# Fluid Mechanics:Volumetric flow rate and average velocity

1. Feb 13, 2016

### jdawg

1. The problem statement, all variables and given/known data
. 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.

2. Relevant equations

3. The attempt at a solution

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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Last edited: Feb 13, 2016
2. Feb 13, 2016

### SteamKing

Staff Emeritus
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.
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.

It doesn't really matter. You appear to be given the specific weight of the air in each section of the pipe.

3. Feb 13, 2016

### jdawg

What continuity equation are you talking about?

4. Feb 13, 2016

### SteamKing

Staff Emeritus
There's only one: What goes in must come out, or Q = A * V.

5. Feb 13, 2016

### jdawg

Ohh ok, thanks!

6. Feb 15, 2016

### Staff: Mentor

This equation give the volumetric flow rate, which is not a conserved quantity if the density is changing.

7. Feb 15, 2016

### Staff: Mentor

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

8. Feb 15, 2016

### SteamKing

Staff Emeritus
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.

9. Feb 15, 2016

### Staff: Mentor

Are we saying the same thing? I'm saying that Q is not the same at both cross sections.

Chet

10. Feb 15, 2016

### SteamKing

Staff Emeritus
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. Feb 15, 2016

### Staff: Mentor

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.

12. Feb 17, 2016

### jdawg

Haha thanks for y'alls help!