Formula derivation for gas volumetric flow rate through hole in pressurized pipe 1

[BruceTheEngineer]

Hello all,
I have an embarrassing question to ask. I was reading through a post here

http://www.eng-tips.com/viewthread.cfm?qid=219324

from around 2008 where someone asked how to calculate the gas lost through a pinhole in a pipe and someone posted a remarkably convenient formula
Q = D^2 * P

Q is volume of gas in MCF/hr based on .6 gravity gas

D is the diameter in inches

P is pressure in line in psia

My question was, how was this formula derived and what to do when specific gravity is not 0.6?

The reason I ask is because at work, I've got a one speed blower that's blowing way too much air in a 4" line to convey plastic pellets. So what I decided to do (while we're waiting to install a VFD) is to just bleed off air just directly downstream of the blower via a 2" gate valve. My pressure of the remaining air that's conveying plastic pellets has dropped from 13 psig to 7 psig and I know from the blower curve how much air in ACFM is being blown at the blower (400 ACFM) and so I was trying to calculate how much air am I bleeding off and how much air is going to the process?

Thank you all!

 

[LittleInch]

I'm pretty sure the formula that was being used was a choked flow scenario and with the particular parameters of natural gas, this formula is pretty close.

However your flow is not choked flow and unless you have a clean 2" hole then the orifice calc doesn't work very well.

Probably easier to measure the velocity of the air coming out of your 2" pipe...

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[zdas04]

I'm not sure that the hole has to be 2-inch, I've seen choked flow in 1-inch vents. The issue is that the D/L ratio has to be small enough that the friction drop in the pipe wall doesn't drop the exit pressure below the critical value for choked flow.

You might find faq378-1864 interesting for openings that take the pressure to atmospheric

[bold]David Simpson, PE[/bold]
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[BruceTheEngineer]

Thanks a bunch zdas04! I took those formulas and put them in this spreadsheet and I got if I had an opening of 1" (so valve opened roughly half-way) I got the air coming out of that valve at 264.0068 SCFM. Of course I'm making some huge assumptions as a gate valve is not even close to looking like a circle when half-opened, but it should get me in the ball park. Here's my Excel file which did the calculations if anyone wants to help me take a look and see if I screwed something up

http://files.engineering.com/getfil...ile=Gas_Flow_Being_Bled_Off_Calculations.xlsx

@LittleInch, is there an easy way to measure the velocity or volumetric flow rate of a gas? The only thing that comes to mind is getting one of these:

https://www.instrumart.com/products...MIrpS-1tmj2gIVxBuBCh0d2AyYEAYYASABEgL8IvD_BwE

As a follow-up, does anyone have any good formulas for determining pressure drop due to a hole?

Another thing I'm trying to figure out if I go from 13 psig to 7 psig, how much air flow in lbs have have I lost? Or are there too many unknowns?

Finally, now that I have my flow volumetric flow rates for inlet and outlet - 400 ACFM = 32 lb/min assuming 0.08 lb/ft^3 and then 21.12 lb/min bleeding off with 10.88 lb/min going to the process - I thought I could figure out the pressure of at least the line going to the process with 10.88 lb/min of air but I'm drawing a blank.

 

[Compositepro]

Why would you be bleeding off excess air rather than throttling the flow at the suction to the blower?

 

[BruceTheEngineer]

Because it's easy to turn that little gate valve that we have honestly. I don't even know if we have that option to throttle the flow at the suction of the blower. Are there benefits to throttling the suction of the blower as opposed to just bleeding off air downstream. I'm not sure if it is an option on our blower to throttle back air but I'd also have to look at if we'd have to go inside the sound enclosure around the blower to do it.

 

[Compositepro]

First, I assume you are talking about a Roots type blower and not a squirrel cage (centrifugal) blower. Roots blowers are positive displacement and operate very differently than centrifugal types. Bleeding air increases the power used by either type of blower. Centrifugal blowers are usually throttled on the outlet side, which cannot be done on a positive displacement blower. So throttling is done on the suction. Throttling will reduce air flow and energy used by the blower.

 

[BruceTheEngineer]

Hi Compositepro, I'm looking through this manual for our blower and it says the following

https://www.pdblowers.com/wp-content/uploads/2016/11/iom_185-205-ram_manual-feb2005.pdf

No attempt should ever be made to control capacity by means of a throttle valve in the intake or discharge piping. This will not only increase the power load on the driver, but can also overload and seriously damage the blower. If a possibility does exist that flow to the blower inlet may be cut off during normal operation of a process, then an adequate vacuum relief valve must be installed near the blower. A pressure type relief valve in the discharge line near the blower is required for protection against cut-off or blocking in this line. Refer to FIGURE 3 for a complete piping schematic.

Thoughts?

 

[georgeverghese]

To get a rough value for the air vented through the 2inch blowoff valve, find out (a) stem travel which would translate to %open then (b) look up the Cv vs % open for this model of gate valve then (c) compute the flow through this valve using expressions for compressible gas flow using Cv - you'll find this procedure in many control valve handbooks also.

 

[LittleInch]

There are many cheaper and simpler air velocity measurement devices - look up pitot tubes e.g. and you might be able to build one your self!

Yes, as composite mentions, you seem to have a PD type blower. Changing the speed is a better long term bet alright, but for experimenting opening a valve is one way of doing it.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.