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

Frequently Asked Questions

How do I find the Darcy friction factor?

For turbulent flow, use the Moody chart or the Colebrook-White equation: 1/sqrt(f) = -2 log10(e/D/3.7 + 2.51/(Re sqrt(f))). For laminar flow (Re < 2300), f = 64/Re exactly.

What about losses from fittings and valves?

Minor losses from fittings are added separately: h_minor = K V^2/(2g), where K is a loss coefficient specific to each fitting type (elbow, tee, valve, etc.). The total head loss is the sum of pipe friction and minor losses.

Does pipe material affect head loss?

Yes, through the pipe roughness. New steel pipes have roughness e = 0.046 mm, PVC is 0.0015 mm, cast iron is 0.26 mm. Rougher pipes have higher friction factors and more head loss.

Learn More

Guide

Understanding Fluid Mechanics Basics: A Practical Introduction

Master the fundamentals of fluid mechanics including pressure, viscosity, Bernoulli's equation, Reynolds number, and flow types. Essential knowledge for engineers working with pipes, pumps, and hydraulic systems.

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