# Breaking the sound barrier underwater?

I know it may not even be mechanically possible to reach the speed of sound underwater (1,484 m/s); but this is just a theory.

After discussing with several people, what would happen if a submarine was to break the sound barrier underwater, a couple of interesting theories arose.

Going along the assumption that due to Air and Water both being Fluids, they then behave in similar ways...

When an aircraft breaks the sound barrier, and Prandtl–Glauert singularity occurs, would the same rule apply for underwater? Would the water that this submarine is travelling through, condense the water further? Would it become denser?

When diving in to water from a great height with nothing to really pierce the water (i.e. For example belly flopping from a great height), it would be like hitting concrete because the water doesn’t have enough time to disperse. If this submarine were to go so fast, that the water doesn’t have time to disperse, would it be like this submarine trying to constantly penetrate a brick wall from a “standstill” (i.e. submarine and water wall travelling at same velocity). Does this link to the theory of water becoming denser from the condensation previously mentioned?

Or, (my favourite theory), would there be a big explosion underwater? A shockwave perhaps?

One last thing, due to the friction being so great on aircraft travelling faster than the speed of sound, and thus becoming extremely hot, would the submarine become extremely hot from the friction of water? Would the water cool down the submarine at the same time? Would the submarine become more brittle? (quenching; haha)

You could probably only achieve this with some sort of cavitating system - so the submarine would be travelling in an air bubble rather than in direct contact with the water

Gold Member
MikeNZ said:
When an aircraft breaks the sound barrier, and Prandtl–Glauert singularity occurs, would the same rule apply for underwater? Would the water that this submarine is travelling through, condense the water further? Would it become denser?

The Prandtl-Gluart singularity would only hold in a compressible medium. Water, being incompressible, would not exhibit the same singularity. For similar reasons you wouldn't have a shockwave (at least not in the same sense that you do in air). The shock would have to be a discontinuity in temperature or something.

MikeNZ said:
When diving in to water from a great height with nothing to really pierce the water (i.e. For example belly flopping from a great height), it would be like hitting concrete because the water doesn’t have enough time to disperse. If this submarine were to go so fast, that the water doesn’t have time to disperse, would it be like this submarine trying to constantly penetrate a brick wall from a “standstill” (i.e. submarine and water wall travelling at same velocity). Does this link to the theory of water becoming denser from the condensation previously mentioned?

This phenomenon is a result of surface tension on the water's surface. If you are underwater, the problem doesn't arise. That also explains why going into the water with a sharp point fixes the problem. If just a sharp tip hits the water, the surface tension is acting on a much smaller area (technically perimeter I suppose) and therefore is much much smaller.

MikeNZ said:
One last thing, due to the friction being so great on aircraft travelling faster than the speed of sound, and thus becoming extremely hot, would the submarine become extremely hot from the friction of water? Would the water cool down the submarine at the same time? Would the submarine become more brittle? (quenching; haha)

The water would cool the surface significantly better than air does, but the increased viscosity would give rise to more friction, so it would be hard to predict without doing some sort of supersonic analysis on water. The problem is, it would be very difficult to verify experimentally. Additionally, since I (and who knows if anyone does) don't know how or if a shock would manifest itself underwater, I am not sure how that heating would really work.

Just to clarify, most heating on supersonic vehicles is NOT due to friction directly. The main thing that happens is that as you get faster, the strength of the shock increases. Stronger shocks mean larger increases in stagnation temperature, so as the flow on the skin of the vehicle slows to zero, it heats up to a temperature known as the adiabatic wall temperature (slightly lower than stagnation temperature do to the isentropic process of a shock wave).

NobodySpecial said:
You could probably only achieve this with some sort of cavitating system - so the submarine would be travelling in an air bubble rather than in direct contact with the water

That is true in a practical sense, though it would then only be moving at supersonic speeds relative to the gaseous water through which it is traveling (not THAT much different than air), not the water itself. Work on this has actually already been done.

cjl
The Prandtl-Gluart singularity would only hold in a compressible medium. Water, being incompressible, would not exhibit the same singularity. For similar reasons you wouldn't have a shockwave (at least not in the same sense that you do in air). The shock would have to be a discontinuity in temperature or something.

You'd definitely get a shock wave - water is not incompressible (if it were, the sound speed would be infinite). It is mostly incompressible, but at speeds approaching or exceeding the sound speed in water, you could no longer assume that it is incompressible for the purposes of flow analysis.

Gold Member
You'd definitely get a shock wave - water is not incompressible (if it were, the sound speed would be infinite). It is mostly incompressible, but at speeds approaching or exceeding the sound speed in water, you could no longer assume that it is incompressible for the purposes of flow analysis.

That is a fair statement. You will have to forgive me if I don't always think everything through when I say it this time of year with finals and all. I am "studying" right now after all, haha.

cjl
That is a fair statement. You will have to forgive me if I don't always think everything through when I say it this time of year with finals and all. I am "studying" right now after all, haha.

Fair enough.

I've been thinking about fluids far too much recently - I had a graduate level fluid mechanics final yesterday

Gold Member
Yeah, I had a hypersonics final Friday and I have a boundary layer stability final on Wednesday, and I am really finding it hard to keep studying...

cjl
Yeah, I had a hypersonics final Friday and I have a boundary layer stability final on Wednesday, and I am really finding it hard to keep studying...

Fun...

(Those do sound interesting though - I haven't taken any of those courses [I don't even think we have a boundary layer stability course here, though I could be wrong], but I'm signed up for molecular gas dynamics and high speed aerodynamics next semester)