Power requirement for pumping a compressible flow fluid through a long pipe
Input(s)
D: Diameter of Pipe (ft)
\(\rho_{1}\): Pressure (psi)
M: Mass (lbs)
\(\mathrm{R}\): Constant \(\left(\mathrm{ft}^{3} \mathrm{psi} / \mathrm{lbmol} \mathrm{K}\right)\)
\(\mathrm{T}\): Temperature \((\mathrm{K})\)
Wm: Energy Required by Compressor (ft lbf/lbm)
\(\mathrm{v}\): Velocity (ft/s)
Output(s)
P: Power (hp)
Formula(s)
\[
\mathrm{P}=\frac{\left(\mathrm{v}_{1}\right) * \pi *\left(\mathrm{D}^{2}\right) * \rho_{1} * \mathrm{M} * \mathrm{Wm}}{4 * \mathrm{R} * \mathrm{~T}}
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 15, Page: 465.