7 replies to this topic

[pyro38]

Hi all,

I a stuck on this problem, if you could point me in the right direction i would really appreciate this.

a process uses an oil of density = 800kgm-3 and a vis 80mPa.s at a flowrate of 0.72 m3hr-1. the feed pipe splits into two smaller pipes and both discharge freely into the process. One pipe has an inner diameter of 5cm and Length 20m while the other has an inner diameter of 2.5cm and a Length 10m

find the rate of flow in each of the smaller pipes....

so far all i have is if i could find a diameter of the feed pipe then i could use continuty equation to solve using the velocities. I am not sure however.

Thanks,

[djack77494]

pyro,

You need more than the continuity equation; it essentially just performs a mass balance. You need to solve the hydraulics of your system. Simply put, at some unknown flowrate, x, you can calculate a pressure drop for your 5 cm/20 m long pipe. Assume a value of x and calculate the resulting pressure drop.

Next, take the remaining flowrate = (0.72 - x)
and calculate the pressure drop through the 2.5 cm/10 m long pipe.

Compare the two calculated pressure drops, and adjust x until they match.

There may be an easier (not trial and error) way of obtaining the answer. Finding it would require you to crack open Crane TP410 or some other hydraulics manual. You could try that if you don't like T&E problems.

[pyro38]

pyro,

You need more than the continuity equation; it essentially just performs a mass balance. You need to solve the hydraulics of your system. Simply put, at some unknown flowrate, x, you can calculate a pressure drop for your 5 cm/20 m long pipe. Assume a value of x and calculate the resulting pressure drop.

Next, take the remaining flowrate = (0.72 - x)
and calculate the pressure drop through the 2.5 cm/10 m long pipe.

Compare the two calculated pressure drops, and adjust x until they match.

There may be an easier (not trial and error) way of obtaining the answer. Finding it would require you to crack open Crane TP410 or some other hydraulics manual. You could try that if you don't like T&E problems.

So i would use the Hagen-Poiseuille Equation in order to determine a pressure drops?

[djack77494]

So i would use the Hagen-Poiseuille Equation in order to determine a pressure drops?

In general, no. The H-P Equation applies to/is restricted to laminar flow of Newtonian fluids. Better to use the more general purpose Darcy Equation, good for laminar or turbulent flow. For performing hydraulic calculations in industry, the near universal reference in my opinion is Crane's Technical Paper 410. I'd highly recommend that you obtain a copy.

[katmar]

The advice given by djack will put you on the right track - the only change I would make is to say that in your trial and error solution I would guess a pressure drop rather than a flow split. The way I read your problem is that the two lines run from a common point (i.e. the split) to a point where they both discharge to the same pressure. If this is true then the pressure drop across the two lines is the same for each. If this is not true you do not know the pressure drops and the problem cannot be solved (by me?).

The procedure then would be
1. Guess a pressure drop
2. Calculate the flow rate in each line for that pressure drop
3. If the combined flow is higher than the target flow guess a lower pressure drop (and vice versa). Go to step 2.

Sometimes when you are faced with a problem of this nature where there may be an easy solution (like the Hagen-Poiseuille Equation ) as well as a more difficult solution (here Darcy Weisbach) then it is worth trying the easy way first, but then remember to verify that your answer satisfies your assumptions. So if you assume laminar flow and use the Hagen-Poiseuille Equation remember to check that your flow is actually laminar once you have the answer.

[katmar]

After I posted my previous reply I realized that this is a student exercise and it seems to be a given that it is a laminar flow problem, so we should tackle it a bit more rigorously than I indicated before. In an industrial situation I would normally be lazy and avoid too much thinking, and therefore simply opt for the trial and error solution. But I suspect that is not the right way in this instance.

By inspection we see that in the Hagen-Poiseuille equation that the volumetric flowrate is inversely proportional to the pipe length, and proportional to the fourth power of the diameter. The 2.5 cm pipe is half the length of the 5 cm pipe so it should have double the flowrate, except that the diameter change means that it will have 1/(2^4) = 1/16 of the flow. Combining these two effects means that the 2.5 cm pipe should have (for the same pressure drop) 1/8 of the flow in the 5 cm pipe.

So the 5 cm pipe has 8 units of flow and the 2.5 cm pipe has 1 unit of flow - a total of 9 units. And your professor has kindly given you a number that is easily divisible by 9. Each unit of flow is 80 litre/hour so the 5 cm pipe delivers 640 liter/hour and the 2.5 cm pipe delivers 80 litre/hour.

Plugging these numbers into my trusty old software verifies the pressure drops are the same, and the flow is laminar.

[djack77494]

Good on you, Harvey, to recognize that the problem really was a laminar flow problem. I failed to catch that. But shame on you, pyro, for soliciting the full answer to what was apparently a homework problem. You should have the tools available to solve the problem for yourself. I think it fair to occassionally ask for a little help in the form of "a hint", but am not sure even this is ethical. In any case, you should not ask for or expect a full solution.

[Qalander (Chem)]

Good on you, Harvey, to recognize that the problem really was a laminar flow problem. I failed to catch that. But shame on you, pyro, for soliciting the full answer to what was apparently a homework problem. You should have the tools available to solve the problem for yourself. I think it fair to occassionally ask for a little help in the form of "a hint", but am not sure even this is ethical. In any case, you should not ask for or expect a full solution.

Dear Doug Hello,
Although I fully endorse your views;but the words can be less harsher for 'pyro38' being student.

For Pyro38, I suggest you to put litlle extra effort before putting the querry to the forum for complete solution;this will help you for future
and additionally give a great degree of self satisfaction/consolation for your own self.
Regards
Qalander