Effect of gravity on a loop 3

[Audionut11]

Hi. I have a question which is probably easy, but I can't get my head around it.

There is a body of water in which a pipe has both ends submerged.

The pipe is a loop, and extends 20 meters high.

The pipe is primed with water, and I want to move water from 1 end of the pipe to the other.

The siphon effect does not count as both ends of the pipe are at the same height.

Do I still need a pump with sufficient head to move the water, or does gravity get cancelled in this arrangement as I am being led to believe?

Thanks.

 

[katmar]

The problem is in the downleg of the loop. If the pipe is to remain full then it is likely that you will get pressures at the top of the downleg that are low enough to boil the water. This leads to vibrations and instability. The solution to this is to have an air vent at the top, but then there is no pressure recovery in the downleg and the pump faces the full 20 m.

You should start your pressure analysis at the outlet - bottom of downleg - and working backwards. By accounting for the static head and the friction losses you can work back up the downleg to get the pressure at the top. With a 20 m high loop you will probably find it is negative at the top. This is clearly impossible and nature solves the problem by boiling the water to lower the static head.

Katmar Software - Engineering & Risk Analysis Software

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[Audionut11]

And the pressure would be directly related to the height of the loop, correct?

If the loop height was smaller so that the pressure at the top was still positive, would there still be an increase in temperature?

Or does the temperature only rise as a result of the negative pressure?

 

[katmar]

The temperature does not rise. The liquid boils because of the lower pressure. Perhaps I should say the liquid vaporizes, then it doesn't sound like it is getting hot.

I see you are a computer engineer, so perhaps a little further explanation is warranted. At any given temperature a liquid exerts a fixed vapor pressure. At higher temperatures the vapor pressure is higher. When the vapor pressure equals the surrounding pressure the liquid boils. At high pressures a higher temperature is required to boil the liquid (as in the domestic pressure cooker) and at low enough pressures the liquid will boil at ambient temperatures.

Katmar Software - Engineering & Risk Analysis Software

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[Latexman]

Yes, you will need a pump.

Good luck,
Latexman

 

[BigInch]

You must pump the water to the top of the loop. Gravity assists with the remaining pipe flow, but only up to a certain flowrate where you essentially begin to try to put more flow through the downleg than gravity will allow alone. That will require that the pump's power be increased to account for that additional head loss due to friction in the downleg friction. Gravity will assist flow up to the point where the flowrate's friction loss is less than or equal to the energy gained by the fluid's drop in elevation.

Only put off until tomorrow what you are willing to die having left undone. - Pablo Picasso

 

[katmar]

BigInch's description is correct, but only covers the high flow part of the picture. At low flows there is no pressure recovery due to gravity. Imagine you start off with a very low flow - say a velocity of a (normal) inch per second and with the pipe loop empty. This low flow will gradually fill the upleg. When the level reaches the top the water will overflow into the downleg. It will fall under gravity and will achieve a velocity of much more than 1 inch/sec. This means the downleg will not run full and there will be no pressure recovery and the pump will still "see" a head of 20m.

Now imagine that you gradually increase the flow rate. Eventually you will reach a flow rate where the downleg runs full. When this is achieved the static head recovery in the downleg will aid the pump and it will "see" less than 20m. Increasing the flow rate beyond this point is what BigInch has described. The friction losses in the downleg cut into the pressure recovery and eventually a flow rate will be reached where the net recovery is zero. In practice, this is a very high flow rate and it is rare (but not unknown) to employ such high flow rates in process plants. At such flow rates the friction in the upleg is also significant.

The nasty part is in the low flow zone where the downleg is not yet full. This is a frequent circumstance. It can cause severe vibration. The cure is leave the top open, or use a vacuum breaker/air vent.

Katmar Software - Engineering & Risk Analysis Software

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[cvg]

pressure sustaining valve / regulating valve should be used to keep the pipe primed to avoid draining and re-filling the pipe each time the pump is started up. There should be no reason to allow the pipe to drain every time.

 

[BigInch]

The point where a flowrate's friction loss becomes equal to or greater than what gravity can sustain alone is called the "critical flowrate", as in open channel flow. If this occurs inside a pipeline instead of an open channel, we call it "cascade flow". Pressure in the line above the liquid level during cascade condition is at all points equal to the vapor pressure of the fluid. There is no pressure recovery possible, until the line once again becomes full, perhaps not until some time after it enters the lake again. I didn't mention that, since with gravity doing all the work after the fluid reaches the peak, it is immaterial as far as the pump is concerned when any flowrate is below "critical flow". The pump has only to supply the head needed to reach the top of the "loop" at any of the "low" flowrates and simply allow gravity to take over as the fluid "cascades" across and down the overbend.

There may be no reason to keep the down-leg full of water and, if so, there is no reason to have a backpressure control valve at the outlet as cvg suggests. Non-pressurized sewer lines, for example, run at similar partially full conditions all the time. In fact, they are designed to flow at about 80% full because that is the point where the flowrate is maximized, since friction does not act between the fluid and the arc at the top of the pipe that the fluid does not touch.

Many petroleum pipelines are designed to run in cascade conditions too. Especially when they are running at "first oil" scenarios, before all the wells are producing and total field production going into the pipeline is still at a bare minimum. The BTC pipeline 42" crude pipeline from (Baku, Azerbijan to Ceyhan, Turkey) has a pressure reduction station just before going down the last slope to the marine terminal at Ceyhan which was used exactly for that purpose, to keep the high mountain head (2800 meters) from raising the pressure and accelerating the flow into the marine terminal. It was operated at cascade conditions for a number of years, before flow was increased enough to lose all (and more) to friction what it gained from its descent down the high mountain slope. During that time the pump stations only had to lift the crude to the 2800 meter head (plus some up-leg flowrate friction) to cross that last 2800 m mountain range.

Only put off until tomorrow what you are willing to die having left undone. - Pablo Picasso

 

[77JQX]

Audionut11 - Without water moving, and with both ends of the pipe open, the theoretical maximum height you can keep water in the loop is about 10 meters above the water surface (depending on the temperature of the water). Any higher than that, and you'll need to do something about the low pressure at the top of the loop. Once you start to pump the water, the 10 meter number can get higher, but only by the amount of friction in the downleg. As long as the absolute pressure in the top of the loop remains above the vapor pressure of water (a function of temperature, about 0.17 meters at 15C), then you get credit for the water in the downleg. Once you get higher enough that the pressure would be below the vapor pressure, then you need to take additional action, as the others above have so ably described.