How to Calculate Flow Rate from Head Loss in a 3 Pipe with Caustic Soda?

[EthanAnderson]

I have head loss (25.95ft) and converted that to pressure (17.19psi). I am trying to find flow rate in 3" sch 80 pipe coming from railcar at 25psi. So outlet pressure is 7.813psi. The fluid is 50% Caustic soda.

 

[EthanAnderson]

Essentially looking for flow rate from outlet pressure(7.81psi) in a 3" sch80 pipe.

 

[Travis_King]

It matters a great deal how long the pipe is, how many elbows, what kind of valves and how many, and what the positive or negative elevation change is between the railcar connection and the discharge connection.

 

[EthanAnderson]

Travis, I've got all of the above. 17ft is my total head loss. Just need flow rate at 7psi through 3" pipe..

 

[EthanAnderson]

Correction, total head loss is 25ft. Pressure is 17psi.

 

[russ_watters]

I'm not sure you understood Travis's point: you need all of that information to calculate the flow rate. What you have provided isn't enough.

Ideally, if you know the pressure drop across a single device, with a well known resistance (CV), that can substitute as an accurate flow meter. Using an entire system is much more difficult, if the piping arrangement is complex.

 

[EthanAnderson]

Sorry for misunderstanding guys. Check the attached snip shot. That's all the info I have. Length of pipe is 283ft from tank to furtherest unloading station. Tank is 30ft tall, top of railcar is 20ft.

 

[russ_watters]

That could work. I'll have to look at it more closely after work when I have more time.

 

[EthanAnderson]

Thanks, Russ.

 

[EthanAnderson]

Would you like for me to email you the spreadsheet so you can see the formulas I used in the cells?

 

[Travis_King]

Quick question, is this system venting to atmospheric pressure (i.e. an open tank) or to a closed system/vessel?

If the former what we've got here is this (correct me if I'm wrong)

You have a measured pressure at the railcar discharge (20ft) of 25 psi (37.7 ft).
(If the pressure is being measured at a lower or higher elevation, you should indicate this)

You have a measured pressure of 7.8 psi (11.8 ft) at the discharge. (Or is this the value you arrived at through your calculations?)

Either way, what you'll want to do is take your measured inlet pressure (head) and subtract from it the known static head (that is the elevation between the inlet measurement instrument and the discharge pressure measurement instrument). This will give you your friction headloss.

Using this, you can use the Hazen-Williams calculation/approximation to get a decent estimate of your flow.

 

[EthanAnderson]

I am a co-op. I have not taken fluid mechanics yet, sorry if I am having trouble understanding, and if I am stating the obvious. The railcar is closed. We'll force air into the vessel to push out the caustic. There are no measurement instruments. I have 283ft of straight pipe and a number of valves and fittings. I found equivalent lengths of straight pipe for the fittings and valves resulting in a total 333ft of straight pipe.

Caustic loses 28.9ft/1000ft. Total head loss is 25.95ft including 20% safety factor. My mentor stated the railcar vessel is at 25psi. Then he converted the head loss from 25.95ft to 17.18psi. He said outlet pressure was 25-17.18= 7.8psi . I have to find what the flow rate will be through a 3" line.. at 7.8 psi? ( I'm assuming). Again, sorry if I've been redundant- This is my first project.

 

[Travis_King]

I don't understand. How did you figure out the loss/1000ft if you don't know the flowrate?

 

[EthanAnderson]

We got a recommended flow rate of 81.5gpm from a process engineer. Used kinematic viscosity of 50.97 centistokes to interpolate between 43.2 and 65.0 centistokes at 81.5gpm. Giving me ft loss/1000ft. Hope that answers your question..

 

[EthanAnderson]

Used the table on page 3-55 of a Cameron Hydralic Data book.

 

[Travis_King]

No problem, ask away.

Yea, but all you did there was find out the expected ft loss/1000 ft at 81.5 gpm. Basically, you assumed a flow of 81.5 gpm in your effort to calculate the flow...

Is the caustic soda discharging into a tank that is open to the atmosphere or into a process?

 

[EthanAnderson]

The soda will discharge into a tank. The tank is covered, but with exhausts- basically atmospheric pressure, right? The tank is only used for storage.

