The following solution is presented for fully developed flow in a square duct that has a half width of \(B\) in the \(y\)-and \(z\)-directions.

\[v_{x}=\frac{G B^{2}}{4 \mu}\left(1-\frac{y^{2}}{B^{2}}\right)\left(1-\frac{z^{2}}{B^{2}}\right)\]

The flow is in the \(x\)-direction. Is this solution correct? If not, state why.

The volumetric flow rate is presented in another paper as

\[Q=0.563 \frac{G B^{4}}{\mu}\]

What expression would you get if the above expression for the velocity profile were used.