Pressure

Overview

Engineering reference data for Pressure 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	—

Absolute vs. Gauge Pressure

Standard Atmospheric Pressure

The Standard Atmospheric Pressure ($p_{atm}$) serves as a reference pressure for many engineering calculations:

$1 \, \text{atm} = 101325 \, \text{Pa} = 101.325 \, \text{kPa} = 1.01325 \, \text{bar}$

In imperial units:

$1 \, \text{atm} = 14.696 \, \text{psi} = 29.92 \, \text{inHg} = 33.90 \, \text{ftH}_2\text{O}$

Important note: All gas law calculations (Ideal Gas Law, etc.) require absolute pressure and absolute temperature values.

Pressure Unit Conversions

Practical Pressure Examples

Pressure Measurement Devices

Common instruments for measuring pressure:

• Manometers: Use fluid columns to measure pressure differential
• Bourdon tubes: Mechanical gauges for gauge pressure
• Piezoelectric sensors: Convert pressure to electrical signals
• Membrane/Bellows sensors: For differential pressure measurement
• Digital pressure gauges: Electronic measurement with digital display

Key Applications by Pressure Range

Application	Typical Pressure Range	Common Units
Weather forecasting	950-1050 hPa	mbar, hPa
HVAC systems	100-500 Pa	Pa, inH₂O
Automotive tires	190-250 kPa	kPa, psi
Industrial hydraulics	10-35 MPa	MPa, bar
Gas cylinders	10-30 MPa	MPa, psi
Vacuum systems	1-10⁻⁶ Pa	torr, mbar

Interactive Charts

References

• Original Source