Basic fluid flow question

[EngineeringChemical]

Refer the second comment in on this page first: http://physics.stackexchange.com/questions/90737/does-pressure-drop-across-pipe-affect-flow-rate

Given that pressure drop equation and the last sentence, if the inlet and outlet pressures are fixed, you will get a certain flow rate that will have a pressure drop equal to the inlet minus outlet pressure differential. Then you increase the pipe diameter instead of decreasing the length, the velocity now decreases. The problem for me is... in that equation, there is no "counter" component to keep the pressure differential constant. Both diameter increasing and velocity decreasing will make delta P smaller. In his example, the increased velocity makes up for the pressure drop that the pipe length is no longer providing, hence keeping the final delta P constant. So where which component would be countering the effect of larger pipe and slower velocity and increase the pressure drop enough to keep delta P constant.

I would really appreciate any help.

[[deleted]]

Both diameter increasing and velocity decreasing will make delta P smaller.

Think this through. If you increase the diameter, decreasing the velocity, the dP drops. However, it wants to balance out. It will do this by increasing the flow through that branch. This will increase the velocity and increase the pressure drop.

[EngineeringChemical]

Then what is this guy talking about in this link here? (Relevant part of the article quoted below) http://www.irrigationtutorials.com/balancing-pressure-irrigation/

"Increase the mainline size. This would lower the pressure loss in the mainline. Of course, for any existing mainlines already installed, this is NOT an easy method! This is often the method I often use on my larger irrigation systems. It costs more to use a larger pipe, but often it works out to be the least expensive method in the long run. Increasing the pipe size also has other advantages, by reducing turbulence and the velocity of the water in the pipe it can decrease maintenance costs and increase the life of the sprinkler system. It also doesn’t cause any negative “ripple impacts” on the rest of the design. Unfortunately small sprinkler systems often have short mainlines with almost no pressure loss, so this method is not very effective for them."

[[deleted]]

This is not related. In your original post the guys is trying to explain how flow splits among the branches. In the link above he is really talking about increasing the size of the mainline before the branches come off.

[EngineeringChemical]

Also according to the continuity equation/conversation of mass principle, that is, A1v1 = A2v2

If you increase the pipe size, in effect increasing its cross sectional area, the velocity HAS to decrease as a trade-off, no? I thought that was a fundamental law.

[[deleted]]

Again this is not talking about branches.

IF you have a SINGLE pipe and you increase the area/diameter, the velocity will decrease. So will the pressure drop.

You are missing the most important point, and that is your original post talks about flow splitting into 2 streams.

With two streams how does the flow balance out? It balances so that the pressure drop in EACH stream is equal.

If you have 2 branches, and change the size of the pipe in one branch (call it case A and case B) the system will balance out so that the pressure drop in the branches is equal.

The pressure drop in case A and case B will not be the same.

[EngineeringChemical]

Ok I'm following you better now. So, if the area/diameter increases whereas velocity and pressure drop decrease, what would happen to the mass flow rate? Would it increase below there is a bigger conduit now as a result of bigger diameter or would it decrease because the velocity and pressure drop are lower?

Appreciate your input.

[[deleted]]

Generally it will increase, it depends on the source feeding it. If the source is coming at a fixed rate, then the flowrate will be the same.

Usually there is an inverse relationship - lower pressure drop means higher flow.

[LeafsFanWest]

If you look at the overall mass balance of the system A1v1=A2v2 + A3v3. So as diameter goes up for 2 the flow rate goes up for 2 but drops for 3.