At $37$ degrees, product gas flows from the biogas reactor at a pressure of $1\mathrm{.}1$ atm and a flow rate of $130$ m$^3/$h$.$

The efficiency of the isothermal compressor is $45$ percent. What should be the power of the pump so that there are $2$ elbows and $1$ valve by moving the compressor? What are our assumptions to calculate it at the lowest cost? What should be the exit speed and pressure of the biogas reactor? How is the pressure difference in the mechanical energy balance calculated?