Thermodynamics: Vertical pipe flow of geothermal water

[mr.learnmore]

1. Water at T1=240 C and P1=16 MPa is at 2 km depth. A drilling hole with diameter 0.2 m has the water flowing up with mass flow rate at 2 kg/s. The hole is considered adiabatic(no heat transfer).
I need to find the following values at the top of the hole:
Enthalpy(h), temperature(T2), pressure(P2) and steam percentage(x) of the water.

There is no pipe friction. At the top of the hole there is a throttling valve which leads to further piping(so the pressure can not be considered to be 1 atm).



3. The Attempt at a Solution
The water is a compressed liquid in the beginning, so using saturated liquid values at T1 gives(from table):
v1=0.001229 m^3/kg
h1=1037.5 kJ/kg

The initial velocity is V =0.078241 m/s, using massflowrate = ρ*A*V.

The mass flow is steady, but as pressure drops with elevation the specific volume changes (I would think).
I'm not sure how to begin solving this, any ideas/hints are very welcome.

 

[mfb]

The pressure gradient can be calculated with the density of your water and gravity. This should allow to calculate the system up to the point where water begins to boil, probably with approximations for the water density. Afterwards, I don't know how water and steam behave in the pipe.