Flow Rate Problem 1

[Hamood101]

I had a long argument on this with my friends( Eng's) therefore, I decided to post it here to get your opinion:

Two Tanks have the same capacity and are at the same height. They are at 10m elevation. Both are open to atmosphere. They contain water. From each an 8” pipe comes down the tank to transfer the water to an open containers in the ground (container A and B). The down-comer from Tank 1 is 9m long. The down-comer form Tank2 is 2m. The Tanks are round with radius of 1 m. The level height at each tank is 2m.
Assumptions:
Assume no friction losses in the down-comer pipes. All conditions are the same in both tanks. Assume there is no splash out from tank 2 down-comer pipe.
The question:
1. In which pipe will the flow rate be higher? And why? i.e. Which container A or B will be filled faster?



see attached.

 

[Artisi]

Is this a trick question or a homework problem?

For interest, how about including the for and against arguments.

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

 

[TD2K]

Hint, look at the hydraulics of the two systems.

 

[katmar]

Because you have defined the pipes as frictionless, the top tank and the downcomer are effectively all one vessel (just with a strange shape). This means that the outlet from Tank 1 has a head of 11m while the outlet from Tank 2 has a head of only 4m. The water will therefore flow faster from Tank 1.

It would probably be a bit more intuitive if you showed the bottom of each downcomer discharging horizontally, rather than vertically downwards. It makes no difference to the hydraulics, but it makes it more obvious that the downcomer is just part of the tank if the discharge is horizontal.

It would also be more obvious if you lowered the platform for Tank 2 by 7m so that the discharge points were at the same elevation. When the tanks are both mounted 10m high (as per your sketch) the distance that the water falls after it leaves the open bottom of the downcomer from Tank 2 has no influence on the flowrate. Think of water flowing over a waterfall. The rate of water flow is not influenced by the height of the waterfall.

I hope this is a genuine discussion and not a homework problem. Frictionless pipes are quite rare outside of homework problems.

Katmar Software - Uconeer 3.0

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[BigInch]

Friction over such a short length of pipe won't matter so much. What does is Bernoulli. There is much more potential energy that can be converted to velocity at the lower elevation of Tank A's downcomer outlet than is available at Tank B's downcomer outlet, so I'll go with Katmar's answer.

But I will allow for some possibility that, if you measure the time it takes all the water to reach the elevation of tank A's downcomer outlet elevation, it could be a tie, or due to the shorter length of B's downcomer, system B might actually empty first, but I'll let someone else analyze that.

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[Hamood101]

katmar,BigInch-thank you.

No, it wasn't a homework. it was a discussion at work. the argument maily was the "head", some say's that in both tanks it shold be 10 m !!!?

 

[BigInch]

IMO it depends on where you draw your system boundry and that depends on, if you consider the system empty when the water leaves the pipe's outlet, or when all water hits the floor.

What do you think? Does all the water finish hitting the floor at the same time? Neglecting friction, of course. My reasoning is that water leaving the outlet of tank B would be subject to gravitational acceleration on the way to the floor and increase velocity.

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[TD2K]

The head in terms of generating flow is not 10m.

For the first tank, you have 11m of head contributing to the flow, that's the 2m of water height plus the 9m of water in the drop leg. Offsetting that is the entrance, piping and exit losses. If you want to ignore piping losses, the resistance to flow K is 1.5 assuming you have a sharp entrance.

For the second tank, you only have 4m of head contributing to flow.

Roughly speaking, I'd expect 50% more flow out of the first setup, at least initially till the water level in the tank starts to drop depending on the makeup system.

 

[Artisi]

A good example to demonstrate the flowrate from these 2 tanks would be single tank with 2 outlets at different heights, the lower outlet will have a greater flowrate than the upper outlet - agreed?

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

 

[BigInch]

smpyjrt trf jrttomh.
Outlet pressure of both pipes is 14.7 psia. Assume there is a very large diameter pipe enclosing, but not touching, the free vertical stream of water exiting tank B that terminates at the floor with a reducer of outlet diameter equal to that of the downcomer of system A. That should make the downcomer pretty much frictionless for the B system.



"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[Hamood101]

Artisi, agreed …..but in this case the level in tank 1 will drop faster i.e. the head will decreases faster . hence, the flow rate will decreases with time. It’s a dynamic system !

We may end up empting the two tanks at the same time. !!

 

[Artisi]

Correct, to solve the problem in terms of time, you will need to calculate the flowrate versus falling head in each tank.
Yes, the head will fall at a higher rate in tank with the longer downpipe but will only be equal to the other tank when the head in each tank measured vertically from the discharge point is equal to each other, if that should ever happen.

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

 

[urgross]

I would expect container A to fill faster. The two tanks are the same, but not total volumes. Tank 1 has 7 meters of 8" pipe which Tank 2 does not have, all closer to the container. Tank A and Tank B are the same for the first 2m of downcomer, for which flow in the absence of friction, would be the same.