Energy requirement of single-stage ideal compressor

Input(s)

$\mathrm{v}_{1}$: Velocity (ft/s)

$\mathrm{P}_{1}$: Initial Pressure (psi)

$\mathrm{P}_{2}$: Final Pressure (psi)

$\mathrm{R}$: Ideal Gas Constant $\left(\mathrm{ft}^{3} \mathrm{lb} / \mathrm{mol} \mathrm{K}\right)$

$\mathrm{T}$: Temperature $(\mathrm{K})$

M: Mass (lbs)

$\gamma$: Adiabatic Constant (dimensionless)

Output(s)

W: Energy (ft lbf/lbm)

Formula(s)

$$ \mathrm{W}=\left(\frac{\mathrm{v}_{1}^{2}}{2}\right) *\left(1-\left(\left(\frac{\mathrm{P}_{1}}{\mathrm{P}_{2}}\right)^{2}\right)\right)+\left(\frac{\mathrm{R} * \mathrm{~T} * \gamma}{\mathrm{M} *(\gamma-1)}\right) *\left(\left(\left(\frac{\mathrm{P}_{1}}{\mathrm{P}_{2}}\right)^{\frac{\gamma-1}{\gamma}}\right)-1\right) $$

Reference(s)

Bird R. Byron, Stewart E. Warren, Lightfoot N. Edward.