Pressure drop in a pipe (ie) Bernoulli 5

[mechengdude]

Forgive me if this is a bonehead question...I have someone telling me one thing that I thought knew what they were talking about but now not so sure...Anywho

If you have a pipe with liquid in it (incompressible) and you know the Pressure, temperature, flow rate, velocity etc. It branches into two pipes of equal size then the pressure does not change correct?! This is assuming no loss due to any fittings, pumps, valves etc.
thanks

 

[IRstuff]

Are the two pipes the same size as the single?

If the cross-sectional area is changed, doesn't the flow have to change? Wouldn't that be reflected in the pressure drop?

TTFN

FAQ731-376

 

[mechengdude]

size of pipe remains the same

 

[twr]

At the tee the pressure will be uniform. Flows will differ depending upon downstream pressure losses, but both sides will have the same pressure to lose.

 

[mechengdude]

twr - what you stated is what I'm thinking but I just got myself into an almost infinite loop trying to disect the bernoulli equation and Q=V*A.

anyone else care to weigh in...
thanks

 

[BigInch]

At the point where flow separates into the two streams the pressure is equal. 1 mm downstream of that point it doesn't have to be so.

http://virtualpipeline.spaces.msn.com

 

[rcooper]

If the pipe upstream of the branch is the same diameter as the two branches, and if the downstream conditions in the branches are the same, then the flow rate through the branches will be half the flow rate upstream of the branch.

The velocity of the flow in the branch will be half the velocity upstream, so the kinetic energy upstream of the branch will be 4 times the kinetic energy downstream. Now, this energy has to go somewhere. mechengdude, stated there is no loss due to the fitting, so the energy has to be retained in the fluid, and it is retained by increasing the internal energy. This manifests itself as an increase in pressure, as the fluid is incompressible.

Therefore the pressure in the two branches is greater than the pressure in the common pipe upstream of the branch.

This pressure rise falls out of the Bernoulli Equation as (v1^2 - v2^2)*density/2

Where v1 is the uptream velocity and v2 is the downstream velocity.

 

[mechengdude]

Thanks for all the responses. Let me state this one more way or the way I beleive the system would NOT behave and see if you agree...

The upstream pipe has a pressure of 100 psig it splits in two ... the pressure in the downstream pipes is NOT 50 psig.

same assumptions as stated earlier apply... thanks

 

[zdas04]

Bernoulli's equation is almost never useful for real flows in pipe and it is the exact opposite of useful for confined, branching flow unless the flows recombine in a relatively short distance.

What you have to do is pick some known distance downstream of the tee to base your calculations on. At the instant that the flow breaks, both streams are at 100 psig. If you assume equal flow rates (which never really happen by the way) then using a real fluid flow equation like Hazen Williams you can back into the downstream pressure from the known flow rate, known length, and the starting pressure.

David

 

[Feric]

Hi there:

I have a suggestion for you.

Instead of asking all kinds of questions and covering what if cases, do a search over the Internet for free pipeline network software.

I am convinced that there are some free demos that you can download.

Once you get your hands on some free demo software, create a sample case that you would like to model and see what the software provides you with as output results for your input data set.

Keep changing the input data until you get all the answers to your questions.

Even eFunda.com --

http://www.efunda.com

-- has a simple pipeline online calculator where in no time you can get some feedback in terms of the output data.

In my opinion, this is the best way to learn and get either right or wrong your answers and assumptions.

When I was a student, there was no software and no computer tools as they are available today. Most of the calculations were done by hand ...

Good luck!

Thanks,

Gordan Feric, PE
Engineering Software

http://members.aol.com/engware

 

[BigInch]

Don't you just love those trick questions?

http://virtualpipeline.spaces.msn.com

 

[mechengdude]

Thanks for the responses.

Feric - not sure what you mean by all sorts of questions. I thought it was pretty specific as to what occurs when one pipe branches into two; relative to pressure.

I have a CFD program but I was less interested in a specific value which I could get by modeling the case and more interested in trying to visualize and understand the relationship and equations.

