3/3 [30 pts] Momentum conservation again U x(t) Incompressible fluid in a column spanning length L contained in a U-tube manometer of radius R is executing oscillatory displacements (t) as shown in the sketch. (a) [7 pts] Use a 1D control-volume momentum-conservation analysis to derive a second-order ODE describing (t). Represent traction forces in terms of a skin friction coefficient Cf. Hint: be careful about the direction of the traction force. (b) [3 pts] Assume Poiseuille flow, for which we will use the following expression for Cr, where |dax/dt is the mag- nitude of the fluid velocity: 16v Cf 2R|dx/dt| Show that the final form of the equation is dx 8v dr 2g + + dt2 R dt T= 0. L Comment on any linearization that might have occurred (and how it has occurred). (2) (3)