# Solve the puzzle

1. Aug 13, 2010

### kathiravan_k

Look at the attached 2 pictures. Tell me in which structure Pipe C will have more water pressure and I can get more water from pipe C.

Some info :– Pipe A – Bigger in size, Pipe B – 1” pipe (1 inch), Pipe B – 3/4” pipe (3/4 inch)

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2. Aug 13, 2010

### Delta2

I think u ll get the same water per time unit from both configuration. I hope i have the right answer though i cant provide a good explanation. Rougly speaking it is probably it depends only on the start (pipe A) and end pipe (pipe C) and not in the intermediate pipe B.

3. Jul 12, 2011

### Lakshmi N

Dear friend,according to the poisuilles formula,

P is inversely proportional to the 4th power of the radius.Therefore,pressure will be more for the tube having small radius.And obviously,more volume of water will be flowing out through the tube having more radius.

4. Jul 12, 2011

### alex_j

Assuming an equal pressure and volume that can pass through pipe C, you can only get as much as the limit of pressure and volume at pipe C and since both are shown to be the same then you should get equal amounts from both configurations.

That is to say that the amount of water than can pass through C-B-A and the amount that can pass through C-A are the same and assuming that pipe C is the same size in both configurations then since the amount or volume of water running through is the same, so should be the pressures in each pipe A.

When we use Lakshmi N's method (Hagen-Poiseuille) the function is:

$\Delta$P = 8$\mu$LQ/$\Pi$r4

P - is the pressure drop or difference
L - is the length of pipe
$\mu$ - is the dynamic viscosity (we will give it a value of 1 here)
Q - is the flow rate
r - is the radius of pipe

So let's assume that in this case the length 'L' is the same for both configurations and we will give it a value of 1 to simplify things. The radius of pipe 'A' is also the same in both configurations so we can give 'r' a value of 1 also to simplify things. We are not taking into account the dynamic fluid viscosity so let's assume that $\mu$ also has a value of 1.

Now we are left with the function: $\Delta$P = Q/$\Pi$
where Q is the volumetric flow rate.
But since Q is determined by pipe 'C' in this case and in both configurations the flow rate is the same for both then when comparing:

Q1 = Q2 , both configurations give equal pressure heads.

How did I do? Am I even close? lol

5. Jul 12, 2011

### OnlyMe

If we assume that the diagrams represent functional relative lengths of each pipe, the length of pipe C is different for the two situations. While static pressure would be equal through out the system, the relative difference in the lengths of pipe C would change the functional flow through pipe C in the two examples. The length of a pipe does have an impact on the rate of flow through the pipe at a given pressure.

In Picture 1 pipe C is shorter than in Picture 2, thus there would be less resistance to flow through pipe C in Picture 1. This would result in a higher rate of flow and a drop in pressure, for the system as a whole, compared to Picture 2.

The pressure and flow rate of Pipe A never plays a significant part as it is the same for both situations.

The pressure and flow rate through pipe B would play a role only if the length of pipe B is sufficient that its effective flow rate is less than the effective flow rate through pipe C in each situation.

There should be a pressure drop in the system as a whole which is greater in Picture 1 compared with Picture 2 and an increased flow rate through pipe C in picture 1 compared with picture 2, assuming that the lengths of pipes C in the two examples are not equal.

Without information defining the length of the different pipes and initial pressure of the system and flow rate through pipe A nothing further can be said about the the actual differences of pressure and flow rate in pipe C.

6. Jul 12, 2011

### alex_j

Oh my! you are absolutely right! I wanted to show my brother the question just now and I noticed I had made a huge error! I confused the direction of the flows of all things!
So in this case the L does make a difference and my answer is completely off, you are right.

Would my answer have been close if the flow were reversed?

7. Jul 13, 2011

### OnlyMe

There would still be a similar problem in that the length of pipe C in each example would continue to be a factor.

Add... that if the direction of flow in pipe C is toward pipe A, the inlet pressure for pipe C would have to be sufficiently greater than the existing pressure in pipe A, that where pipe B or pipe C enters pipe A, in either example, it remains greater than the existing pressure in pipe A. There must be a positive pressure in the pipes C & B when compared to pipe A for any flow to occur toward pipe A. How big that positive pressure is together with the lengths of pipes C & B, in their respective examples will determine the effective flow rate into pipe A.

Beyond that there is a potential that pipe B could have a greater impact on the effective pressure when the flow enters pipe A in example 1. In other words as far as pipe B is involved the impact it has on the flow rate, though not dominant, is greater when the flow is toward pipe A, than when the flow was from pipe A toward pipe(s) B & C.

When the flow is from pipe A toward pipe C, the resistance to flow in pipe B would only be an issue if it decreases the flow to less than the maximum flow for pipe C at the involved pressure. When the flow is toward pipe A, any resistance to flow and/or decrease in pressure resulting from pipe B is added to the flow and pressure limitations of pipe C.

Sometimes I think I am talking in circles but there is no help for that...