Pipes Fluid Flow Pressure Loss

Overview

Engineering reference data for Pipes Fluid Flow Pressure Loss 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	—

Key Engineering Equations and Applications

The following table summarizes important pressure loss equations and their typical applications, extracted from the referenced engineering documents.

Definitions and Properties

Darcy-Weisbach Equation

The Darcy-Weisbach equation is a fundamental relation for calculating the major (friction) pressure or head loss due to fluid flow in a pipe or duct. It is valid for both laminar and turbulent flow and applicable to any incompressible Newtonian fluid.

Hazen-Williams Equation

The Hazen-Williams equation is an empirical formula used primarily for water flow in pipes. It calculates the friction head loss (typically in ftH₂O per 100 ft of pipe) based on the pipe's internal diameter, flow rate, and a roughness coefficient (C-factor).

Hydraulic Diameter

For non-circular ducts and channels, the hydraulic diameter ($D_h$) is used as the characteristic length in Reynolds number and pressure drop calculations. It is defined as four times the cross-sectional area ($A$) divided by the wetted perimeter ($P$): $D_h = \frac{4A}{P}$

Flow Regime: Reynolds Number

The nature of the fluid flow (laminar, transitional, or turbulent) is characterized by the dimensionless Reynolds number ($Re$). It relates inertial forces to viscous forces: $Re = \frac{\rho v D}{\mu}$ where $\rho$ is density, $v$ is velocity, $D$ is diameter, and $\mu$ is dynamic viscosity.

References

• Original Source