Homework Help: Supersonic water nozzle?

1. Jul 1, 2009

kandelabr

1. The problem statement, all variables and given/known data
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?

2. Relevant 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

3. 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.

2. Jul 1, 2009

3. Jul 1, 2009

kandelabr

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

4. Jul 2, 2009

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.

5. Jul 2, 2009

kandelabr

ok, i get it.
thanks for replies.