 

[Feric]

mechengdude:

School of engineering says that you need to put on a piece of paper:

- what you would like to model
- write down the basic governing laws, equations and assumptions
- for given set of input data define and determine the system steadt state conditions
- do basic steady state modeling and simulation
- plot the system parameters
- make observations and draw conclusions
- share the findings with people and engineers who know the subject area

In my opinion, there is no better way than this when trying to visulize an engineering problem.

That is what I meant.

Believe me, one thing is solve problems in your head, but in order to master the subject area you need to do what the school of engineering says. It is time consuming, requires effort, but if you do what you need to, you will get the feel for the subject area and become an expert and get ready to help others who are getting familiar with the subject area.

I am not trying to be smart, just trying to explain what works and what school of engineering says how it should be done ...

Thanks,

Gordan Feric, PE
Engineering Software

http://members.aol.com/engware

 

[BigInch]

No, Its an easy answer. Rrcooper alluded to the trick, but did not explain further, although I believe he understood what he did not say. Bernoulli's equation can be used to solve for the original question as posed. The answer (as predicted by Bernoulli) is that the pressure downstream of that branch is higher than the "inlet" pressure, which of course means that the assumed flow direction must be reversed and flow is from the branches to the single "inlet".

http://virtualpipeline.spaces.msn.com

 

[Feric]

To All:

I have a suggestion.

Can mechengdude provide us with some kind of schematic layout so everybody can be on the same page?

This should not be difficult to do, for example, MS PowerPoint can be used ...

Thanks,

Gordan Feric, PE
Engineering Software

http://members.aol.com/engware

 

[BigInch]

================== 1st ==================================
Bernoulli
z1 + P1/[γ]1 + v1^2/2g -HL = z2 + P2/[γ]2 + v2^2/2g

incompressibility => [γ]1 = [γ]2
short branch fitting => z1 = z2 and => frictional Hl ~= 0
outlet areas same as inlet area =>
Voutlet velocity = 1/2 inlet velocity

z1 + P1/[γ]1 + (V)^2/2g = z1 + P2/[γ]1 + (1/2 V)^2/2g

P1/[γ]1 + (V)^2/2g = P2/[γ]1 + (1/2 V)^2/2g

for convenience [γ]=1

P1 + (V)^2/2g = P2 + (1/2 V)^2/2g
P1 - P2 = 1/4 V/2g - 1 V/2g
P1 - P2 = -3/4 V/2g
P2 = P1 + 3/4 V/2g
P2 > P1 => flow is reversed

====================== 2nd ==============================
Upstream Pressure = 100 psi

Downstream pressure P2 = 100/[γ]1 + 3/4 V1/2g
P2 > P1 => Flow is Reversed

Since velocities are known, as per the OP, you can solve for P2.

http://virtualpipeline.spaces.msn.com

 

[BigInch]

whoops missing [γ]2 in the last P2 equation. "P2/[γ]2"

http://virtualpipeline.spaces.msn.com

 

[rcooper]

BigInch,

Please correct me if I am wrong, but why do the flows reverse? The question is based on a system in which there are no losses. The total energy through the system stays constant so there is not need to reverse the flow. Fluids can and do flow from a low pressure region to a high pressure region so long as the TOTAL ENERGY reduces. Given a very low friction environment, the water flowing through a canal into a lake has a lower top water level than the water in a lake. The water moves up hill as the kinetic energy is converted to potential energy.

The equations presented are based on a system with the fluid flowing in a particular direction. If the flow reverses then a new set of equations would have to be set up to represent this alternative situation.

 

[BigInch]

If "downstream" pressure is higher than upstream pressure, what usually happens?

I don't know of any flow that goes from a low pressure point to high pressure point. That's one of the few times I can use "ALWAYS" flow is from high pressure point to low pressure point.

http://virtualpipeline.spaces.msn.com

 

[BigInch]

The pump mfgr's wouldn't be happy with flows that go from low to high pressure without use of their equipment, right?

http://virtualpipeline.spaces.msn.com