Water (constant density) is to be pumped up a hill (gravity = (0,0,−g)) through a pipe which tapers from an area a1 at the low point to the smaller area a2 at a point a vertical distance l higher. what is the pressure p1 at the bottom, needed to pump at a volume rate q if the pressure at the top is the atmospheric value p0? (express in terms of the given quantities. assuming inviscid steady flow, use bernoulli’s theorem with gravity and conservation of mass. assume that the flow velocity is uniform across the tube in computing fluid flux and pressure.)