Need to calculate pressure increase from heating water going through a pipe that is open 1

[978industries]

So I am working on a project at work and need some help. I am trying to calculate how much the water pressure, velocity and flow rate would increase inside a pipe that is being heated, when it's flowing through the pipe, and coming out the other end. Please see the example below.

Example:
So let say the pipe section that is being heated is 10 feet long and 1 inch in diameter. The pipe has an inlet water temperature of 68ºF/20ºC and the water exiting the pipe will be 248ºF/120ºC (180ºF/100ºC increase). The outlet of the pipe is open ended without any nozzle on it, so water is coming out the other end. The pipe is laying horizontally and at the same level as the pump. The water flowing through it is not under any pressure from the pump, and it's flowing at 1 gallon per minute and moving at 1 inch per second (these are all just example numbers).

I have spent the weekend trying to find an equation to determine what the overall pressure increase would be, the exiting velocity would be, and the increase in the flow rate would be, but I can't find anything to represent a pipe with moving water and an open exit point. Everything I see is for moving water in a sealed pipe, non-moving water in a sealed container, or non-moving water in an open container. But nothing for this type of scenario.

As the water temperature increases, the overall volume of the water should increase as well because of thermal expansion, right? And as that volume increases, the exiting pressure, velocity, and flow rate should also be increasing, right? If I need to find more data on this type of scenario, please let me know what else would be needed to solve this problem. Thermal dynamics is not my strong suit. I know the gist of it, but I'm striking out with this currently.

I'm just stuck and can't find the correct equation I need to solve this problem. If someone could explain how to determine the answers from the hypothetical example above, and provide the equations they used, that would be awesome! I just can't figure it out!

Thank you in advance!

 

[IRstuff]

??120C means it's boiled, so it's steam?

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[978industries]

Yes, it's wet steam.

 

[BronYrAur]

I think you are missing IRstuff's point. It will no longer be water flowing through a pipe. It will also not be above 212 degrees unless you have some way to contain pressure. The thermal expansion of the heated liquid water will be insignificant compared with the expansion from phase change of liquid to Vapor. I'm really confused about your overall question. You also mention that the pump is not delivering any pressure to the water which makes no sense.

 

[IRstuff]

and I try sooo hard...

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[BigInch]

I think that, before the OP found out that he was making steam, he thought the flow in the pipe would be driven by thermal effects only, without any pressure added by a pump. Flow caused by thermal density changes only, which is normally driven by buoyancy. In a horizontal pipe bouancy wouldn't be able to contribute much to flow, as buoyant forces are vertical, so the only thing forcing flow out of the pipe would be the change in volume as the water went from cold to hot water. Change in volume divided by the time needed to heat up the water would equal flow rate. Apparently the cold water would be feed in at the same inflow rate as the outflow rate, for which he was not expecting to need a pump. I expect that it would be a pretty small flow, until 100C was reached and steam began to flow. If steam is being generated, the outflow would be limited to the volumetric steam generation rate obtainable from the power being delivered to the water in contact with the heat source.

 

[LittleInch]

978,

As noted above I can only assume some of your figures are just gueesse, but here goes.

What you're describing is a very simple boiler.

The thermal effects on the water volume increase from 20C to 99.5C is virtually negligible ( <1%).

Your pump I can only assume is some sort of PD pump which is pushing a fixed volume at very low pressure through such a small pipe with an open end.

what's happening is that your water is then turning to steam.

As Born says, your steam simply cannot be at 120C at atmospheric pressure. It's just not physically possible. You could get water at 120C, but you would need to pressurise this to stop it boiling. This would be a minimum of 1 barg. This would result in an approx. 2% increase in the volume of water. Releasing this water into the atmosphere would result in some / most of it turning into steam (superheated water).

Using an online steam table like this

http://www.spiraxsarco.com/Resources/Pages/Steam-Tables/saturated-steam.aspx

You need to decide if the heat input you are using is actually capable of turning all your water flow to steam or not - that's a different question.
assuming all the water turns to steam then what you find at 100C and atmospheric condition is that your cubic metre of water has turned into 1,604 m3 of steam (WOW) or in your case 1,604 gallons (volume) of steam. NOTE - This is at atmospheric pressure.

This will, even in short pipe need some sort of pressure to eject that amount of steam so everything starts getting a bit complex, but it gives you the basic idea, maybe.

The amount of heat you will need though is significant (2,600MJ/m3) and hence if you have a constant flow then your fluid coming out of the pipe could end up being a mixture of steam and v hot water (<100c). That's even more complex, so try and let us know what it is you're trying to do a little better and we may be able to get you there.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[BigInch]

I'm not exactly sure how the OP seems to have missed that he was landing on the steam side of the table.

 

[Drexl]

I can't really think of what kind of application this would be, are you sure you describe it correctly?
In your example, if you have 120C at the outlet (at atmospheric pressure at equilibrium) you must have pure steam and it is not possible to supply that much heat through such a short pipe.

If you instead have 100C at the outlet at equilibrium you can have any degree of wet steam. Do you know how much heat you are supplying to the fluid? You can calculate backwards from the exit and see what the pressure need to be in order to relieve the fluid at the specified rate. This is in practice a very complicated problem as you need to calcuate 2-phase pressure drop.

Please give the actual setup and not an example.