$34.-100$ kg$/$h$.$ of pure CO$2$ are to be passed from a gasometer to a reactor. The gas is in the gasometer at a gauge pressure of $20$ cm of water, while the discharge gauge pressure $($at the reactor inlet$)$ is $20$ cm of water.

The gas is in the gasometer at a manometric pressure of $20$ cm of water, while the discharge manometric pressure $($at the reactor inlet$)$ is $500$ cm of water.

Gasometer and reactor are connected by a standard $2$ steel pipe, with a length equivalent to $1900$ m of straight pipe.

The energy required for the operation must be supplied by a centrifugal compressor attached to the gasometer. $0,837$ HP

Calculate the theoretical power of the compressor in HP$.$

DATA AND NOTES.

Assume gas temperature constant and equal to $15\backslash$deg C throughout the system.

$-$ Viscosity of pure CO$2$ at $15\backslash$deg C $=0\mathrm{.}0143$ c$.$p$.$

$-$ Exponent corresponding to the real compression curve, n $=1\mathrm{.}28.$

$-$ Standard $2$ pipe; Di$=2\mathrm{.}067$; De$=2\mathrm{.}375"$; $\backslash$epsi $=0\mathrm{.}00005$ m