A siphon connects two large tanks of water. Point 1 is at the inlet where the tube meets the upper tank and is located at the same height as the upper water surface. Point 2 is the highest point of the tube, 0.10 m above Point 1. Point 3 is the outlet into the lower tank, which is 0.60 m below Point 1. The tube diameter is 1.5cm at Point 1 and Point 2, but narrows to 0.80cm at Point 3. Ignore viscosity and assume steady, incompressible flow.
(a) Derive an expression for the speed v3 of the water at Point 3 in terms of the gravitational constant g, the given height differences, and the cross-sectional areas of the tube at Points 1 and 3.
(b) Using the given dimensions, calculate the numerical value of v3.
(c) Determine the mass flow rate of water through the siphon.