The figure below shows an indoor wall fountain, where water flows down in a narrow layer over a flat surface. The velocity profile for well-developed flow within the water layer is given by: 4 (x)- egs? 8-x 1- where u, is the downward velocity, x is the distance in the direction normal to the wall (x = 0 corresponds to the wall surface), and 8 is the thickness of the film. (a). flowrate V of the water and the width W of the fountain (the density and viscosity of the water and the acceleration of gravity will appear in the expression). (b). of the fountain. If the fountain is 2 ft wide and the temperature in the room is 68 F, what is the approximate maximum volumetric flowrate (in ft'/min) that can flow through the fountain without the flow becoming turbulent? What is the thickness (in mm) of the water layer at this flowrate? Find an expression for the thickness 8 of the water layer as a function of the total volumetric The fountain operates properly as long as the flow remains laminar, otherwise water will splash out