The De Laval Nozzle

Find the wall before learning how to get past it.

1. Make a simple converging nozzle — a smooth taper down to a small throat — and fit it to a regulated compressed air supply.
2. Raise the supply pressure in steps, measuring the mass flow each time by timing the pressure drop of a known tank volume.
3. Plot mass flow against supply pressure.
4. Keep raising the pressure well past the point where the plot stops climbing.

Mass flow rises with pressure and then stops rising, no matter how much more pressure you apply. The nozzle has choked: the flow at the throat has reached the local speed of sound and cannot be told to go faster, because the information that would tell it to — a pressure change — travels at exactly that speed and can no longer make it upstream.

Now do the thing that sounds wrong: widen the passage to speed the flow up.

1. Machine a second nozzle with the same throat diameter but add a gently diverging cone downstream — a half-angle of about 15° is a good starting point.
2. Run it at the same supply pressures and measure the thrust with a spring scale on a pivoted mount.
3. Compare thrust with the converging-only nozzle at identical pressure and mass flow.

Same mass flow, more thrust — so the gas must be leaving faster. The diverging section has accelerated the flow past sonic into genuinely supersonic exhaust.

The reason the rule inverts is worth stating carefully. Below the speed of sound, gas behaves nearly as if incompressible: squeeze the passage and it speeds up. Above the speed of sound, the gas expands so rapidly as it accelerates that its DENSITY falls faster than its velocity rises — so to pass the same mass, the area must increase. The area rule does not change; which term dominates does.

A nozzle is correct at exactly one pressure ratio and wrong everywhere else.

1. At a fixed supply pressure, listen and look at the exhaust as you vary the pressure.
2. Watch for visible shock structure in the plume — with sufficient pressure and humidity you may see standing diamonds.
3. Note the pressures at which the plume looks smooth, pinched, or flared.

When exit pressure matches ambient the nozzle is correctly expanded and the plume is smooth and straight. Below that — over-expanded — the atmosphere squeezes the plume inward and shock waves form inside the nozzle. Above it — under-expanded — the plume billows outward after leaving, and that outward expansion produces no thrust at all.

Those standing bright diamonds in a rocket or jet exhaust are shock cells: the flow repeatedly over-corrects, compressing and expanding as it equalises with the surrounding air. Every visible diamond is a small confession that the nozzle is not perfectly matched to the altitude.

Define the number that governs everything in the next blueprint.

1. Measure thrust and mass flow rate simultaneously for each nozzle.
2. Divide thrust by mass flow to get effective exhaust velocity.
3. Divide that by standard gravity to express it as specific impulse in seconds.
4. Tabulate for the converging and converging-diverging nozzles.

Specific impulse is thrust per unit of propellant flow — how much push you get per kilogram per second you are willing to throw away. It is the single figure of merit for a rocket engine, and the diverging section buys a substantial improvement in it for the cost of some machined metal and nothing else.

Make several nozzles differing in one parameter only, and let the measurement decide.

1. Machine three or four nozzles with the same throat but expansion ratios — exit area divided by throat area — of roughly 2, 4, 8 and 16.
2. Measure thrust and specific impulse for each at the same chamber pressure, in ambient air.
3. Plot specific impulse against expansion ratio.

Performance improves with expansion ratio up to a point and then falls away, and the peak is where exit pressure equals ambient pressure. Beyond it you are over-expanding: the plume is being squeezed by the atmosphere, and at extreme ratios the flow separates from the nozzle wall entirely, which is violent and destructive.

So the nozzle is not a component you optimise in isolation — its correct shape is a function of where the rocket will be flying. That is a genuinely awkward constraint for a vehicle whose entire purpose is to leave the atmosphere behind.