Fluid Mechanics:Volumetric flow rate and average velocity

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Discussion Overview

The discussion revolves around a fluid mechanics problem involving the flow of air through a pipe reducer, specifically focusing on the volumetric flow rates and average velocities in two sections of the pipe with differing diameters and specific weights. The participants explore the implications of the given flow rate in N/s and the relationship between mass flow rate, density, and velocity.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants express confusion regarding the flow rate of 30 N/s and question whether it can be converted to mass flow rate by dividing by gravity.
  • There is a discussion about the formula for average velocity and whether it differs from the mass flow equation, with some participants suggesting that the specific weight provided makes calculating mass flow rate unnecessary.
  • Participants mention the continuity equation, with one stating it as "What goes in must come out" and another noting that volumetric flow rate is not conserved if density changes.
  • One participant suggests converting weight flow rates to mass flow rates and specific weights to mass densities for clarity in calculations.
  • There is a contention about whether the volumetric flow rate (Q) is the same at both cross sections, with participants acknowledging that it may not be due to changing density.
  • Concerns are raised about the clarity of the problem statement, particularly regarding the use of weight flow rates and densities instead of mass equivalents, which could confuse students.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to the problem, with multiple competing views on the necessity of calculating mass flow rates and the implications of using weight flow rates. The discussion remains unresolved regarding the clarity of the problem statement and its impact on understanding.

Contextual Notes

Participants note limitations in the problem's wording, particularly the use of weight flow rates and specific weights, which may lead to confusion for those unfamiliar with the concepts. There is also an acknowledgment of the assumption that gravitational acceleration remains constant throughout the pipe.

jdawg
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Homework Statement


. Air, at a flow rate of 30 [N/s], flows through the reducer shown below. In the 300 [mm] diameter section of the pipe the specific weight of the air is 9.8 [N/m3 ]. When flowing through the reducer the pressure and temperature will fall causing the air to expand and producing a reduction of density. The specific weight in the 200 [mm] diameter section of the pipe is 7.85 [N/m3 ]. Find the volumetric flow rates and average velocities in both sections of the pipe.

Homework Equations

The Attempt at a Solution


[/B]
Ok, so I'm a little confused on what the flow rate of 30 N/s is! I've never seen that combination of units before. Can I divide it by gravity to get the mass flow rate?

When the problem asks for average velocity at inlet and exit, is this a different formula than this one?

mass=Area*velocity*density

Also, is this flow moving from right to left?
 

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jdawg said:

Homework Statement


. Air, at a flow rate of 30 [N/s], flows through the reducer shown below. In the 300 [mm] diameter section of the pipe the specific weight of the air is 9.8 [N/m3 ]. When flowing through the reducer the pressure and temperature will fall causing the air to expand and producing a reduction of density. The specific weight in the 200 [mm] diameter section of the pipe is 7.85 [N/m3 ]. Find the volumetric flow rates and average velocities in both sections of the pipe.

Homework Equations

The Attempt at a Solution


[/B]
Ok, so I'm a little confused on what the flow rate of 30 N/s is! I've never seen that combination of units before. Can I divide it by gravity to get the mass flow rate?
You can, but the problem isn't looking for the mass flow rate. The problem gives the specific weight of the air in both sections of the pipe.
When the problem asks for average velocity at inlet and exit, is this a different formula than this one?

mass=Area*velocity*density
Since you are given the specific weight of the air, it's really not necessary to calculate the mass flow rate. You are looking for the volumetric flow rate and the average velocity. The standard continuity equation can be modified to find this information.

Also, is this flow moving from right to left?
It doesn't really matter. You appear to be given the specific weight of the air in each section of the pipe.
 
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What continuity equation are you talking about?
 
jdawg said:
What continuity equation are you talking about?
There's only one: What goes in must come out, or Q = A * V.
 
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Ohh ok, thanks!
 
SteamKing said:
There's only one: What goes in must come out, or Q = A * V.
This equation give the volumetric flow rate, which is not a conserved quantity if the density is changing.
 

Homework Statement


. Air, at a flow rate of 30 [N/s], flows through the reducer shown below. In the 300 [mm] diameter section of the pipe the specific weight of the air is 9.8 [N/m3 ]. When flowing through the reducer the pressure and temperature will fall causing the air to expand and producing a reduction of density. The specific weight in the 200 [mm] diameter section of the pipe is 7.85 [N/m3 ]. Find the volumetric flow rates and average velocities in both sections of the pipe.

Homework Equations

The Attempt at a Solution


[/B]
Ok, so I'm a little confused on what the flow rate of 30 N/s is! I've never seen that combination of units before. Can I divide it by gravity to get the mass flow rate?

When the problem asks for average velocity at inlet and exit, is this a different formula than this one?

mass=Area*velocity*density

Also, is this flow moving from right to left?
You should really convert the weight rate of flow in N/s to the mass rate of flow in kg/s. You should also convert the specific weights to mass density. Just divide by 9.8 in each case. Then you can use your formula mass flow rate = ##\rho Q=\rho v A##

Chet
 
Chestermiller said:
This equation give the volumetric flow rate, which is not a conserved quantity if the density is changing.
But you are given the density of the air in each section of the pipe. There is only one weight flow rate of air given for the entrance.
 
SteamKing said:
But you are given the density of the air in each section of the pipe. There is only one weight flow rate of air given for the entrance.
Are we saying the same thing? I'm saying that Q is not the same at both cross sections.

Chet
 
  • #10
Chestermiller said:
Are we saying the same thing? I'm saying that Q is not the same at both cross sections.

Chet
That's correct. The reason I advised that calculating mass was unnecessary was that presumably g remains constant throughout the length of this pipe, and since we have a weight density for the air given rather than a mass density, the required information could still be determined using the geometry of the pipe.
 
  • #11
SteamKing said:
That's correct. The reason I advised that calculating mass was unnecessary was that presumably g remains constant throughout the length of this pipe, and since we have a weight density for the air given rather than a mass density, the required information could still be determined using the geometry of the pipe.
I guess I was confused by the wording of your response.

Regarding the problem statement, I think it's a bad idea in textbook problems to give the weight rate of flow and the weight density, rather than the mass rate of flow and the mass density. This just confuses novice students. I hope my comments have not rekindled jdawg's confusion.
 
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  • #12
Haha thanks for y'alls help!
 

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