Incompressible fluid flows steadily through a plane diverging channel. At the inlet, of height \(H\), the flow is uniform with magnitude \(V_{1}\). At the outlet, of height \(2 H\), the velocity profile is

\[V_{2}=V_{\mathrm{m}} \cos \left(\frac{\pi y}{2 H}\right)\]

where \(y\) is measured from the channel centerline. Express \(V_{\mathrm{m}}\) in terms of \(V_{1}\).