Question

I need to design an air nozzle for a compressed air system with multiple outlets. All I know about the current system is there is 109 psi available in the air line. If I use the mass flow rate equation for a compressed ideal gas, how do I know the pressure hasn’t dropped in the line to decrease the Mach number as I increase the area of the nozzles? If the flow is choked, will the velocity remain constant as area increases? At what point does the increase in area start to decrease the velocity of the flow?

Answer 1

We will assume that the prsesure at the entry of the nozzle = 109 psi ; regardless the number of outlets used.

As it is the function of the air line to always supply air at pressure of 109 psi.

So after the above assumption inlet conditions are fixed

Pressure= 109 psi;

Area at inlet =a₀

The inlet pressure will remain constatnt for whatever value of area is chosen.

The relation which governs area change and mach number inside the nozzle is:

dA/A=(M²-1)(dV/V)

Where A= area ; dA= change in area; V= velocity, dV= change in velocity.

if the flow in the throat is subsonic, the flow downstream of the throat will decelerate and stay subsonic.

So if the converging section is too large and does not choke the flow in the throat, the exit velocity is very slow.

If the converging section is small enough so that the flow chokes in the throat, then a slight increase in area causes the flow to go supersonic. if the flow in the throat is subsonic, the flow downstream of the throat will decelerate and stay subsonic.

So if the flow chokes at the throat increase in area will lead to increase in velocity;

The increase in area will decrease the velocity of the flow when a normal shock occurs before the flow reaches the exit. A sudden energy loss will make the flow subsonic and from that point the velocity will go on decreasing