Does anyone recognize this equation for pressure loss? 2

[CanucKev]

Hello all,

I'm trying to validate a spreadsheet we have for calculating pressure drop of gas flowing through pipe, but unfortunately the documentation is lacking - none of the "more obscure" formulas used have a source attached to them, and there's one in particular I can't find.

I've looked through a number of different resources (including GPSA and some others found here) but haven't spotted it yet - I was hoping to draw on everyone's experience just to see if this one formula looks familiar, and if anyone can identify where it's from.

The spreadsheet I'm checking uses iteration to find downstream pressure, assuming turbulent, isothermal flow of a real gas. The formula I can't find is referred to only as the "Loss Factor" and is this:

f_L = f*L/d + 2*ln(P₁/P₂)​

where L is the length of pipe, d is the pipe ID, P₁ is the entry absolute pressure, P₂ is the exit absolute pressure, and f is the Darcy friction factor found from the Haaland equation (this also wasn't documented in the spreadsheet, but we managed to track it down):

1/sqrt(f) = -1.8*log[(e/D/3.7)^1.11 + (6.9/Re)]​

where e/D is the relative roughness and Re is the Reynold's number. Obviously all the units cancel out to make f_L and f unitless.

This "loss factor" is used in a formula labelled only as "p12-p22" which actually means P₁² - P₂² (the units work out):

(P₁² - P₂²) = (W/A)²*(Z_avg*T*R/M)*f_L​

where W is the mass flow rate, A is the pipe cross-sectional area, Z_avg is the average compressibility factor, T is the absolute temperature of the flow (assumed isothermal), R is the universal gas constant, and M is the molar mass of the gas. (The flow rate input in the spreadsheet is at standard conditions.)

Obviously, given P₁ and (P₁² - P₂²), it's not too much of a stretch to figure out the first iteration of P₂.

Does anyone recognize these formulas, particularly the first one (the loss factor)? If so, would you be able to point me in the right direction as to where it's from? The f*L/d term makes sense to me, but the next term - two times the natural log of the ratio of upstream to downstream pressure - is throwing me off.

Thanks in advance!

 

[sailoday28]

I believe your first formula is based on choked flow.

Regards

 

[LittleInch]

"I'm trying to validate a spreadsheet we have for calculating pressure drop of gas flowing through pipe, but unfortunately the documentation is lacking". Try File Delete.

If you have no idea how this is put together how are you going to check it?? How can you validate any of the constants or typical values?? Any significant pipeline length needs several iterations as for the same mass flow the velocity constantly changes and you need to start again - a spreadsheet just won't do this.

Just buy a ready made program or get someone to run pipesim or something similar. They have it all validated and checked.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[katmar]

It is the standard isothermal compressible equation you will find in most fluids text books. If you can get your hands on a Crane 410, compare your first equation with the denominator of the first term in their Equation 1-6. Your 3rd equation is the same as Crane's Equation 1-7, but they use the specific volume and your equation calculates the specific volume from ZTR/M. There are many ways of expressing these equations, but they are all basically the same.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[CanucKev]

Thanks very much for the help - that got it for us.

As for the spreadsheet itself, we know, work with, and trust the engineer that made it - but of course we still need backup. He was able to track down the Haaland equation but wasn't able to find where he'd got the other one (with the natural log). The sheet is intended for facility piping moreso than pipelines, and we identified it as a potentially useful preliminary tool for getting the rough sizing done - provided we could validate it. Obviously I haven't described all the details of the sheet, but everything else within it (including the constants) checks out within the constraints/assumptions listed, and for the stage of the project we're at (+/- 30% cost estimate), it should do the trick. (We do have other pipe sizing software, which we'll use at the detailed stage, but not now as the licenses are limited and the scope isn't 100% defined either.)