Volumetric flow from vessel through pipe to another vessel

[saxman2u]

Hi,
I am trying to calculate how much water can flow with just gravity from water tank A to water tank B. Each tank as a 2" orifice on the side wall at the bottom. If water tank A is 100% full and water tank B is completely empty, if someone opens a 2" ball valve at the bottom of tank A, how many GPM's flow through a 2" SCH40 PVC pipe that is 50 feet long? no elbows, just straight pipe. Both tanks are 12 feet high and 12 ft diameter. Tank A is 50% full with water 6 feet higher than the orifice. Let's also say the orifice of tank A is short tube with Cd=.81 I am just curious about the max flow when tank A is pretty much full or the first 60 seconds of flow after someone opens the 2" ball valve.

I https://www.haywardflowcontrol.com/assets/documents/flowcontrol/pdf/VessFlow.pdf where the water is 6 feet higher than the 2" orifice and calculated that about 150 GPM can flow out of the vessel if someone opens or drills a 2" hole in the tank. Can someone please confirm i did this math correctly, https://www.haywardflowcontrol.com/assets/documents/flowcontrol/pdf/VessFlow.pdf . What I don't understand is what does friction loss or a 50 ft piece of 2" SCH40 PVC pipe do to that flow of 150 gpm? I thought that 2" PVC pipe can handle around 55 GPM with low pressure and water traveling 6 ft/sec. How can 150 GPM flow out of a 2" opening in a tank but tables out there show that 2" PVC pipe can only handle 55 GPM (link here about flow rate through pipes)? is it because the 6 feet of water in the tank is increasing the velocity of the water therefore more water can be shot through the 2" pipe?

Finally, if the tanks keep there 2" orifices and their 2" ball valves, and I remove the 50 ft of 2" PVC pipe and install 3" PVC pipe instead to minimize friction loss, does this really improve the flow or GPM and how much faster does tank B fill up at peak flow when tank A is full during the first 60 seconds? Is it worth it to spend more money on bigger pipe and labor??

Thanks,
-S

 

[jrmichler]

This tank to tank gravity flow problem needs to be analyzed as a system. You have a length of pipe, a valve, and an entrance. Each has a pressure drop, where that pressure drop is a function of the flow rate.

The procedure is as follows:
1) Start with an assumed flow rate.
2) Calculate the entrance loss using the orifice flow equation with entrance coefficient.
3) Calculate pressure drop through the ball valve. If it's a full port ball valve, where the inside diameter is equal to the pipe ID, you can ignore this.
4) Calculate the pressure drop for the length of pipe. The Moody chart (search the term) is one way. An easier way is the design tables in a book such as Cameron Hydraulic Data.
5) Add up the pressure drops and compare to the difference in level between the two tanks. Then iterate the flow rate, go to Step 2, and repeat until the calculated pressure drop matches the difference in level.

Now that you have calculated the flow rate for 2" pipe, you can change to 3" pipe and repeat for the new conditions.

Things to look for if you want to speed up the flow:
1) Entrance loss. If the entrance loss is a significant portion of the total pressure drop, then rounding the inlet to increase the orifice coefficient will increase flow.
2) Ball valve. A reduced port ball valve has some flow restriction, while a full port ball valve has near zero restriction.
3) Pipe. Your calculations will show if the pipe is the major restriction. If it is, a larger pipe will increase flow.

 

[BvU]

http://www.pressure-drop.com/Online-Calculator/

shows 100 Gpm causes 0.25 Bar of pressure drop.

 

[saxman2u]

This tank to tank gravity flow problem needs to be analyzed as a system. You have a length of pipe, a valve, and an entrance. Each has a pressure drop, where that pressure drop is a function of the flow rate.

The procedure is as follows:
1) Start with an assumed flow rate.
2) Calculate the entrance loss using the orifice flow equation with entrance coefficient.
3) Calculate pressure drop through the ball valve. If it's a full port ball valve, where the inside diameter is equal to the pipe ID, you can ignore this.
4) Calculate the pressure drop for the length of pipe. The Moody chart (search the term) is one way. An easier way is the design tables in a book such as Cameron Hydraulic Data.
5) Add up the pressure drops and compare to the difference in level between the two tanks. Then iterate the flow rate, go to Step 2, and repeat until the calculated pressure drop matches the difference in level.

Now that you have calculated the flow rate for 2" pipe, you can change to 3" pipe and repeat for the new conditions.

