We know that $Q$ is given as $Q = A \cdot V_{avg}$, where $A$ is the area and $V_{avg}$ is the average velocity. The area can be written as $A = \frac{\pi}{4} \cdot D^2$, where $D$ is the diameter. So, we can write $V_{avg} = \frac{4Q}{\pi D^2}$.
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