Pressure Energy

Overview

Engineering reference data for Pressure Energy 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	—

Example: Pressure Energy in a Water Tank

To apply the formula for pressure energy in an incompressible fluid, consider a water tank pressurized to 10 bar.

Given:

• Pressure difference, $\Delta p = 10 \text{ bar} = 10^6 \text{ Pa}$
• Density of water, $\rho = 1000 \text{ kg/m}^3$

Calculation: Using the formula $\Delta E = \frac{\Delta p}{\rho}$:

$$\Delta E = \frac{10^6 \text{ Pa}}{1000 \text{ kg/m}^3} = 1000 \text{ J/kg}$$

The potential pressure energy stored per kilogram of water is 1000 J/kg.

References

• Original Source