pressure_drop — Pipeflow

Calculates the pressure drop due to friction down a pipe

Interface

#include <codecogs/engineering/pipeflow/pressure_drop.h>

using namespace Engineering::Pipeflow;

double pressure_drop(double diameter, double flow)

As a fluid moves down a pipe, friction with the pipe generates heat and sound and leads a loss of energy within the fluid. Due to Bernoulli law, if there is a loss of energy yet constant flow, then there must be a reduction in pressure.

This function computes this pressure drop for a 100ft length of pipe. To compute the pressure drop for a shorter or longer pipe length, scale the number as appropriate.

The Reynolds number of the flow is first computed from the mean velocity, pipe diameter and the properties of water. An initial estimate of the Darcy friction factor is obtained from the explicit Moody (1947) approximation:

$$f_a = 0.0055 \left[ 1 + \left( 20000\,\frac{\varepsilon}{d} + \frac{10^6}{Re} \right)^{1/3} \right]$$

(1)

This estimate is then refined by substituting it into the (implicit) Colebrook-White equation:

$$\frac{1}{\sqrt{f}} = -2\log_{10}\left( \frac{\varepsilon}{3.7\,d} + \frac{2.51}{Re\sqrt{f_a}} \right)$$

(2)

where $\varepsilon$ is the pipe roughness (taken as 0.00015 ft, typical for commercial steel pipe). The head loss is then found from the Darcy-Weisbach equation, $H = f \frac{L}{d}\frac{V^2}{2g}$, and converted from feet of water to psi.

Parameters

diameter

diameter of the pipe in [inches]

flow

the rate of flow through the pipe [US gpm]

Returns

the reduction in pressure [psi]

Interactive Calculator

diameter

flow

Result –