Liquid Flow Rate: A vs B - Understanding Fluid Dynamics

[s_mack]

Hi. I used google and found this place. I figure its as good as any to ask this question, which I'm sure forces you guys to dumb yourselves down about 3.14 notches.

And this very well may not be the place to ask this question, so feel free to tell me to sod off if there's somewhere else I should be asking (but please also feel free to guide me in the correct direction if that's the case).

Let's not worry about the "why" if we can... I've simplified this example as much as I could such that if you give me the answer, I should then be able to figure out the real application on my own.

Refer to the diagrams. Let's say these are pipes containing water. A vs B... Question: Is the flow rate of the water at point X in system A greater than in system B ? or the same? Not enough info? Same input, same demand, same pipe diameters, etc... just splitting the path is the only difference.

I'm not a student. I'm certainly no engineer. I'm just trying to figure out something and it occurred to me that there may be something about fluid dynamics that goes against my intuition. My intuition tells me that the flow rate @ X for A is greater than for B because the water crossing X has some going down that parallel pipe in B... but I guess I wouldn't be shocked to find out they're equal.

Thanks.

 

[Bill_K]

Not enough info. The answer depends on what you mean by "same input." It depends on how the source will respond to the change. There's an analogy with electric circuits in which the pressure corresponds to voltage, pipe diameter to resistance, and flow rate to current.

By adding the extra pipe you've lowered the resistance. If "same input" means the same number of cubic feet per minute, then clearly the flow at X in diagram B is less, since it gets only a fraction of the water. On the other hand, if the source can respond with more water, maintaining the same pressure as before, then the flow at X will be unchanged.

 

[s_mack]

Thank you. The source can respond with unlimited water for this purpose, so then the flow at X will be unchanged. That's what I needed to know but I didn't word it properly. Thanks again.

 

[russ_watters]

Im not aware of a way to make it constant without an active control system designed specifically to do that. Any standard supply system will supply less water to x in B.

 

[s_mack]

Hmm... OK then... two viewpoints. Now which is it? :)

Both make sense to me. That's the problem.

 

[Studiot]

Really you need to ask a central heating plumber, not a physicist. This is a common problem people encounter when adding extra piping to an existing system and they find that there is reduced flow at the tap or radiator at point X.
Plumbers overcome this with a manifold or reducing pipe sizes.

The difficulty is that the input pipe to the letter B in your diagram has not changed so why would you expect it to suddenly be able to carry more flow?

 

[s_mack]

Youi're probably right that a plumber could (maybe) answer the Q... but he wouldn't know why. He'd also charge me $90 a hour (with a minimum 30 minute) and insist on coming to inspect the diagram in person prior to answering :)

Input B wouldn't carry more flow, so I'm not sure I understand the question. The demand hasn't changed so the input flow wouldn't change. The question is whether or not branching the supply decreases the flow at the branches or if they both have the same flow as one did before.

Again, intuitively it seems like each branch would have (approximately) 1/2 the flow in B then the single branch did in A. Same amount of water being carried down two routes instead of one.

Your example about adding pipe reducing flow... does it? Your proposed solution to that "reducing pipe sizes" increases pressure, not flow. No?

Let's use the plumbing analogy with the diagram because actually its pretty close. Say the "input" is city water. Relative to the house requirements, that's pretty much "unlimited" flow and pressure. Let's say X is a meter of some sort (we don't have metered water here but I think many people do so that shouldn't be too unrealistic) and the output is a shower running down the drain. Now let's add a pressure reducer valve right before the shower so that output has constant flow and pressure (because we're assuming everything upstream from there is effectively not a limiting factor). Assuming all pipes are the same diameter and the branch location is close enough to be a non-factor... is X lower in B or the same as A?

Does the system saturate (probably wrong term) such that the flow rate in both branches is constant (whether or not at same pressure isn't relevant to me)? Or does my intuition hold that both branches would distribute the flow evenly between them? Or I suppose a 3rd option that is feasible in my brain... the nearest branch has all the flow and the furthest branch essentially has none as the water takes the shortest path? I kinda doubt that... but I'm not the smart one here :)

- Steven

 

[Studiot]

I'm not sure if you are trying to ask a question or expound an answer.

Taking your two diagrams the length of pipe from the arrow to the point labelled A in the first diagram and the point labelled B in the second is stated to be identical.

Any fluid that reaches the single or double branch has to transit this length of pipe first.

Flow in this length of pipe is not determined by the subsequent number of branches.

In other words this length of pipe controls the flow into the branches or acts as a bottleneck.

Reducing pipe sizes has not to do with pressure. A plumber will take an inch a quarter feed from the source, reduce it to three quarters after a certain distance, reduce it again to a half inch further down the line. The pressure falls continuously all the way down the line due to pipe friction losses.

Alternatively he might use an inch and three quarter pipe as a manifold with several half inch take offs.

 

[Curl]

If the input is just a pressure source, the flow at X is lower (but not too much lower) than without the parallel pipe.

If you remove the parallel pipe you'll always get more water.. how much more is a little tricky to explain, I don't really know your level or if you have studied fluid mechanics or pipe flow theory. You said you are not a student or an engineer, so what is your profession and experience in physics?

 

[s_mack]

Next to none. I took a 100-level physics course in University to satisfy breadth requirements... but my education is in business.

Lol. I guess it wasn't a simple question. I have one person saying A vs B will be equal. One stating it won't be. One stating it'll be close. One... I'm not sure what's being said there.

Thanks anyway guys.

 

[russ_watters]

Really you need to ask a central heating plumber, not a physicist.

Or an engineer who designs such systems...

 

[russ_watters]

Lol. I guess it wasn't a simple question. I have one person saying A vs B will be equal. One stating it won't be. One stating it'll be close. One... I'm not sure what's being said there.

Thanks anyway guys.

It is a simple question if it is defined clearly, but you didn't define it clearly. We need to know about the source of water. One could easily design a system with controls necessary to keep the flow constant in that branch. It's pretty common.