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Flow rate is calculated using only the parallel velocity

by davidbenari
Tags: calculated, flow, parallel, rate, velocity
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davidbenari
#1
Jul25-14, 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.
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Nathanael
#2
Jul25-14, 02:07 PM
Nathanael's Avatar
P: 683
If the entire velocity were perpendicular, what would be the flow rate?
b34n5
#3
Jul26-14, 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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