fluid-dynamics is not my preferred discipline, yet I have been landed with this problem and just seeking some clarification.

I have a nozzle at the end of a tube, with 8 holes in it, and we are going to block 1 hole to change the air flow

My though was if we blocked 1 hole, and the net flow remains the same, because the air just increases through the other 7. (restricting the area, increases velocity, constant flow rate)

But we are trying to achieve a velocity of mach 1, which totally alters the dynamics right?. So at supersonic speeds some pressure effects means that restricting the area will restrict the flow?


By continuity (assuming steady state) the outlet flow must equal the inlet flow. If you have constant mass flow rate into the tube and block one hole, the flow through the others will increase. Whether the flow is sonic or not, that will force an increase in the pressure in front of the nozzle. Well below sonic speed the flow rate is proportional to the square root of the pressure differential across the orifice. When the flow is sonic, the mass flow is proportional to the square root of the upstream pressure


Watch out for the choked flow situation. The flow is only purely proportional to $\sqrt{P}$ if density is constant.

In practice the working gas often returns to ambient temperature as it passes from compressor to the nozzle. So that density will increase. The end result is that you'll have $\dot m \sim P$. This effect is terribly convenient for control purposes, I often use choked nozzles in the middle of gas lines to easily get mass flow rates that I want.

As a handy note: when choked the flow will be at $M=1$ in the throat of the nozzle (narrowest point). After the nozzle $M > 1$.

If you want a controlled mass flow rate and high speeds, I'd use a two stage system. Start at high pressure $P_1$ and put the flow through choked nozzles to an intermediate pressure $P_2$ ahead of the nozzles that you've got. Then those nozzles will discharge to atmospheric pressure $P_0$ (or where ever they're discharging). You only need to make sure that the pressure ratios $P_1/P_2$ and $P_2/P_0$ are high enough to maintain choked conditions. (Hint: choose $\dot m$ and work backwards).

At a very practical level: you can buy pre-made, calibrated sonic nozzles with a variety of pipe/hose fittings built in. You just screw them into the middle of your gas lines and you're all set.


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