Givens: - Cell culture medium is constantly pumpted through the channel from left to right, resulting in fluid flow in the positive x-direction - The channel has dimensions of length L=50mm, width W=5mm, and a total height 2H=0.2mm - Cell culture medium has a dynamic viscosity =0.93cP - Cells are cultured on the bottom surface of the channel, at y=H - To derive the velocity profile (given below), several simplifying assumptions were made: - Incompressible fluid - Newtonian fluid - Laminar flow - Steady flow - Unidirectional flow in the x-direction - Infinite flow field in the z-direction - Negligible effects of gravity - The resulting velocity profile of the parallel plate flow chamber is given by the equation: u(y)=(2LP1P2)(H2y2) Please respond to the following (remember to show your work to receive maximum credit): a. (18 pts) Derive an expression for the volumetric flow rate Q from the velocity profile u(y). Briefly explain how you performed your derivation. b. (18 pts) Derive an expression for the shear stress t from the velocity profile u(y) ). Briefly explain how you performed your derivation. c. ( 8 pts) What volumetric flow rate Q is required to achieve the desired shear stress of 0.5 dynes cm2 ? extract cells' RNA from? If so, why