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Flow rate is calculated using only the parallel velocity 
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#1
Jul2514, 01:38 PM

P: 78

So flow rate is calculated using only the parallel velocity to the area vector. Why is this? How can I mathematically prove this? Namely, how do I prove any perpendicular component of the velocity vector is not contributing to any volume output? I know this is the result of the dot product; I want to know why the dot product is valid reasoning for this scenario.
thanks. 


#2
Jul2514, 02:07 PM

P: 683

If the entire velocity were perpendicular, what would be the flow rate?



#3
Jul2614, 04:14 PM

P: 3

Consider the definition of the volumetric flow rate
[itex]\dot{V}[/itex]=[itex]\frac{dV}{dt}[/itex] say [itex]V=\vec{A} \cdot \vec{x}[/itex] substitution yields [itex]\dot{V}=\vec{A}\cdot\frac{d\vec{x}}{dt}=\vec{A}\cdot\vec{v}[/itex] where [itex]\vec{v}=\frac{d\vec{x}}{dt}[/itex] and [itex]A[/itex] materially conserved 


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