1. Newtonian fluid (p, μ=constant) flows steadily through a channel (height 2h). In the middle of the channel, an infinitely thin splitter plate is mounted. The channel walls move with a constant velocity U in the positive x1-direction. The two fluid streams separated by the plate are mixed at the end of the plate. At station [2], far away from station [1], a new velocity profile u₁ = u₁(2) is developed that does not change anymore with x1. The body forces can be neglected. (a) Using the equation of motion, on what spatial coordinates does the pressure gradient depend at station [2]. Justify your answer. (b) Calculate the volume flow rate (per unit depth) Q at station [1]. The pressure gradient is zero here. = (c) Obtain the velocity profile u₁ [1] and [2] should be the same. u1(x2) at station [2]. Note that the volume flow rate at station (d) What is the pressure gradient at [2] ? There is no need to perform a shell balance. Proceed using the Continuity equation and the Navier- Stokes equation (see reverse) [10 marks]. + h h U Splitter plate [1] [2]