Gas Flow Rate Calculation using Pressure Drop

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Discussion Overview

The discussion revolves around calculating the flow rate of air through a straight tubing system, specifically focusing on the pressure drop from 20 psi to 14.6 psi as it flushes a 100 mL vial. Participants explore various methods for calculating the volumetric flow rate, including the Darcy-Weisbach equation and other pressure-related formulas, while addressing potential issues with unit conversions and assumptions regarding friction factors.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • The original poster (OP) seeks to confirm a flow rate calculation of 0.002 cubic meters per second and questions whether the Darcy-Weisbach equation can be simplified by ignoring the friction factor due to the short length of the tubing.
  • Some participants suggest that the flow rate calculated by the OP seems excessively high, questioning the validity of 2000 liters per second and clarifying that 0.002 m³/s equates to 2 L/s.
  • One participant calculates the velocity of air in the tubing and notes that it approaches the threshold where compressibility effects may be significant, although they believe the flushing frequency is manageable.
  • Another participant provides a rough estimate of the pressure drop based on a calculated Reynolds number, suggesting that the results align with the pressure drop described in the problem.

Areas of Agreement / Disagreement

There is no consensus on the best approach to calculate the flow rate, as participants express differing opinions on the significance of friction factors and the validity of the flow rate results. Disagreement exists regarding the interpretation of the flow rate values and their implications for the system.

Contextual Notes

Participants note potential issues with unit conversions and the assumptions made in the calculations, particularly regarding the friction factor and the conditions under which compressibility effects become relevant.

mallorn
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Homework Statement


Hi everyone,

I'm trying to calculate the flow rate of air in straight tubing that is 30cm long and has a diameter of .1875 in and has an outlet into a 100 mL vial which is vented to the atmosphere. The starting of the system pressure is 20 psi and the ending psi is 14.6, since it's in equilibrium with the atmosphere. The end goal of the problem is to see how long it takes to completely flush the vial with air three times. To do that, I'd need the volumetric flow rate of the air in the tubing.

Homework Equations

and

The Attempt at a Solution



I was using the flow rate calculator from pipeflowcalculations.com but got a result (.002 cubic meters/sec, which is 120,000 mL/min) that I wanted to confirm using manual calculations.

However, I've been running into some problems that I wanted to consult with you guys:

I was thinking to calculate it using the Darcy-Weisenbach equation V=sqrt(2g*Pressure Drop/density* (length/diameter)*darcy friction factor. Would it be ok to ignore the friction factor in this case since the length is so small?

Another option would be to use the definition of pressure as density*head*gravity and the equation as follows:

V= Square root (2*g*h)
Pressure/g*density= h

But when I try to solve it the units don't match up, even when I convert them all to SI.

What do you all think is the best approach and is my train of thought correct? Thank you very much!
 
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I can't comment on your calculation unless you show them, units and all.

Looking at a flow rate of 0.002 cu.m./s and a tubing diameter of 3/16", the velocity of the air flowing in the tube is approximately M = 0.32, which is the threshold of where compressibility effects start to become significant.

However, given that the vial is flushed about 1200 times over, I think you're safe, although I can't figure out why this is a matter of such importance.
 
Does 2000 liters/sec really sound reasonable to you for this system?

Chet
 
Chestermiller said:
Does 2000 liters/sec really sound reasonable to you for this system?

Chet
Not sure where 2000 L/s comes from. OP was talking about 0.002 m3/s, which I believe is 2 L/s.
 
SteamKing said:
Not sure where 2000 L/s comes from. OP was talking about 0.002 m3/s, which I believe is 2 L/s.
Oops. My mistake.
Chet
 
I checked to see whether, at 2 L/s, one predicts a pressure drop of ~5 psi in this tube. I get a Reynolds number of about 50000 for this flow, so it's in the turbulent region. Assume that the temperature remains about constant. For this Reynolds number, the friction factor is about 0.005. This leads to a wall shear stress of 0.0074 psi, and a pressure drop of about 2 psi in the tube. This is on the order of the 5 psi pressure drop in the problem description. So the results are probably about right, give or take.

Chet
 

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