Tank draining flow rates with opening different valves?

[mdefense]

This question is a little different than previous questions that I've seen regarding tank draining problems. I have an 800 gal. tank, with a wetted height of 28". Attached to the main 2" exit pipe of the tank are 6 spigots/valves each with a diameter of 3/4". Solving for the flow rate for one of the spigots is relatively straight forward, using the standard Bernoulli equation. Opening 2 or more spigots is where my equations are falling apart. Preliminary lab tests show that the flow rate (at each spigot) is the same with either 1 spigot or all spigots open. Is this correct? Any comments?

 

[zdas04]

Let me start with some terminology. Out of the tank you have a riser. The riser exits into a header. The spigots exit from the header.

Total flow rate out the sum of the spigots is a function of the dP between the header and the exit pressure (let's say atmospheric pressure). Header pressure is a function of the height of the liquid in the tank minus friction losses to get the liquid from the tank to the spigot. With one 3/4" spigot open (14% of the flow area of the 2" riser), the flow rate in the riser and header is low enough that the friction loss is approximately zero. Opening the second spigot (28% of the flow area of the riser and header) is still about zero friction loss in the riser and header. Opening 6 spigots (84% of the flow area) is probably getting to the point where your header pressure is slightly less than hydrostatic, but not much. My guess is that with all 6 spigots open you'll see something like 99% of six times the flow rate of one spigot open--most likely the difference is smaller than your uncertainty in measurement.

David

 

[ione]

The more binding component of pressure drop in your system is given by the spigot itself. If the spigots are placed closed enough to keep pressure drop in the riser near to zero, each one of the secondary branches (outlet) “sees” the same upstream pressure. Each spigot discharges to atmosphere and so each branch experiences the same pressure drop. This leads to approximately the same flow rate through each spigot.

 

[MiketheEngineer]

Agree

 

[waterpipe]

Considering your system sizes, and the shown distance between spigot 1 and 2, I do not expect to see a meaningful difference between one or two spigot.

Now, neglect the distance between spigots and consider 100 spigots (well, let's consider 50 for the moment!) are connected to the same pipe next to each other. Do you expect to see the same flow rate? I don't. obviously there will be a flow rate for each valve, but the amount is less comparing to the situation with only two valves. So how can you analyse this more scientifically? I would suggest to draw the friction curve of your pipe (available head at the end of the pipe versus flow) and consider the cure steepness. you can get a picture of your system and the expected flow rate from where adding more spigots would decrease the flow of each one.

I suggest using Epanet with its extended time simulation, to model your system and calculate the draining time of your system under different scenarios.

 

[zdas04]

When you get enough spigots open (5? 6?, 7? somewhere in there), then the flow rate will be controlled by friction in the riser. I'd just use D'Arcy Weisbach to calculate the flow rate in the riser and not bother with fancy simulations.

David

 

[waterpipe]

zdas04,
I like your approach and the solution for this case and do agree that concrete understanding of fluid dynamics is the essence before each simulation.

 

[cvg]

your assumption of equal flow in each spigot is not correct. the closest spigot will have a higher flow rate than the furthest. Each will be different.

given that you have not indicated:

lengths of pipe
smoothness of the pipe
type of valves / spigots
specific gravity or viscosity of the liquid

this could be a minor difference in flow (and perhaps not measurable in the lab) or a large difference. the difference in flow will be more pronounced with longer, rougher pipes or with liquids with higher viscosity and is due to friction losses in the pipe.

you don't need epanet to do this problem, but you do need to include friction losses for the pipe