Flow Section Channels

Overview

Engineering reference data for Flow Section Channels 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	—

Hydraulic Diameter

The hydraulic diameter $D_h$ is an equivalent diameter used to characterize non-circular channels, defined as:

$D_h = \frac{4A}{P}$

where $A$ is the flow area and $P$ is the wetted perimeter. For a circular channel flowing full, $D_h$ equals the actual diameter $D$.

Channel-specific Hydraulic Diameter

Rectangular Channel: $D_h = \frac{4 b h}{b + 2 h}$

Trapezoidal Channel: $D_h = \frac{4 \left( \frac{h(b + T)}{2} \right)}{b + 2 \sqrt{\left( \frac{T - b}{2} \right)^2 + h^2}}$

Triangular Channel: $D_h = \frac{4(z h^2)}{2h \sqrt{1 + z^2}} = \frac{2z h}{\sqrt{1 + z^2}}$

Circular Channel (partially filled): $D_h = \frac{4 \left( \frac{D^2}{4} \left( \alpha - \frac{\sin(2\alpha)}{2} \right) \right)}{\alpha D} = D \left( 1 - \frac{\sin(2\alpha)}{2\alpha} \right)$

Where $\alpha = \cos^{-1}\left(1 - \frac{h}{r}\right)$ and $r = D/2$.

Geometric Section Properties

Note: For all channel shapes, the hydraulic diameter $D_h = 4R_h$.

References

• Original Source