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.