• 100 foot of pipe(lets assume it is straight)
  • Diameter of pipe 2"
  • Flow rate at point of entry into pipe and exit 50gpm
  • Temperature of water 100F
  • 50 psi

Or stated another way if I was able to introduce substance into water(the same viscocity as water) at the entry of pipe, how do I calculate how long it would take to come out the other side?

If the pipe wasn't straight would that change calculation?


closed as off-topic by John Rennie, user36790, Martin, Kyle Kanos, John Duffield Dec 2 '15 at 13:39

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  • $\begingroup$ The person who wrote the problem is probably asking for an average value based on the volumetric flow rate and an assumption of incompressibility (nearly exact approximation). That's fine as far as it goes but is physically incorrect for real pipes and liquids with non-zero viscosity. $\endgroup$ – dmckee Dec 2 '15 at 1:08
  • $\begingroup$ Since you specified the pipe length and diameter, and the flow rate, you don't need to know the temperature or pressure. $\endgroup$ – Daniel Griscom Dec 2 '15 at 1:26
  • $\begingroup$ It sounds like the examiner is trying to see if you are confused by things that don't matter. I used to do that too. It's a good way to tell if you understand. $\endgroup$ – Mike Dunlavey Dec 2 '15 at 1:31
  • $\begingroup$ Are you asking for the solution to the specific problem described by your parameters, or are you trying to ask how this type of problem is done in general? $\endgroup$ – DanielSank Dec 2 '15 at 9:22

The velocity profile in a pipe depends on whether the flow is turbulent or laminar - for the laminar case, you get a parabolic profile so water "near the center" would travel much faster than water "near the wall".

However, I believe your situation is turbulent, so we don't have to worry about that. This means we can just calculate the velocity of the liquid based on the flow rate and the area - volume per unit time divided by area is length per unit time (velocity).

I won't do the math for you - it should be easy once you realize the above. And again, since the flow rate is given, it doesn't really matter whether the pipe is straight or not.

When you get the velocity, you will want to calculate the Reynold's number of the flow (look it up if you need to) to confirm you have turbulent flow so the assumption of "uniform velocity profile on average" is more or less true.


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