By methodically reducing the downstream pressure while monitoring static pressure taps along the nozzle, you can directly observe the exact point where gas flow transitions from subsonic to supersonic.
A converging-diverging nozzle in a pilot plant behaves like a calibrated window into compressible flow. As you lower the back pressure, the gas accelerates through the converging section, reaches the speed of sound at the throat, and—if the pressure ratio is low enough—exits the diverging section at supersonic velocities. The pressure-profile you record along the nozzle wall will either fall continuously (pure supersonic expansion) or jump abruptly where a shock wave forms, giving clear visual proof of the transition.
Core Takeaway: The demonstration hinges on achieving the critical pressure ratio and interpreting the static pressure distribution. When the throat pressure drops to roughly 53% of the supply pressure, the flow chokes at Mach 1. Any further reduction in back pressure forces the gas to accelerate to supersonic speeds in the diverging section, a change you verify by a steady pressure decline without a shock.
Why the Nozzle Geometry Matters
The shape of a converging-diverging nozzle deliberately manipulates the area-velocity relationship in compressible flow. Upstream of the throat, decreasing area drives subsonic gas to higher speeds. At the throat, the area is at a minimum—an ideal spot to hit sonic velocity.
The Area-Velocity Link
For subsonic flow, a shrinking cross-section increases velocity and lowers pressure. In supersonic flow, the opposite happens: the flow accelerates only when the area expands. The nozzle uses this reversal to physically force the transition.
Throat as the Choking Point
Once the flow at the throat reaches Mach 1, mass flow rate cannot increase no matter how much you lower the back pressure. The throat is “choked,” and all excess pressure drop must be converted into kinetic energy farther downstream.
The Diverging Section’s Role
If the back pressure falls below the critical value, the fluid continues to expand in the diverging section. Because the flow is now supersonic, the increasing area further accelerates the gas. This yields the counter‑intuitive result: a wider pipe actually increases speed.
Setting Up the Demonstration in a Pilot Plant
A typical unit operations pilot plant runs on compressed air and includes a converging-diverging nozzle fitted with multiple pressure taps. The setup is straightforward but requires precise control of the back-pressure valve.
Required Instrumentation
You need a calibrated upstream pressure gauge, a fine‑control valve at the nozzle exit, and several static pressure taps spaced along the nozzle wall. A data acquisition system or a simple manometer bank can record the pressures in real time.
Step-by-Step Procedure
Start with the back‑pressure valve fully open so that the nozzle operates far from critical conditions. Gradually close the valve while recording the steady‑state pressure at each tap. At each valve position, plot the pressure profiles. When the throat pressure ratio drops to about 0.528 (for air), the sonic line appears at the throat. Further closure pushes the flow supersonic downstream.
Visualizing the Transition
A continuous and smooth pressure decline from throat to exit tells you the entire diverging section is experiencing supersonic expansion. A sharp, vertical pressure jump signals a normal shock wave, inside which the flow jumps from supersonic back to subsonic.
Interpreting the Pressure Profile
The static pressure distribution along the nozzle wall is the primary diagnostic tool. It reveals exactly what the gas is doing without needing any velocity probes.
Subsonic‑to‑Sonic Behavior
Before choking, pressure falls steadily through the converging section and continues to drop—albeit more gently—in the diverging section. The minimum pressure is at the throat, but the flow remains subsonic everywhere.
The Moment of Choking
When the throat pressure reaches the critical value, the sonic barrier appears. At this point, the downstream pressure no longer influences the mass flow; the nozzle is “choked.”
Supersonic Expansion Without a Shock
If you continue to lower the back pressure, the pressure trace after the throat shows a persistent, often steep decline. Every further expansion accelerates the supersonic stream. This is the textbook isentropic supersonic case.
Shock‑Wave Signature
If the back pressure is not low enough to sustain fully supersonic flow to the exit, a normal shock forms inside the diverging section. On the pressure profile, you will see a sudden, almost instantaneous pressure rise—a hallmark of a dissipative shock.
Understanding the Trade‑offs
While the demonstration is elegant, pilot‑plant conditions introduce real‑world deviations that can confuse students if not acknowledged upfront.
Sensitivity to Back‑Pressure Control
A tiny change in the exit valve position can flip the flow from shock‑free supersonic to a shock‑containing pattern. This sensitivity makes the transition dramatic but demands a steady hand and a high‑quality metering valve.
Friction and Boundary‑Layer Effects
No real nozzle is perfectly isentropic. Wall friction thickens the boundary layer, which can slightly delay the sonic transition or shift the shock location. The pressure trace may not match ideal theory exactly, but the qualitative trend remains.
Limited Pressure‑Ratio Range
A typical compressed air line might supply only a few bar above atmospheric. This limits how low you can drive the back pressure, potentially restricting the supersonic Mach number you can achieve. Still, even modest pressure ratios are enough to demonstrate the core phenomenon.
Making the Right Choice for Your Teaching or Research Goal
The converging-diverging nozzle pilot plant can serve different educational objectives. Tailor the operating strategy to the message you want to emphasize.
- If your primary focus is demonstrating choked flow: Reduce the back pressure just until the mass flow stops increasing. Show that the throat pressure remains fixed despite further pressure drops, proving that downstream signals cannot propagate upstream.
- If your primary focus is visualizing supersonic acceleration: Go further and create a shock‑free supersonic expansion. Point out the continuous pressure decline in the diverging section and link it to the area‑velocity principle.
- If your primary focus is explaining shock waves: Deliberately set a back pressure that generates a normal shock. Have students compute the pressure jump across it and compare with Rankine‑Hugoniot theory.
- If your primary focus is connecting to industrial equipment: Relate the nozzle’s pressure profile to steam ejectors, rocket nozzles, or gas‑phase reactor nozzles. Show how choking dictates mass flow limits and how supersonic velocities enable efficient thrust or mixing.
A single pilot‑plant nozzle, operated with attention to the pressure ratio, can transform abstract compressible‑flow equations into a tangible, measurable event that students will not forget.
Summary Table:
| Flow Regime | Throat Mach Number | Diverging Section Behavior | Pressure Profile Signature |
|---|---|---|---|
| Subsonic Flow | < 1 | Decelerates flow & increases pressure | Gentle drop, minimum at throat |
| Choked Flow | = 1 (Critical) | Begins transition to supersonic | Throat pressure ratio drops to ~0.528 |
| Supersonic Expansion | = 1 | Accelerates flow as area increases | Continuous pressure decline to exit |
| Shock Wave Flow | = 1 | Abrupt deceleration to subsonic | Sudden pressure jump along nozzle |
Bring Compressible Flow Theory to Life in Your Lab
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