# Portable compressor power calculation

Hello

I have been trying to calculate the theoretical power required for compression of a small portable 2 stage compressor with the following spec.

Volume flow rate Q = 2x10-5 m3/s
Inlet pressure P1 = 1 Bar (105Pa)
Outlet pressure = 200 Bar
interstage pressure Px = 14 Bar
k = 1.4
N = number of stages
Motor power = 400 w

Using the equation for power during adiabatic compression

$$\large \large p=\frac{k}{k-1}P_{1}QN \begin{bmatrix} \left ( \frac{P_{x}}{P_{1}} \right )^{\left ( \frac{k-1}{k} \right )} & -1 \end{bmatrix}$$

$$\large \large p=\frac{1.4}{1.4-1}10^{5} \times 2\times 10^{-5} \times 2 \begin{bmatrix} 14^{0.3}-1 & \end{bmatrix}$$

I get a theoretical power of 16 watts. Why the huge discrepancy between the theoretical and the actual power required? Is my calculation correct? I am aware there are mechanical losses and inefficiency's in the pump but are they so great as to require 25 x the power?
Thanks very much for any help.