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Discussion in 'Calculations' started by optymista93, Aug 12, 2021.

1. optymista93Member

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Hi,

I'm wondering how You can calculate volumetric flow rate (SCFM=ft2/min) without rotameter installed.

We need to change from 1,625" to 1,25" Cold End. This will change the SCFM.

Liquid nitrogen is pumped by a hydraulic pump to a vaporizor. How can I calculate gasses volumetric flow rate out of vaporizor?

Last edited: Aug 12, 2021
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3. s.weinbergWell-Known MemberEngineeringClicks Expert

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Not sure if this is what you're looking for, but if your fluid has a consistent density, you can measure volumetric flow with 2 pressure sensors - one in a dead area (i.e. no flow) and one in the area with flow.

Using Bernoulli's equation, you can convert your measured pressure to velocity. Multiply by the cross-section of your pipe or whatever, and you have volumetric flow.

4. optymista93Member

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Thank You for the answer Weinberg. All inputs are greatly appriciated Yeah, the thing is I have to obtain volumetric flow of the gass coming out of vaporizor. I have a pressure sensor for the pressure out of vaporizor (backpressure).

On the datasheet for vaporizor used, it states that:
- Gas ρ = 0,072 lb/ft3
- Specific volume = 13,8889 ft3/lb
- Vapor density = 0,967 and Liquid [email protected]: 50,46 lb/ft3

I also read that liquid to gass expansion ratio of nitrogen is 1:694 at 20deg C.

The Bernoulli's equation is: P1+1/2ρv1^2+ρgh1=P2+1/2ρv2^2+ρgh2

Known data:
P1 = Pressure out of hydraulic pump
P2 = Pressure of gas coming out of vaporizor (backpressure)
ρ = density of fluid
g, h1 and h2

As I want to solve for v2, which is the velocity of the medium going out of vaporizor, I need one more input, v1. How can I obtain velocity of the fluid going in to the vaporizor?

Also, can I really use Bernoulli's equation if the density of fluid going in is different than density of gass coming out of vaporizor?

If my understanding is correct, having found v2, I can use v2 = q2/A = 4q/(D^2*π) or
q2 = (v2*D^2*π)/4 to find volumetric flow rate (q2). However, this equation only stands for flat, plane cross-sections. Otherwise, it's q = vAcosθ. Where θ is the angle between the unit normal and the velocity vector v of the substance elements.

Cheers and thank You!

Last edited: Aug 13, 2021
5. optymista93Member

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Hi again,

I found out that the value I'm looking for is not exactly the volumetric flow rate... The value I want to find is SCFM (Standard Cubic Feet Minute), which is not the same as volumetric flow rate, as I first thought.

SCFM is not dependant on either temperature or pressure, as it takes standard values for these. (P=1atm, T=68°F).

My former collegue came with the strange assumption that SCFM = 3*RPM of the pump. How can that be?

Last edited: Aug 13, 2021
6. s.weinbergWell-Known MemberEngineeringClicks Expert

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Your former colleague may have simply been using the pump's rating, which would be given in SCFM. The pump will have a set displacement every rotation. RPM puts it in terms of time, so can be converted to SCFM.

As far as using Bernoulli's equation, if that's what you wanted to do, I'd suggest putting both pressure sensors after the vaporizer, as that's what you want to measure. You put one in 'dead air' (e.g. you make a branch off of the line that goes to a dead end), and the other in the location of flow. the velocity in the dead air section is 0.

7. optymista93Member

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Thank You for the explanation, Weinberg.

I can't operate with numbers. I have to come up with the equation that gives SCFM as an output. I can't install any additional equipment. The client wants to change cold ends from 1,625" to 1,25" on 901-01966 ICP-200 pump.

It seemed only logical to me that this will change SCFM output. However, the equation my former collegue used was 3xRPM and this would imply that SCFM is independent of both pressure, temperature and is just dependent on pump's RPM.

From the data chart of the pump, flow rate: pump speed is a linear function. We can write Flow Rate (GPM), as a function of RPM.

For Ø1.625 Cold Ends: Flow Rate (GPM) = 0,032*RPM
For Ø1.250 Cold Ends: Flow Rate (GPM) = 0,019*RPM

Above proves that SCFM will be different, when changing cold ends on the pump.

Attached Files:

• ICP-200 (Flow).PNG
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8. s.weinbergWell-Known MemberEngineeringClicks Expert

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I'm not sure what's being shown on the chart, and I really don't know that much about your application, but just glancing at it, it looks like they might be simply accounting for the cross-sectional area. (Flow rate is flow velocity times cross-sectional area).

If your flow is about 12GPM, for a 1" diameter, and it scales with cross-sectional area (which it, approximately, would, if the pump displacement varies with cold-end diameter), flow for 1.25,1.5,1.625,2,2.375 and 2.875" diameter cold-ends would be 18.75, 27,31.7,48,67.7 and 99.2, which lines up fairly well with what is shown.

Hopefully, that is of some use

9. optymista93Member

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I got some tips here & other places and finally figured it out. I thought it would be helpful to share the solutions for the future use.

Inputs are marked with orange color. There is only one variable, RPM.

Calculating for "Cold end" (pump's piston) with diameter 1,625in.

Cylinder diameter, D1 = 1,625 in
Cylinder Area, A1 = (π*D1)/4 = 2,074 in^2
Stroke = 1,375 in
Volume per stroke = VS1 = A1*Stroke = 2,852 in^3
Volume efficiency = EFF = 87%
Cylinder discharge volume = Vdisch = VS1 * EFF = 2,481 in^3/stroke

Pump Speed = RPM
Cylinder volume per minute (in^3/min) = Vcm = Vdisch * RPM = 2,481 * RPM
Cylinder volume per minute (GPM) = Vcm,GPM = Vcm * 0,0043290042761699 = 0,01074026*RPM
Number of cylinders, nc = 3
Pump Liquid Discharge = nc*Vcm,GPM = 0,0322...*RPM

Liquid density at STD, ρliq = 50,46 pcf
Gas density at STD, ρgas = 0,072 pcf
Density ratio, ρratio= ρliqgas = 701x

Gas vol (GPM) = Pump Liquid Discharge*ρratio = 22,5867...*RPM
Gas vol (cfm) = 0,13368...*Gas vol(GPM) = 3,0194...*RPM

This proves statement 3*RPM and the assumption that its value will be different for other piston diameters. As of 1,25" piston it will be:

Gas vol(D2=1,25in) = 1,7865...*RPM

@EDIT
I now went a little bit further and developed an equation for "gas volume per minute" for any given piston diameter for this case scenario.

Vcmf(D,RPM) = 1,1434241355938155786971828180212*D^2*RPM = 1,1434*D^2*RPM

Last edited: Aug 17, 2021
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