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 / 1000Variables
| Variable | Description | Default |
|---|---|---|
friction_f | Darcy Friction Factor (f) | 0.02 |
pipe_length | Pipe Length (L)(m) | 100 |
diameter | Pipe Diameter (D)(mm) | 100 |
velocity | Flow Velocity (V)(m/s) | 2 |
d_m | Derived value= diameter / 1000 | calculated |
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.
- 01D = 0.1 m
- 02V^2 / 2g = 4 / 19.62 = 0.2039 m
- 03h_f = 0.02 x (100/0.1) x 0.2039 = 0.02 x 1000 x 0.2039 = 4.08 m
- 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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