Velocity and Pressure Drop 9

[KC12]

Hi All,

Lets say you have a pipeline of 100 ft with various fittings, reducers etc, and a velocity of about 5 ft/s entering the pipe line intially. I want to find how much allowable pressure drop there can be so that 5 ft/s does not reach 0 ft/s after its journey through the pipe. Which calculation methods are good for this? The velocity will remain constant if there are no forces there to decelerate or accelerate it. Frictional losses would decelerate the velocity. Pump design would take into effect the frictional losses in the pipe required to push through the constant velocity of 5 ft/s.

Now for my clarification:

Bernoulli's equation says that a lower pressure (gauge pressure after 100 ft of piping) will correspond to a higher velocity. Im having a hard time wrapping my head around this and using bernoulli in my case above would give bizarre results! Can someone clarify? Reality wise, a gauge pressure of zero on the line would mean no flow?

TY!

 

[Latexman]

Bernoulli's equation says that a lower pressure (gauge pressure after 100 ft of piping) will correspond to a higher velocity.

Not really, there are other factors involved. Bernoulli's equation says the change in potential energy (pressure and elevation) plus the change in kinetic energy (velocity) minus frictional losses equals zero (conservation of energy).

Good luck,
Latexman

 

[KC12]

Such that an included head loss term in Bernoulli will be able to show me a velocity decrease with the pressure decrease?

 

[Compositepro]

Liquid velocity is essentially constant in a pipe of constant cross-section. If this is school work you should ask your teacher. School work is not allowed here.

 

[hydtools]

For an incompressible fluid, and no leakage along the way, flow in must equal flow out. If areas are equal, velocities will be equal. Q = V * A = constant.

Ted

 

[zdas04]

Damn guys, doesn't anyone remember fluid mechanics? mass flow rate must be constant for a flow with no additions or removals within the control volume. To achieve that with a real fluid (who's density is a function of pressure and temperature), velocity must be ever changing. If velocity keeps changing, then volume flow rate must also keep changing. There is nothing in fluid mechanics that requires velocity to be constant and it isn't. The only way for a fluid to move in a pipe is if the pressure on one end is lower than the pressure on the other end. For a fluid like water over a short distance, this change in density and velocity can be very small, but it can't be zero. The OP contention that velocity can remain constant with a pump is simply nonsense.

With regard to Bernoulli's equation. His first assumption as he developed it from Euler's equation is that the flow is incompressible and inviscid. That means zero change in density and zero friction drop. Consequently it is only valid for very short distances. Typically it is used across the length of an airplane wing, or to determine the pressure change across a diameter change. It is not applicable to try to determine the pressure drop DUE TO FRICTION down 100 ft of pipe.

David

 

[rmw]

Gee David, I am sitting here laughing my head off. After first reading premise put forward by the OP, if you read your post too fast it would almost sound like you are saying that with a long enough pipe line you would be pumping in at one at a given velocity and having none at the other end when in fact the opposite it true.

At least that is what the OP made it sound like was going to happen when referring to 0 velocity. Composite Pro said "essentially" so he covered himself with respect to our post.

But, the OP also mentioned reducers, and once you change the cross sectional area of the flow path, with respect to velocity considerations everything changes. Most of the subsequent posts seemed to assume constant flow area.

If the OP is a student, he/she needs to read the chapter before trying to work the problem. If the OP is a practicing engineer, he/she needs to dig the old fluids text book out and re-read the applicable chapter. If the OP is not an engineer, he/she needs to find one to explain it to him/her.

Bernoulli needs to roll back over in his grave because the laws of physics didn't change after all.

But, good job of nailing the essence of the matter.

rmw

 

[dcasto]

ok, the OP's question and possible class room question, must be a compressible flow or some telescopic pipe, The annswer could be a .25 in pipe at first and a 200 mile diameter pipe at the end.

 

[BigInch]

You have to use the "long" version of Bernoulli's equation, one that includes the head loss due to friction term.
Z1 + P1/[γ]1 + V1^2/2/g - HL = Z2 + P2/[γ]2 + V2^2/2/g

HL, head loss between points 1 and 2, can be found using any pipe head loss equation for frictional flow, Fanning, Darcy, Colebrook, Churchill, etc. Use one that is suitable for your fluid and flow conditions. Now the Bernoulli equation applies to any length of pipe, 1 foot or 1000 miles.

