Horsepower Compressed Air

Overview

Engineering reference data for Horsepower Compressed Air in dynamics.

Key Formulas

Newton's Second Law

$F = ma$

Force = mass × acceleration.

Kinetic Energy

$E_k = \frac{1}{2}mv^2$

Energy of motion.

Momentum

$p = mv$

Mass × velocity.

Work

$W = Fd\cos\theta$

Force × displacement × cos(angle).

Variables

Symbol	Description	Unit
$F$	Force	N
$m$	Mass	kg
$a$	Acceleration	m/s²
$v$	Velocity	m/s
$E_k$	Kinetic energy	J

Horsepower Formula

The horsepower required for adiabatic compression of air is given by:

$$HP = \frac{144 \cdot N \cdot P_1 \cdot V \cdot k}{33000 \cdot (k - 1)} \left( \left( \frac{P_2}{P_1} \right)^{\frac{k - 1}{N \cdot k}} - 1 \right)$$

where:

• HP = horsepower required
• N = number of compression stages
• P1 = absolute initial (atmospheric) pressure (psi)
• P2 = absolute final pressure after compression (psi)
• V = volume of air at atmospheric pressure (scfm, ft³/min)
• k = adiabatic expansion coefficient (≈ 1.41 for air)

Unit Conversions

• Volume Flow: 1 cfm (ft³/min) = 1.7 m³/h = 0.47 l/s = 28.3 l/min
• Pressure: 1 psi (lb/in²) = 6894.8 Pa (N/m²) = 6.895×10⁻² bar
• Power: 1 hp = 745.7 W

Adiabatic Process

Adiabatic compression (or expansion) is a thermodynamic process that occurs without the transfer of heat between the system (the air being compressed) and its surroundings. This is an ideal assumption; in practice, real compressors will generate and dissipate some heat. The theoretical horsepower calculated above assumes this perfect, heat-loss-free condition.

References

• Original Source