Can water be propelled at supersonic speeds from a small hole?

[kandelabr]

Homework Statement

suppose we have a water reservoir with some pressure in it and a small hole through which the water exits. on the other side, there is just atmosphere.
by increasing pressure on the "water side", the velocity of exiting water increases.
what happens when pressure is large enough to propel the water stream at supersonic speed?

Homework Equations

bernoulli's equation: (r = density; 1 - water tank, 2 - atmosphere)
h₁ + v₁²/2g + p₁/rg = h₂ + v₂²/2g + p₂/rg

h₁, h₂ = 0 (at the same level)
v₁ = 0
p₁ = some high pressure
p₂ = 0

so

v₂² = 2p₁/r

The Attempt at a Solution

according to this equation, it would be possible to achieve both supersonic speed in air and in water. i know though, that strange things happen at that speeds, but have no clue what exactly is going on.

 

[minger]

How are air and water different? What properties do they share?

After that, if there is simply a hole, then the flow will reach a point called "choked flow". This is the point where the fluid can no longer accerate without a further change in back pressure or area.
http://en.wikipedia.org/wiki/Choked_flow
http://www.okcc.com/PDF/Choked Flow of Gases pg.48.pdf

 

[kandelabr]

ok, then at which speed will this stop? 340 m/s (supersonic in air) or 1440 m/s (in water)?

 

[minger]

Well, if there is water being driven into air then there are a lot of other things at play. We refer to things like this as multiphase flow. However, if the fluid is contained all the way to the choke point, then I would assume that the fluid would reach the speed of sound for the liquid at that specific back pressure.

 

[kandelabr]

ok, i get it.
thanks for replies.