The common friction equations assume constant fluid density and viscosity but if your density changes between point 1 and point 2 (its a compressible fluid), perhaps you can approximate by using the average density in a short segment. If you have a long piece of pipeline and density changes significantly, you will have to break that piece of pipeline into shorter segments. Same for viscosity; use the average viscosity, if it changes significantly in any segment of pipe. If the pipe diameter changes, that's a great place to break the pipe into another segment.

Assume an inlet pressure and a flowrate. Calculate the velocity in each segment of pipe and in each fitting. Now calculate the head loss for each segment of pipe using whatever friction equation you have chosen, add the head losses from the fittings using a table of equivalent lengths for fittings, or by using fitting "K" factors. The sum of all those individual head losses is HL. Calculate the outlet pressure. If the outlet pressure is less than zero (absolute), increase the inlet pressure, or reduce the flowrate, or make some combination of those two and recalculate again.

If you keep track of any fluid density changes, the velocities will change between points 1 and 2 and everywhere else, even if you have a constant diameter pipe. It is much easier if you approximate a constant density in each segment and in each fitting by using the average density in each segment.

If you have fluid streams entering or leaving the pipeline, then simply recalculate the velocity in each segment to account for the increase or decrease in mass flow according to how much fluid has entered or left the pipeline.

If the temperature changes along the pipeline; no problem. you may need to recalculate the density and perhaps viscosity too. If there is a big difference in density, recalculate the velocity. You may need to keep track of viscosity changes too. Calculate viscosity at each point and if there is a large difference, then just as always, try to use the average. If at any place using the average value of any of those variables is not accurate enough, make the pipe segment length shorter, recalculate the average value for the variable giving problems, then use a new average value of the shorter pipe segment and recalculate.

OK. I think Mssr. Bernoulli can now go back to sleep ...

As you can see, it is much easier if you can assume constant diameter, density, viscosity, velocity, mass flow. You can even assume no friction, if your pipeline is very short, but if you use the proper form of the Bernoulli equation, you can accomodate any changes you may need to consider for your particular conditions. That increases the complexity of the calculations quite a lot, so if you're going to do a lot of these calcs, do a simple one by hand to see how it works, then buy some pipe hydraulic analysis program. Have a look at

http://www.aft.com.

**********************
"The problem isn't working out the equation,
its finding the answer to the real question." BigInch

http://virtualpipeline.spaces.live.com/

 

[Latexman]

BI - a star for someone that knows fluid mechanics.

Good luck,
Latexman

 

[zekeman]

"Bernoulli's equation says that a lower pressure (gauge pressure after 100 ft of piping) will correspond to a higher velocity. Im having a hard time wrapping my head around this and using bernoulli in my case above would give bizarre results! Can someone clarify? Reality wise, a gauge pressure of zero on the line would mean no flow?"


Bernoulli equation does not apply here;it is the frictionless form of the adiabatic energy equation. And BTW, you can have zero gauge with velocity; happens every time you use a hose.

Your problem in analyzing friction is you haven't considered the effect of pressure in the momentum equation.

Consider this example for clarification:
If you take a section of straight pipe say 1 foot long and invoke conservation of momentum you get that the differential pressure drop times the area should be equal to friction force + the mass change of momentum. Since the mass change of momentum for this section is zero (constant velocity) you get that the pressure drop= friction force*area. Your model forgot to include pressure.

 

[BigInch]

zekeman,

I explained how the Bernoulli equation can be applied to cases where friction is significant by including HL. Please don't say that "Bernoulli's equation doesn't apply", even if you only mean that in its basic form. That conclusion is already obvious and further discussion of unapplicability only serves to confuse the issue.

Velocity at zero gage certainly can't be stated as a generalized rule for flow within any conduit, be it a rigid pipe or a hose, except for the one particular case where a conduit discharges into a volume that happens to be at reference pressure.

IMO the OP's problem is not that he hasn't considered momentum, as that is ignored in steady state flow. Nothing causes me to assume that the flows in this case are unsteady.

**********************
"The problem isn't working out the equation,
its finding the answer to the real question." BigInch

http://virtualpipeline.spaces.live.com/

 

[zdas04]

BigInch,
In spite of Latexman's unqualified support of the equation you presented, zekeman is right. There is no friction or HL term in the Bernoulli Equation. Sorry, but a "long" version of the equation that you presented is some sort of after-the-fact construct that ignores the fact that in the derivation of this useful equation from Navier-Stokes (through the Euler simplification) discards the friction terms and converts the derivatives of density with regard to time and space to a constant. If friction is not close enough to zero to be safely ignored then the derivation is invalid and all airplanes could be expected to fall from the sky.

