A) For a rectangular coordinate system, we developed the Navier Stokes equation for vx. Now, reduce that equation to balance the pressure force with shear stress (or frictional force) and develop an expression for vx in a rectangular channel of height h (y=0 is the centerline and no slip at y= +- h/2; use the concept of symmetry). Then develop an expression for vmax, average velocity, flow rate (Q) and shear stress at the wall (For flow rate calculations, assume a width of the channel to be w. Therefore the cross sectional area of the channel is wh).
B) Design of a chamber that will be used to study cell culture under a flow field: Determine the channel height that can be used to determine the wall shear stresses as high as 20 dyne/cm2 with flow rates less than 2 cm3/s. The viscosity of the tissue culture medium is 0.0087 gm/cm.s. The width of the channel is 2 cm.