 

[Travis_King]

Correct, if the tank is vented, you can assume it is at atmospheric pressure, even with additional volume being added (that is, the caustic soda). The way fluids work is that the system will attempt to balace itself out.

It should be noted that, depending on how much soda is above the railcar discharge, the actual available head could be higher than the 25 psi, as the total pressure at the discharge point will be the pressure of the railcar plus the static pressure of the volume--or more correctly, the height--of soda above the discharge point.
But let's say it's 25 psi. This translates to 37.7 ft.
Your discharge pressure is atmosphere, 0 psig. Tanks that are vented to atmosphere do not put any back pressure on the system, so the pressure at the discharge is 0 psig.
However, you do have static and friction head losses due to elevation and, well, friction which it will have to overcome in order to discharge into the tank.
You say the tank is 10 ft above the tank, so that static head loss leaves us with 27.7 ft to lose by the time it discharges.

As I said, the system will balance itself, you have 25 psi at the railcar and it has to lose that pressure by the time it reaches the tank. You see that it loses some pressure due to elevation change, but the remaining must be eliminated by friction. The way a system controls this (thanks to physics) is: the caustic soda will find equilibrium at a flowrate which results in just the right amount of friction losses so that it discharges at atmospheric pressure.

You'll find that with your railcar pressurized to 25 psi, your flow will be significantly higher than 81.5 gpm.

Hazen-Williams
ANSI Sch. 80 Steel Pipe Info

 

[EthanAnderson]

Just to be sure, the tank will be filled from the top. Like filling a glass of water. So tank pressure, volume shouldn't matter?

 

[Travis_King]

Sorry, that was worded strangely. I meant exactly that. The tank is at atmospheric pressure. Feel free to ask me to clarify anything you might like elaboration on in post #18.

 

[EthanAnderson]

So how can I find the exact flow rate? The formula from engtoolbox.com is only for water with detailed properties. How did you arrive at the conclusion of being higher than 81 gpm?

 

[Travis_King]

Yea, friction losses for viscous fluids is a different process, but I figured that would help to at least show you the general viscinity you are in. A specific gravity of 1.53 is not that much more than water, relatively speaking.

Here's a link that shows you the expected losses in sch. 40 pipe for various viscous fluids. 50.97 CentiStokes is roughly 260 SSU (conversion), so bear that in mind when looking at the lines.

Viscous Fluid Friction Losses

I have a fluid dynamics program for process plants, running a quick simulation put it in the 130 gpm range. Some online calculators suggest around 100 gpm. When I said significantly higher, I didn't mean that it would be like 600 gpm, I just mean that it was a measurable and physically significant difference.

The thing to take from this, though, is that if you are going to use the method you used. What you want to do is make an initial guess (say 81.5 gpm) and figure out what the discharge pressure is. In this case you got over 7 psi. So you know your flow is too low. So you increase it to 150, you'll get a negative pressure, so it's too high. Keep doing these iterations, with logical progressions, and you will hone in on the correct answer.

Or, you can use the Darcy-Weisbach equation and do all the math:
Helpful link on that
However, because you don't know the flow, this becomes an iterative process for you anyway...
The table you are referring to likely used the D-W equations.

Unluckily for you, this scenario seems to be in the transition zone (Reynolds number in the 2000's), making an accurate calculation using the D-W equation difficult.

 

[EthanAnderson]

Thank you for your help Travis! Greatly appreciated!

 

[jim hardy]

Years ago where i worked, before computers, the "Crane Handbook" was regarded as "The Source" and was on every ME's desk.

I see it's on the web now.

http://www.craneengineering.net/pro...ingFlowOfFluidsThroughPipesValvesFittings.pdf

hope it's some help. I downloaded one to my 'desktop'.

old jim

 

[russ_watters]

Would you like for me to email you the spreadsheet so you can see the formulas I used in the cells?

Can you attach it to the thread?

For a first pass by a co-op, that's a really good start. Adding-up all the components and then guess-and-check the flow rate vs the friction loss is the way to go if you can get accurate information on the friction loss.

Travis has given some good help -- more than I could have given. Your solution being far different from water really threw me. I probably would have used software for that.

Stupid question though: Does the railcar or tank have a sight-glass or other way to measure the volume of fluid in the tank? That plus a stop-watch equals a flow meter...