Fluid Mechanics -- Volume flow rate

[Chris18]

Hey guys. I could use some explanation since I am new to FM: So my problem is the following one: Fluid flows with an average velocity 8 m/s in a pipe with diameter 3m. What is the volume flow rate?
Now, I think the formula I got to use is Q= v.A Yet, I found my solution from a formula I found on the net where (1/4π * pipe diameter^2 * V). I got my result I need 18π but I just can't understand where I got this formula from and what does it mean! Would be grateful for any assist

Homework Equations

1/4π * 9 * 8 = 72/4.π or 18π

 

[Nidum]

1/4π * pipe diameter^2 * V)

Try putting the π above the divider line instead of underneath .

What is the formula for area of a pipe of given bore diameter ?

 

[Asymptotic]

Hey guys. I could use some explanation since I am new to FM: So my problem is the following one: Fluid flows with an average velocity 8 m/s in a pipe with diameter 3m. What is the volume flow rate?
Now, I think the formula I got to use is Q= v.A Yet, I found my solution from a formula I found on the net where (1/4π * pipe diameter^2 * V). I got my result I need 18π but I just can't understand where I got this formula from and what does it mean!

Q=v*A where v is fluid velocity and A is cross-sectional area.

Restating your formula, Q=v*(D²π/4) where D is diameter. An equivalent formulation is Q=v*(r²π) where r is the pipe radius. The way I think of it is,

• "How much volume fits into a pipe one meter long?" 1 meter of length times the cross-sectional area (r²π) is, in this case, 7.068 m³.
  
• "How many of these volumes pass through the pipe per unit time? In this case, it is 8 linear meters per second multiplied by the volume contained within a meter of that diameter pipe.

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