2. (40 pts) You have been very busy over this past week preparing for the CHBE 421 exam and decide that it is finally time to take some nice bath to relax before the midterm. Unfortunately, you find that your water supply has been cut off due to the recent cold weather in Illinois. As an engineering student who is taking ChBE 421 , you realize that you can simply pump water (= 1000kg/m3 ) from a large pond located L=100m and h=10m from your house as shown in Figure A. The diameter of the pipe discharging water into your bathtub is D=10cm. Because you are in a hurry, you want your V=1m3 bath to be fully filled with water in t=20 seconds. A) (15 pts) How much energy should you supply to the pump? Assume that your bathroom is at the same atmospheric pressure as the outside and that there is no loss work from friction. NOTE: Assume that the pond is not frozen (yet) B) (25 pts) You have finally made it work using your calculation in A) but it took approximately t=30 seconds to fill the bathtub instead of 20 seconds. Frustrated, you find that there is a 2cm diameter spot for leakage on the pipe 5 meters above the ground as shown in Figure B. What is the velocity of this water leak? 1) Start from the integral energy balance treating it as a one inlet two outlet problem. 2) You can use wolfram alpha or other tools to solve the final equation