California Pipe Flow Metering Method

Overview

Engineering reference data for California Pipe Flow Metering Method 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	—

Unit Conversion Factors

Applicability and Limitations

This empirical method is specifically designed for measuring the discharge from open-ended, partially filled horizontal pipes that discharge freely into the air.

The primary formula is: $q = 8.69 \left(1 - \frac{a}{d}\right)^{1.88} d^{2.48}$

Important constraints:

• Pipe Diameter Range: The equation is valid for pipes with an internal diameter (d) between 3 inches (76.2 mm) and 10 inches (254 mm).
• Measurement Condition: The pipe must be horizontal and discharge freely (not submerged).
• Variable a: This is the vertical distance from the top of the pipe's interior surface down to the water surface at the open end, measured in the plane of the pipe's opening.

References

• Original Source