air water H Figure P539 Problem 5.39 (1) (2) The paddle wheel of an old sawmill is located in a water stream of width W = 2 m. The water driving the mill is supplied by a reservoir whose water surface is a height ho=5 m above the stream bed. The water is accelerated by passage under a sluice gate, approaching the paddle wheel at a depth of h₁ = 1 m (see figure P5.39). The flow downstream of the paddle wheel has a depth h₂ = 2 m. The flow from the reservoir to station 1 may be considered inviscid, but between 1 and 2, where the paddle wheel churns in the water, viscous dissipation occurs, and the flow cannot be considered inviscid. However, the viscous shear force on the stream bed is negligibly small Calculate (a) the velocities V₁ and V2 at stations 1 and 2, and (b) the horizontal force F, exerted by the flowing stream on the paddle wheel