Velocity Head

Overview

Engineering reference data for Velocity Head 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	—

Formulas

$p_d = \frac{1}{2} \rho_f v^2$

$h_w = \frac{p_d}{\gamma_w} = \frac{\rho_f v^2}{2 \rho_w g}$

Water Flow (ρf = ρw): $h_w = \frac{v^2}{2g}$ Metric: $h_w(\text{m H2O}) = 0.051 v^2$ or $h_w(\text{mm H2O}) = 51 v^2$ (v in m/s) Imperial: $h_w(\text{ft H2O}) = 0.0155 v_{fps}^2$ or $h_w(\text{in H2O}) = 0.186 v_{fps}^2$ (v in ft/s)

Air Flow (ρf = 1.205 kg/m³, ρw = 1000 kg/m³): Metric: $h_w(\text{m H2O}) = 6.1 \times 10^{-5} v^2$ or $h_w(\text{mm H2O}) = 6.1 \times 10^{-2} v^2$ (v in m/s) Imperial: $h_w(\text{ft H2O}) = \frac{(v / C)^2}{12}$ or $h_w(\text{in H2O}) = (v / C)^2$ (v in ft/min)

Data Tables

Practical Notes

The dynamic pressure or velocity head is commonly measured using a pitot tube. The simplified air flow equations (4, 4b, 4c, 4d) are valid for the specified air density of 1.205 kg/m³ (70°F / 21°C). For different air temperatures and densities, the constant C must be recalculated, as shown in the table above, or the general formula (2) must be used with the appropriate fluid density.

Interactive Charts

References

• Original Source