Evaluations for input

A pipe of radius R has a fully developed laminarflow of air at P0, T0 with a velocity profile of V = Vc[1 - (r/R)2], where Vc is the velocity on the center-line and r is the radius, as shown in <image 1>. Find the total mass flow rate and the average velocity, both as functions of Vc and R.

(A) $\begin{aligned}V&=\frac{V_c}{3}\\\dot{m}&=\frac{\pi}{2\cdot\nu}\cdot V_c\cdot R^2\\\\\end{aligned}$

(B) $\begin{aligned}V&=\frac{V_c}{2}\\\dot{m}&=\frac{\pi}{2\cdot\nu}\cdot V_c\cdot R^2\\\\\end{aligned}$

(C) $\begin{aligned}V&=\frac{V_c}{2}\\\dot{m}&=\frac{\pi}{2\cdot\nu}\cdot V_c\cdot R^3\\\\\end{aligned}$

Answer with the option's letter from the given choices directly. No punctuation.