Pipe Velocity

Overview

Engineering reference data for Pipe Velocity in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Variables

Symbol	Description	Unit
$Re$	Reynolds number	—
$\rho$	Fluid density	kg/m³
$v$	Flow velocity	m/s
$D$	Characteristic dimension	m
$\mu$	Dynamic viscosity	Pa·s
$P$	Pressure	Pa
$f$	Darcy friction factor	—

Pipe Velocity Formulas (Imperial Units)

The fluid flow velocity in a circular pipe can be calculated using Imperial or American units with the following equation: $v = \frac{1.273 \cdot q}{d^2} = \frac{0.4084 \cdot q_{gpm}}{d_{in}^2}$ Where:

• $v$ is the velocity ($ft/min$, $ft/s$)
• $q$ is the volume flow ($ft^3/s$, $ft^3/min$)
• $d$ is the pipe inside diameter ($ft$)
• $q_{gpm}$ is the volume flow ($US \ gal/min$, $gpm$)
• $d_{in}$ is the pipe inside diameter ($inches$)

Pipe Velocity Formulas (SI Units)

For calculations using SI units, the velocity formula is: $v = \frac{1.273 \cdot q}{d^2}$ Where:

• $v$ is the velocity ($m/s$)
• $q$ is the volume flow ($m^3/s$)
• $d$ is the pipe inside diameter ($m$)

Practical Example: Velocity in a Steel Pipe

Consider a flow of $60 \ US \ gal/min$ through a 4-inch schedule 80 steel pipe. The internal diameter of the pipe is $3.83 \ in$.

The flow velocity can be calculated as follows: $v = \frac{0.4084 \cdot 60 \ gal/min}{(3.83 \ in)^2} = 1.7 \ ft/s$

This example demonstrates the direct application of the Imperial formula for a common engineering scenario.

Reference Diagram

A downloadable diagram showing pipe velocity relationships for Schedule 40 steel pipes is available: Download Schedule 40 Steel Pipe Velocity Diagram (PDF)

References

• Original Source