Water is contained between two vertical plates with a gap width of \(2 \mathrm{~cm}\). The temperatures of the plates are 25 and \(75^{\circ} \mathrm{C}\). Find the velocity profile and plot the velocity profile as a function of distance. Also find the maximum velocity in the system.

Use the following physical properties, the values of which are evaluated at \(50{ }^{\circ} \mathrm{C}\), the average temperature in the system: density \(ho=988 \mathrm{~kg} / \mathrm{m}^{3}\), viscosity \(\mu=565 \times\) \(10^{-6} \mathrm{~Pa} \cdot \mathrm{s}\), and coefficient of volume expansion \(4.54 \times 10^{-4} \mathrm{~K}^{-1}\).