Does Flow Rate Remain Constant Throughout a System?

[JimiJams]

Hi, yesterday my dad and I were debating whether flow rate stays constant throughout a system. I told him we learned this in physics and he refused to believe it. He's a plumber so he may have thought his reasoning was more justified than mine. He finally said, "I can disprove it now" and opened the tap a little and then a lot. Obviously when it was open a little the pressure was not greater than when it was opened a lot.

So opening the tap must change the flow rate, which would mean the conserved flow rate would only exist within the system. So if I were to open or close a valve in a pipe in the system would flow rate still remain constant on both sides of the valve and, if not, why would it differ?

I'm guessing if you close the valve all the way then open it you're changing the flow rate because there's no water in front of that water to restrict it. But if the valve is left quarter inch open for a while the water pressure would be greater than if we left the valve an inch open for a while, but they both would have the same flow rate so long as the opening on the tap is constant.

 

[Khashishi]

It sounds like your misunderstanding comes from messing up the wording of the problem statement. The correct statement is something like, the flux of water through a pipe is the same across any cross section of the pipe, assuming the pipe doesn't fork off. This is because water is incompressible. More generally (which works for any network of pipes with forks), the total flux of water across a closed surface is zero. You can choose a surface which cuts several pipes, so the statement ensures that the volume of water flowing into some region exactly equals volume of water flowing out.

Obviously, your father is right that the flow doesn't stay constant (in time) when the valve is changed.

 

[Studiot]

Hello jimi,

Well your father may have had a point it rather depends upon what he was talking about.

If you take a large (ish) bore pipe, say 30mm and connect it to a smaller one, say a 20mm and this to smaller one, say 15mm and so on down through 10mm, 8mm and 6mm and then pass water through from the 30mm pipe down the line, the water that comes out of the other (6mm) end will be have passed through each pipe in succession and so have the same flow rate in each.

We call this connecting pipes in series..

Now say instead of connecting the pipes one after the other, both the 20mm and the 15mm were connected to the 30mm pipe and we measured the water coming out of each, since there are now two outlets.
Obviously the total water coming out of both smaller pipes combined equals to total water going into the bigger (30mm) pipe.
So the flow rate is not constant in each pipe but depends upon the pipes and the arrangement.

There are now branches in the system and the flow rate will vary.

Does this help?

It may be worth noting if you have done any electrics in your studies that this is the same for electric circuits and electric current. But do not worry if you have not seen this yet.

 

[JimiJams]

My dad claimed flow rate was never constant in a system, whereas I told him it was, as we learned that in physics.

He tried to prove this by opening the tap varying degrees on a faucet and showing that the flow rate was changing there.

I feel since this was the end of the water line flow rate is free to change because there is no water in front to resist the flow rate. I was wondering if this is the same inside the system, like opening a valve, for instance.

I think I've realized myself, though, that flow rate is subject to change at "the head" of the water because there's nothing there to control it. But in a system between the beginning and end of a water line, the flow rate must be the same throughout. Please correct me if I'm wrong.

 

[JimiJams]

Thank you studiot, that was very helpful. I was really questioning myself after he did the faucet example, but I think since it's the opening to the system the water's flow rate is subject to change. That makes sense about the branches. So each branch will have a lesser flow rate than the total, but does it still remain that the flow rate of a given branch will be constant throughout that branch?

 

[Studiot]

jimijams
So each branch will have a lesser flow rate than the total, but does it still remain that the flow rate of a given branch will be constant throughout that branch?

There is an old engineering saying

Input = Output + Accumulation

or
What goes in must come out or stay there

So either it builds up within a single branch or it comes out the other end.

An example of accumulation might be a dehumidifier.

Moist air flows in through the inlet, to a chamber where the moisture is removed, and back out through the outlet.
The water condensed out of the air collects in a receiving bucket that has to be emptied periodically.

 

[SteamKing]

It's also helpful to realize that flow rates can change when changes are made to a piping system. Obviously, if an outlet valve is closed, flow out will be zero. If the valve is opened, then the flow is not zero any longer.

So, if the system remains unchanged in its configuration, then it is possible for the flow rate to remain the same.

 

[russ_watters]

This is a simple matter of whether the system is open or closed. A domestic water system is open and the flow rate in different parts of the system can be different. In a closed system with no branches, anywhere that the water is moving the flow must be the same. Otherwise it would accumulate.

