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# Gravity Flow Control Valve Calculation

gravity flow

6 replies to this topic
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### #1 rikakose

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Posted 06 August 2019 - 09:52 AM

https://www.cheresou...r-gravity-flow/

I am confused by the pressure difference across  the CV.

In the calculation, the pressure at CV inlet is the total static head from liquid level to the drain point minus the line resistant.

In the later discussion, it is static head from the liquid level to the CV level. Which means, the inlet pressure is even lower than the down stream pressure.

What will be the right solution.

### #2 katmar

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Posted 06 August 2019 - 10:31 AM

The thread to which you have linked has many drawings with many changes and many opinions.  It is very hard to know what your question is.  Rather make a new drawing showing exactly what is troubling you.

### #3 rikakose

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Posted 06 August 2019 - 11:00 AM

The thread to which you have linked has many drawings with many changes and many opinions.  It is very hard to know what your question is.  Rather make a new drawing showing exactly what is troubling you.

I attached the calculation

In this calculation, pressure at the inlet of CV is 2.818 barg, at the outlet of CV is 2.466

Another idea is that the inlet pressure CV is 0.11 barg (liquid level to the CV location level)

Which one is the right solution?

### #4 katmar

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Posted 06 August 2019 - 12:50 PM

To work out the pressure at any point in the line you need to start at the discharge end of the line where you know the pressure, and work backwards.  There is no information on what the pressure is at the discharge end and it is therefore impossible to calculate the pressures you want.  For example, unless you know what the pressure is in the 3" vertical section you cannot know whether it is running full or not - and this changes the calculation completely.  If there is slack flow in the vertical section then there is no pressure drop.  As it is presented, this is an indeterminate problem.

### #5 breizh

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Posted 06 August 2019 - 10:16 PM

Hi rikakose ,

You may find some interest reading this pamphlet .

Breizh

### #6 rikakose

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Posted 07 August 2019 - 02:07 AM

To work out the pressure at any point in the line you need to start at the discharge end of the line where you know the pressure, and work backwards.  There is no information on what the pressure is at the discharge end and it is therefore impossible to calculate the pressures you want.  For example, unless you know what the pressure is in the 3" vertical section you cannot know whether it is running full or not - and this changes the calculation completely.  If there is slack flow in the vertical section then there is no pressure drop.  As it is presented, this is an indeterminate problem.

The discharge flow is flooded.

Discharge point is under sea water 25 m.

### #7 katmar

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Posted 07 August 2019 - 04:19 AM

Although gravity-driven flow downwards in a vertical pipe seems simple, it gets very complicated when you get into the details. The most common example of this in everyday life is the domestic effluent drain lines (stacks) in highrise buildings. To get around the complications, the plumbing codes stipulate very safe rules of thumb for the pipe sizes, flowrates and venting requirements. In fact, you would probably get to a better design using these codes than by using a simple Darcy-Weisbach calculation.

The crux of the problem is illustrated if you calculate the pressure in the vertical drain line at exactly sea level. The pressure required is just the 0.54 m head you calculated to overcome the friction losses because the static heads in the pipe and open sea cancel each other. Now that you know that the pressure is 0.54 m at the sea level point you can start to work back up the pipe. To give this 0.54 m of head all you need is 0.54 m of water in the pipe. If the level in the pipe was more than 0.54 m then the pressure would be higher than needed and the level would drop as the excess flow caused by the higher pressure drained the pipe down to the equilibrium point of 0.54m again.

If you cannot have a level in the drain pipe of more than 0.54 m above MSL, what is above the water in the pipe? At start-up the pipe will be full of air, but with time the air will be dissolved or entrained into the water and will be removed. This could take days or even weeks. Once the air has gone the pipe must be filled with vapor, but to provide vapor the water must boil. Now you get into all sorts of problems with vibration and cavitation and you should avoid anything that could cause vacuum conditions here.

The solution is to take the same approach as the plumbing codes and to install a vent immediately after the control valve so that there is a supply of air to fill the pipe above the equilibrium water level. So now we have fixed the pressure at the downstream side of the valve at atmospheric pressure, and the pressure drop across the valve is simply the static head in the supply tank. That solves the valve sizing problem, but we still have the pipe sizing problem to contend with.

A flow of 10 m3/h in a 3" Sch 80 pipe gives a velocity of 0.65 m/s and a Froude Number of 0.76. This means that there will be a continuous entrainment of air into the falling water and air will be sucked in through the vent after the control valve. I have come across some quite serious whistles in situations like this and there is a danger of sucking debris, birds etc into the vent. In some instances entrained air can also impact the process at the discharge point, but that is probably not a problem here.

To prevent the air entrainment the Fr No must be kept below 0.31, which translates to a 5" pipe for 10 m3/h. On the other hand, the pipe below sea level will always be full of water, so from about 1 m below the sea level to the discharge point you could switch to 2" pipe (which would raise the equilibrium level in the drain pipe to 3 or 4 meters, but there is plenty of head to play with here).