An incompressible fluid is pumped at flow rate Q out of a pipe into the center of a very large reservoir. You may assume that the fluid flows radially outward from the end of the pipe in all directions, that the pipe does not perturb the flow, and that the flow is steady. Required:
a. Find the speed of the fluid u(r), where r is measured outwards from the tip of the pipe.
b. Assuming inviscid flow, and neglecting gravitational effects, determine the pressure in the reservoir p(r). Assume that the reservoir pressure far from the end of the pipe is constant and equal to p0