Instructions: Clearly show your steps when solving problems and if you feel additional information are needed, state clearly any assumptions you are making. Lack of clarity and failure to include assumptions result in loss of points. Homework must be done individually, you may discuss the problems with classmates, but do not copy solutions; the solutions must be written up independently. Copying other students work or sharing solutions with others will result in zero grades for the homework set for both parties. Copying solutions from solutions manuals or homework solution sets from prior years will result in a zero grade.
1. A large lake with a volume of 2.0 x 109 ft3 is filled by art inflow stream with a flow rate of 20 ft3/s and a non-conservative pollutant concentration of 5 ppm. A sewage outfall also discharges into the large lake with a flow rate of 3.5 ft3/s and a non-conservative pollutant concentration of 30 ppm. A outflow stream leaves the lake with the same flow rate of the inflow stream plus the outfall. The non-conservative pollutant has a decay rate coefficient of 0.20/day. Assume the pollutant is completely mixed in the lake and there is no evaporation or other gains or losses. What would be the steady state concentration in the outflow stream leaving the large lake?
2. A coal-fired power plant converts 40% of the coal's energy into electrical energy. The electrical output of the plant is 750 MW. The rest of the energy is converted to waste heat with 12% in the smokestack and 88% using cooling water from a stream. The river has a flow of 80 m3/s and temperature of 15°C.
a. What is the cooling water flow rate if the water temperature increases 12°C?
b. What is the new temperature of stream just downstream of the plant?