Things to look for if you want to speed up the flow:
1) Entrance loss. If the entrance loss is a significant portion of the total pressure drop, then rounding the inlet to increase the orifice coefficient will increase flow.
2) Ball valve. A reduced port ball valve has some flow restriction, while a full port ball valve has near zero restriction.
3) Pipe. Your calculations will show if the pipe is the major restriction. If it is, a larger pipe will increase flow.

This is great information. three questions:
1. is "assumed flow rate" that you mention in line item 1 the https://www.haywardflowcontrol.com/assets/documents/flowcontrol/pdf/VessFlow.pdf
2. For line item 4, pressure drop, is this friction loss or PSI loss across the pipe?
3. for line item 5, what is the pressure drop for water entering tank B? I don;t quite understand that

-S

 

[jrmichler]

Friction loss in a pipe is pressure drop.
In order to calculate pressure drop, you need the flow.
In order to calculate the flow, you need the pressure drop.
You have pressure drop from entrance loss, valve restriction, and pipe friction. That's three sources of pressure drop, and they are calculated separately.

The total pressure drop is the difference in level between the two tanks. Part of that pressure drop is entrance loss, part is across the valve, and the rest is pipe friction.

Because you need the answer in order to calculate the answer, you solve this by iteration. Guess a flow, calculate the total pressure drop for that flow, compare to the actual pressure drop, estimate a flow, repeat. Your starting guess is just that - a guess. Say you guess 500 GPM, and the calculated pressure drop is 1000 PSI (numbers are wild guesses). In that case, your next guess would be much smaller, say 5 GPM, and the calculated pressure drop 0.01 PSI. That would be way too small, so the next guess would be in between. There are ways to speed this up, but this way will get you to a correct solution.

 

[Chestermiller]

https://www.engineeringtoolbox.com/steel-pipe-schedule-40-friction-loss-diagram-d_1145.html

6 ft of water is about 2.6. psi. 2.6 psi over at 50' pipe is about 0.05 psi/ft. That would result in an initial flow rate of about 7 gpm for a steel pipe.

 

[jrmichler]

First iteration: The chart in my Cameron Hydraulic Data shows head loss of 12.0 ft per 100 feet of copper or brass pipe at 90 GPM. The entrance loss at the velocity of 8.6 ft/sec is 1.15 feet of water.

Second iteration: Since the entrance loss is 1.15 feet, the available head for pipe friction is 4.85 feet, or 9.7 feet per 100 feet. The Cameron chart shows 80 GPM at 9.7 feet per 100 feet. If I was more ambitious, I would recalculate the entrance loss, and iterate a third time.

All of this assumes a full port ball valve. A reduced port valve will introduce an additional restriction, so the flow would be less. I used the chart for copper and brass pipe because those pipes have smooth interiors similar to PVC.

My Cameron got a lot of use when I used to work in a paper mill. I found it to be accurate.

 

[saxman2u]

First iteration: The chart in my Cameron Hydraulic Data shows head loss of 12.0 ft per 100 feet of copper or brass pipe at 90 GPM. The entrance loss at the velocity of 8.6 ft/sec is 1.15 feet of water.

Second iteration: Since the entrance loss is 1.15 feet, the available head for pipe friction is 4.85 feet, or 9.7 feet per 100 feet. The Cameron chart shows 80 GPM at 9.7 feet per 100 feet. If I was more ambitious, I would recalculate the entrance loss, and iterate a third time.

All of this assumes a full port ball valve. A reduced port valve will introduce an additional restriction, so the flow would be less. I used the chart for copper and brass pipe because those pipes have smooth interiors similar to PVC.

My Cameron got a lot of use when I used to work in a paper mill. I found it to be accurate.

Thanks for the info. For your first iteration, are you using 2" copper pipe? Can you send me a link to chart that is similar to the one you are using so I can follow you better? Thanks.

 

[saxman2u]

http://www.pressure-drop.com/Online-Calculator/

shows 100 Gpm causes 0.25 Bar of pressure drop.

let's say there is not another water tank, just a 50 foot piece of pipe connected to the tank that has 6 feet of water in it. If 100 GPM has a pressure drop of .25 bar or 3.63 PSI, can the pressure drop over the length of the 50 foot pipe be greater than the pressure at the orifice or the bottom of the tank which is 2.6 PSI? My orifice equation states 220 GPM is coming from the orifice, and 220 GPM flowing through 50 feet of SCH40 2" pipe has a PSI loss of 14.65 PSI. 2.6 orifice PSI subtract 14.65 PSI ends up being negative, I don't understand how this works out? Thank you for your help.

-S