Velocity of flow (V) Vs. Flow (Q)

[Gear2d]

Homework Statement

Something I cannot seem to understand is this:

When looking at the velocity of flow (V), if I were to increase radius (r) that would mean I increase the cross sectional area (A) which means I decrease V.
Yet at the same time if I were to increase radius (r) I would decrease resistance (R) and my flow would increase (Q).

I do not understand how this is possible. That if I increase flow (Q) that my velocity decreases when the radius is increased? Are the 2 equation independent of one another?

Homework Equations

V = Q/A where A = ∏r^2

Q = ΔP/R where R = (8ηl)/∏r^4

 

[jbsteele]

The Attempt at a SolutionV = Q/A is independent of the equation Q = ΔP/R. When you increase r, as you said, A increases so V decreases. On the other hand, when you increase r, R decreases so Q increases. So yes, it is possible for Q to increase while V decreases.