Your engineering consulting firm has been sent the design for a simple piping system connecting two large water reservoirs (both at 10C ) as shown in the accompanying figure. a. Your client has informed you that this system is scheduled to operate for many years. Thus, they want you to determine the flow rate in the cast-iron 5 SCH80 piping for two conditions: i) The "best case" scenario where the piping is brand new. ii) The "worst case" scenario (according to what is mentioned in Daugherty \& Franzini's book Fluid Mechanics with Engineering Applications) where the piping has become all rusty on the inside. b. In order to eliminate the change in flow rate over time that you predict will happen in part a), a colleague suggests partially closing the gate valve when the piping is brand new and then gradually opening it as the piping becomes more and more rusty on the inside. By citing specific terms in the Bernoulli equation, give a brief explanation on how this technique works. c. Determine the gate valve loss coefficient that must be set to initially when the piping is brand new so that the flow rate of water matches the final conditions (i.e, when the piping has become all rusty on the inside and the gate valve is fully opened)