Energy requirement of single-stage ideal compressor

Input(s)

v1\mathrm{v}_{1}: Velocity (ft/s)

P1\mathrm{P}_{1}: Initial Pressure (psi)

P2\mathrm{P}_{2}: Final Pressure (psi)

R\mathrm{R}: Ideal Gas Constant (ft3lb/molK)\left(\mathrm{ft}^{3} \mathrm{lb} / \mathrm{mol} \mathrm{K}\right)

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

M: Mass (lbs)

γ\gamma: Adiabatic Constant (dimensionless)

Output(s)

W: Energy (ft lbf/lbm)

Formula(s)

W=(v122)(1((P1P2)2))+(R TγM(γ1))(((P1P2)γ1γ)1)\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.


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