Liquids involving continuity equation

[sophzilla]

Any help would be appreciated -

The water flowing through a 1.9 cm (inside diameter) pipe flows out through three 1.3 cm pipes. (a) If the flow rates in the three smaller pipes are 28, 15, and 10 L/min, what is the flow rate in the 1.9 cm pipe?

The basic continuity idea is A1v1 = A2v2.
The flow rate equation is R = Av.

For each of the 3 pipes, the flow rate is given (R) and the area can be calculated (pi*r^2).

To find the flow rate of the 1.9cm pipe, we need to know the speed of water flow (v, since R =Av).

But I don't know how to put them all together and relate them. I tried things but I always got the wrong answer. Please give me a hint or help. Thanks.

 

[Doc Al]

What does "flow rate" mean? Hint: All the water in the main pipe must end up in the smaller pipes.

 

[Pyrrhus]

The conservation of mass is the concept from which the continuity equation is derived. Therefore, if you have a Q from one main pipe and it divides into 3 other pipes, the Q on the main pipe must be the sum of the Qs on the 3 smaller pipers, so mass is conserved.

 

[sophzilla]

Okay,

I understand what both of you guys said, and you're thinking, "well...if she understands it then why can't she do the problem?" It is because I'm a dumbass.

Anyhow, I understand the concept (at least, I think). I'm not asking for a completely solved problem, but can you help me a bit more with how to set up the problem? I promise I will try my hardest to solve it...I just need a starting point.

I set the initial pipe as A1v1, and the 3 respective pipes as A2v2, A3v3 and A4v4. I did everything I know but still got it wrong.

Thank you.

 

[sophzilla]

Never mind! I got it: you just add all the flow rates of three pipes together. This makes sense, although I hate it when they put problems like this...it seems too easy.

Thanks for your help.

 

[Pyrrhus]

I'd still advise you understand the underlying concept of the continuity equation. Good luck.