A compressible fluid flows through a compressor that increases the density from 1 kg/m3 to 5 kg/m3. The cross-sectional area of the inlet pipe is 3 m2 and that of the discharge pipe is 1 m2. The relation between the discharge volume flow rate and the inlet volume flow rate is

The relation between the discharge volume flow rate and the inlet volume flow rate is .

Explanation:

No matter if fluid is compressible or not, mass throughout compressor, a device that works at steady state, must be conserved according to Principle of Mass Conservation:

(Eq. 1)

Where and are mass flows at inlet and outlet, measured in kilograms per second.

After applying Dimensional analysis, we expand the equation above as follows:

(Eq. 2)

Where:

, - Fluid densities at inlet and outlet, measured in kilograms per cubic meter.

, - Volume flow rates at inlet and outlet, measured in cubic meters per second.

After some algebraic handling, we find the following relationship:

(Eq. 3)

If we know that and , then the relation between the discharge volume flow rate and the inlet volume flow rate is:

The relation between the discharge volume flow rate and the inlet volume flow rate is .