The zero psig point on the pressure continuum does not have a physical significance in most fluid mechanics, and certainly not in the Bernoulli Equation. With the exception of some poorly constructed empirical equations, arithmetic with pressure must always use absolute pressure.

The OP's "problem" is a nearly total lack of understanding of the subject.

David

 

[KC12]

Thanks everyone - you have all been very helpful

 

[ione]

I agree with zds04.
Bernouilli’s equation comes from Navier-Stokes equations with the hypothesis of dealing with an ideal fluid, where ideal means:

1) Incompressible
2) Inviscid
3) Steady state (this means partial derivative with respect to time equal to zero and flow-in equal flow-out)

Bernouilli’s equation is a particular case of the most general mechanical energy balance, where the resistance to the fluid motion due to its viscosity is equal to zero. Entering the head loss in the Bernouilli’s equation accounts for the effect of the fluid viscosity, but assuming “steady state hypothesis” stands still, implies heavy simplifications of the problem.

 

[desertfox]

Hi Gbur

Have a look at these sites they might help:-

http://www.efm.leeds.ac.uk/CIVE/CIVE1400/Section3/bernoulli.htm

http://www.ajdesigner.com/phpbernoulli/bernoulli_theorem_equation_head_loss.php

desertfox

 

[desertfox]

Hi Gbur

Scroll down on this link till you see the title:-

Friction & Bernoulli's Equation

http://webpages.eng.wayne.edu/~ah8818/Webpage1.htm

desertfox

 

[zdas04]

desertfox,
One of the long-time posters on eng-tips.com used to have a signature line that said something like "anything your read on the Internet is suspect until proved otherwise". I looked at your last link and I have to say that "wayne.edu" got it wrong and could use a bit more "edu" himself. His original statement of Bernoulli's equation was lazy and incomplete. Saying you could extend it to viscous flow is just wrong.

There are many empirical equations in the world that describe real flows pretty effectively. The one I use most often for gas is called the "AGA Equation", but there are others as comprehensive. My point is that every flow equation does not have to be labeled "Bernoulli". Daniel Bernoulli did an amazing piece of work deriving the equation that bears his name, but he never claimed it was a closed-form solution to the Navier Stokes Equation, and it isn't. It has MANY places where it does a good job of describing fluid flows and it is invaluable in those places. Pipeline flow is not one of those places. Adding a friction (or head loss) term to his elegant equation and calling it meaningful is just wrong.


David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

"It is always a poor idea to ask your Bridge Club for medical advice or a collection of geek engineers for legal advice"

 

[ione]

I think zdas04 posts are unobjectionable (at least to me they are).

For those who wanted further info on equations available beside the AGA equation quoted by David....

http://www.scielo.br/pdf/jbsmse/v29n3/a05v29n3.pdf

 

[Latexman]

David,

I admire your devotion to keeping the Bernoulli equation pure and unadulterated and in it's original form with it's classical assumptions and boundary conditions. However there have been many engineers for many years that have been taught the principles of the Bernoulli equation mainly using a "mechanical energy balance" between two points in incompressible pipe flow that includes a frictional head loss term. I know the textbook for my first fluid mechanics course, McCabe and Smith's Unit Operatioins of Chemical Engineering, used it. Crane Technical Paper 410 uses this mechanical energy balance with a frictional head loss term too. Crane TP410 does not call it the Bernoulli equation, but do say it was derived from the Bernoulli equation. In fact TP410 says, "All practical formulas for the flow of fluids are derived from Bernoulli's theorem, with modifications to account for losses due to friction." I don't have access to my McCabe and Smith now, so I can't say what they called it. I'll look later. Given all this, it is not surprising to me that a lot of folks identify this mechanical energy balance by the label "Bernoulli equation". This mis-labelling is wrong, and I agree with you there. Having a mechanical energy balance with a frictional head loss term for incompressible pipe flow is fine though. It's worked for me for many years. You know this could be mainly a Petroleum and Chemical Engineering thing. After all, Petroleum and Chemical Engineering were originally together (over time they became separate disciplines), and McCabe and Smith has probably been used in both curriculums for well over 40 years (my textbook was the 3rd Edition in 1977). Yep, I gotta check my McCabe and Smith when I get back to the office.

Good luck,
Latexman