Pressure Drop Calculator Formula

Understand the math behind the pressure drop calculator. Each variable explained with a worked example.

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Formulas Used

Pressure Drop

delta_p = friction_f * (length / d_m) * 0.5 * density * pow(velocity, 2) / 1000

Equivalent Head Loss

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

Variables

VariableDescriptionDefault
friction_fFriction Factor (f)0.02
lengthPipe Length (L)(m)50
diameterPipe Diameter (D)(mm)80
velocityFlow Velocity (V)(m/s)2.5
densityFluid Density (rho)(kg/m^3)1000
d_mDerived value= diameter / 1000calculated

How It Works

Pressure Drop in Pipes

Pressure drop is the energy lost to friction as fluid flows through a pipe.

Formula

delta_P = f (L/D) (0.5 rho V^2)

This is the Darcy-Weisbach equation expressed in pressure units (Pa) rather than head (m). The two forms are related by delta_P = rho g h_f.

Worked Example

Water at 2.5 m/s through 80 mm pipe, 50 m long, f = 0.02.

friction_f = 0.02length = 50diameter = 80velocity = 2.5density = 1000
  1. 01D = 0.08 m, L/D = 50/0.08 = 625
  2. 02Dynamic pressure = 0.5 x 1000 x 2.5^2 = 3125 Pa
  3. 03delta_P = 0.02 x 625 x 3125 = 39,063 Pa = 39.1 kPa
  4. 04Head loss = 39,063 / (1000 x 9.81) = 3.98 m

Frequently Asked Questions

What causes the highest pressure drop?

Small diameter pipes cause the highest pressure drop because velocity increases as D^-2 and the L/D ratio increases. Doubling the pipe diameter reduces pressure drop by roughly a factor of 32 for the same flow rate.

How do I reduce pressure drop in a system?

Increase pipe diameter, reduce pipe length and number of fittings, smooth the interior surface, or reduce flow rate. Using schedule 40 instead of schedule 80 pipe also slightly increases the bore diameter.

What pressure drop is acceptable?

This depends on the system. For water distribution, 1-3 kPa per metre of pipe is common. For HVAC ducting, 0.8-1.5 Pa/m is typical. Excessive drop requires larger pumps or fans and wastes energy.

Learn More

Guide

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