Question about saturated fluids...

[packdad]

Say you have a container that holds saturated water at some pressure and temperature (the specific values don't matter). The bottom half of the container holds saturated liquid and the top half holds saturated vapor. If you punch a hole in the container, does the mass flow rate out of the container depend on where the hole is located? In other words, does the mass flow rate depend on whether the hole is in the liquid half or the vapor half of the container? Or is it the same regardless of location?

 

[zdas04]

Mass flow rate will depend on driving force. If you punch your hole below the surface of the liquid, gravity will cause a much higher mass flow rate than if you punch the hole in the gas because of the differential density (delta rho) between the liquid and the surrounding air and the potential energy stored in the liquid above the hole.

The only driving force for the gas flow is the marginal delta rho between the saturated air and the (supposedly) sub-saturated ambient air - not much force to be had there.

David

 

[packdad]

Hmm, I think maybe I need to clarify my question (sorry). The lower half of the vessel contains saturated water. The upper half contains saturated steam (no air). Although I didn't say it, I'm assuming that the outside of the vessel is at STP, and the inside is well above STP in order to reach and maintain saturation conditions.

See, I'm thinking that, with a hole in the steam region, flow would exist as (be modeled as) a compressible fluid through an orifice or pipe. In the liquid region, due to the fact that it's a saturated liquid, the flow would also be that of a compressible fluid (ie, steam) since any pressure drop at all would cause the water to flash to steam.

Maybe I'm wrong. Or, maybe it really depends mnre on the nature of the "hole" in the tank.

It's a strange question of little practical value, but I thought it was interesting to think about.

 

[ccfowler]

Being a bit fussy, you would not likely have saturated liquid throughout the bottom half of the container because the pressure would increase proportionately with depth below the water surface. Therefore, most of the liquid phase would be compressed liquid.

I believe that it would be most likely reasonable to estimate flow through a hole in the bottom half as liquid initially, but it would flash to a two phase flow. If the vessel wall is very thin, the flashing probably would not affect the flow rate very much, but if the wall is relatively thick, the flashing would be important to the flow rate.

Actually, a variation of your problem can be observed in practical power boiler (steam generator) operation with tube leaks. Very often, continued operation and an orderly shut-down is practical with substantial leakage from steam-filled tubes, but substantial leakage from water-filled tubes will likely force an immediate shut-down due to the much greater mass flow rate.

 

[pmureiko]

The mass flow rate will be different due to the difference in density between the water and the steam. Mass flow can be increased with sonic flow by increasing the upstream density even though the volumetric flow is limited by sonic velocity.