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.