C3. 1 In a certain industrial process, oil of density p flows through the inclined pipe in Fig. C3. 1. A U-tube manometer, with fluid density pm, measures the pressure

difference between points 1 and 2, as shown. The pipe flow is steady, so that the fluids in the manometer are stationary. (a) Find an analytic expression for p1 - p2 in terms of the system parameters. (b) Discuss the conditions on h necessary for there to be no flow in the pipe. (c) What about flow up,from 1 to 2? (d) What about flow down, from 2 to 1?

Fig: 1

Fig: 2