(a) The annual capital cost of a pipeline supplying 1200 L min- of water is 6000 x D,where D is the pipe diameter in metres. The pipeline is 0.25 km long. Assume that the friction coefficient, f == 0.000575, p where is density, T is the local shear stress and u is the mean flow velocity. For all flow conditions; the annual cost of pumping power is 260 per kW and the pump efficiency is 80%. (i) Provide the equation for the total annual operating cost as a function of the pipe diameter, f (D). (ii) Calculate the most economical pipe diameter. (b) There are many common dimensionless numbers used to describe different physical effects. Such dimensionless numbers are usually a ratio of specific properties, for example, the Reynolds number represents the ratio of inertial to viscous forces. Choose three of the following dimensionless numbers and describe what properties the ratio represents and the context in which these numbers are important: Froude Number, Euler Number, Mach Number, Weber Number Nusselt Number, Prandtl Number. (c) A hose is connected on one side to a tall tank containing water and the other side is lying on the ground. Once the open side is lying on the ground it has water coming out of it at a speed of 7.4 meters per second. How much do you need to lift the hose to stop water coming out of it?