Q3.The Darcy-Weisbach equation states that the power generating capacity in a hydroelectric system that is lost due to head loss is given byP=QH, whereis the efficiency of the turbine,is the specific gravity of water,Qis the flow rate, andHis the head loss. There is a hydroelectric system with = 0.65 0.02, H = 3.58 0.10 m, Q = 40 1 m3/s, and = 9800 N/m3 with negligible uncertainty.

1. Estimate the power loss (the units will be in watts) of this hydroelectric system, and find the uncertainty in the estimate.
2. Find the relative uncertainty in the estimated power loss.

The maintainer of this hydroelectric system has a chance to reduce the uncertainty of any one variable within the , H, and Q to half of its original uncertainty. Which option (, H, or Q) would provide the greatest reduction in the uncertainty in P?