What is the relationship between flow rate and pressure in pipes?

[yun]

1. Good day to all.

Would appreciate all your help for my understanding please. I am quite new to this topic of fluid dynamics.

a) Say i have a 1200mm pipe which eventually serves a main distribution network. However, I will close the valve to the distribution and allows the water to flow via a 300mm tee-off from this main pipe. How will pressure and flow rate change when water flows in this 300mm pipe?

b) Is there a pressure limit on the pipe? i.e. how much pressure the pipe can withstand? From my understanding using Bernoulli's, a smaller area will result in a higher velocity as flow rate must be the same in both pipes hence a greater velocity in the 300mm pipe will equate to a smaller pressure in the 300mm pipe is that right?

c) Now say i want to increase the flow rate (by using more pumps supplying the water). How can i achieve this? My layman understanding is that the 300mm pipe cannot withstand a higher pressure due to this increase in flow through the pipe. Will there be a higher pressure in this case? I am thinking that we can increase the size of the pipe, or add another pipe that tee-offs from the main 1200mm pipe.

I appreciate all and any help on this please. Thank you all so much!


2. Benoulli's Eqn, Conservation of flow... are these even the correct eqns to use?



3. Pretty much as in the problem statement, my understanding is that the higher flow will result in a higher pressure as well. Is that right to begin with?

 

[S.E.]

A) If I'm reading your question properly, by closing the valve it is no longer steady state and thus the continuity equation can not be applied. At this point all that will be moving the fluid is inertia and gravity. If I misread what you wrote and the water continues to flow through the 120 cm pipe to the 30 cm pipe then you can determine the change in pressure with the energy equation (Bernoulli Eq. assumes that headloss is negligible) and the flow rate with the continuity equation.

B) This depends on the material and geometry of the pipe. The pressure will create hoop and normal stress along the pipe.

If σ_max > σ_h/a; the pipe will be fine.

C) When you add a pump to a system, what you're essentially doing is adding head (energy) to account for headloss caused by anything from pipe friction to minor losses from geometry. Why do you assume that the pipe will fail?

 

[yun]

Hi S.E., thank you for your reply.

"A) If I'm reading your question properly, by closing the valve it is no longer steady state and thus the continuity equation can not be applied. At this point all that will be moving the fluid is inertia and gravity. If I misread what you wrote and the water continues to flow through the 120 cm pipe to the 30 cm pipe then you can determine the change in pressure with the energy equation (Bernoulli Eq. assumes that headloss is negligible) and the flow rate with the continuity equation."

To clarify, i meant actually that there is a pump providing 40m head to water which is pushed out through a 1200mm pipe. 50m down this 1200mm pipe, there is a valve which allows me to stop water flowing further down this pipe. Instead, there is a 300mm pipe beside this valve. So basically, when I close the valve, water will flow via the 300mm pipe instead. In this case, will the continuity equation still apply? and bernoullis? Keep in mind that the pump is still pumping water. So will flow be affected since water is 'constricted' when moving into the 300mm pipe?


"C) When you add a pump to a system, what you're essentially doing is adding head (energy) to account for headloss caused by anything from pipe friction to minor losses from geometry. Why do you assume that the pipe will fail?"

the pump I am adding is only adding extra flow but not extra pressure. What I am thinking is that the pipe cannot take this extra flow. Or should i be thinking about pressure instead?

Sorry, I am really a novice in this and might be missing just some simple logic.

Thanks again!

 

[S.E.]

Can you draw me a sketch for a)?

So does this valve actually stop flow or will it redirect the flow to another pipe? In either case the continuity equation will apply but the flow will suffer minor losses along the valve. Bernoulli's Equation is for the most ideal case possible (which may be good enough for most Physics courses but not in Fluid Mechanics).

Consider the mass flow rate. Where else is it going to go? Since the density remains constant (I'm assuming), the velocity vectors will get closer together in the smaller cross section in order for the flow rate to remain constant, therefore it will not be effected.

Flow merely describes the flux through a cross section of the pipe. The pressure of the fluid on the pipe wall is what will cause stress in the pipe itself. Have you taken a course in mechanics/strength of materials?

 

[yun]

Hi S.E.,

I have attached a drawing. the valves are basically there to redirect flow.

"Flow merely describes the flux through a cross section of the pipe. The pressure of the fluid on the pipe wall is what will cause stress in the pipe itself. Have you taken a course in mechanics/strength of materials?"

My understanding is that pipes can only allow a certain flow rate through it? If it is pressure instead, it is merely the pressure component in Bernoulli's equation right? and not the total head of the water?
Would you happen to know where i can find a neat chart that allows me to see the flow rate possible for different pipe materials and sizes? That might make things easier for a quick reference. And no, I have not taken any of the courses yet :(

Thanks for all you help so far btw!