In a parallel one-dimensional flow in the positive \(x\) direction, the velocity varies linearly from zero at \(y=0\) to \(30 \mathrm{~m} / \mathrm{s}\) at \(y=1.5 \mathrm{~m}\). Determine an expression for the stream function, \(\psi\). Also determine the \(y\) coordinate above which the volume flow rate is half the total between \(y=0\) and \(y=1.5 \mathrm{~m}\).