 

[JimiJams]

so suppose there's a single pipe that forks into two branches, how do you calculate the flow rate of each branch? Would it be divided equally, or would it depend on which branch has the smallest section within its branch, or which branch begins with the largest diameter?

 

[Studiot]

russ_watters
anywhere that the water is moving the flow must be the same

Are you suggesting that in a small bore heating system the flow into a manifold is the same as the flow out through one of the radiator pipes?

Surely you should reconsider this?

And yes it can accumulate (to a limited extent) in a sealed system in the expansion vessel.

 

[russ_watters]

Are you suggesting that in a small bore heating system the flow into a manifold is the same as the flow out through one of the radiator pipes?

You cut the qualifier out right before that quote! The total of all parallel branches must always be equal and is equal to single pipes.

And yes it can accumulate (to a limited extent) in a sealed system in the expansion vessel.

"To a limited extent". Ie, not continuously and as an insignificantly small fraction of the system flow.

 

[Studiot]

Yes I'm sorry I see now that you have a very small heating system or live in a very warm place. The fault was entirely mine what you said was true of closed pipe system with no branches.

However we should be careful in making all-encompassing statements. Consider another closed system - the atmosphere.

Now tell me that the flow rate 10 metres in front of of a jet engine is the same as the flow through the engine, and 10 metres after the engine.

 

[russ_watters]

However we should be careful in making all-encompassing statements. Consider another closed system - the atmosphere.

Now tell me that the flow rate 10 metres in front of of a jet engine is the same as the flow through the engine, and 10 metres after the engine.

That is a very poorly defined system and it most certainly is not closed. The engine is burning fuel and dumping the combustion products into the atmosphere. Both the jet engine (typically, the boundary of the system is at the inlet and outlet) and atmosphere are open systems. But since the atmosphere is so much larger than the engine, it is usually treated as an infinite source/sink in thermodynamics.

And I must amend what I said before about the accumulation in a surge or expansion tank: since it only occurs during transitional periods (when a domestic water system is just opened or when it is off and cooling), I think it can be completely ignored here.

 

[Studiot]

Why do you say it is not closed?

The compressor runs even in the absence of fuel, or if you like replace the jet engine with one of those whirly things that children wave about, or with a wind turbine, or take away the equipment altogether.

I certainly consider the atmosphere as a whole to be a closed system for most purposes, however the air flow is anything but constant, from location to location.

 

[russ_watters]

You sait it was a jet engine. If it isn't running, then it isn't a jet engine, it is just an overly complicated turbine.

I think purposely obfuscating this with nontypical and INTENTIONALLY MISLEADING scenarios does a disservece here. I've seen enough examples of people making errors with the general/basic concept of conservation of mass to know it is enough of a problem on its own.

 

[russ_watters]

so suppose there's a single pipe that forks into two branches, how do you calculate the flow rate of each branch? Would it be divided equally, or would it depend on which branch has the smallest section within its branch, or which branch begins with the largest diameter?

It depends on size and other restrictions and can get very complicated.

 

[engnr_arsalan]

flow rate has simple formula velocity X area. your dad is turning tap to various degrees means he is changing the area through which water is coming out..
and flow rate remain constant for steady flow system..a system in which properties or dimensions does not change with time..as long as area remain same (tap is not turned and remained opened as it was) flow will remain same..as u can see in diagram( drawn in 5 minutes )
as long as tap is untouched inflow will be equal to outflow..what your father doing is changing the dimensions..so how can be flow steady

 

[Khashishi]

so suppose there's a single pipe that forks into two branches, how do you calculate the flow rate of each branch? Would it be divided equally, or would it depend on which branch has the smallest section within its branch, or which branch begins with the largest diameter?

This problem is fully analogous to solving an electrical circuit. See https://en.wikipedia.org/wiki/Kirchhoff's_circuit_laws

The standard way to do this is to assign a resistance to each pipe section. A fork is a point where multiple pipe sections meet. Then you calculate the currents in each pipe section and "potentials" (essentially water pressure) at each node (fork point).

 

[Studiot]

Kashishi
The standard way to do this is to assign a resistance to each pipe section. A fork is a point where multiple pipe sections meet. Then you calculate the currents in each pipe section and "potentials" (essentially water pressure) at each node (fork point).

Please, please do not introduce this analogy. It does not work for pipe networks. That is the reason Professor Hardy Cross introduced his famous method.

http://en.wikipedia.org/wiki/Hardy_Cross_method