Question

battle has erupted over a local power plant owner's decision to raise the power delivered by the plant from 242 MW to 689 MW (The delivered power accounts for energy losses). The local population is increasing, so the area needs more power. However, the plant expends its heated waste water* into the Frustration River, local citizens are concerned that the heated water will raise water temperatures to the point where the endangered river smelt will die from oxygen depletion. Local biologists called into the fray report that the smelt can only withstand an average increase of 3.44°C. The river is 222 ft wide at the point where the waste water is dumped, but the depth and cross section is not well known. Farther downstream, however, the water flows through a narrow man-made concrete channel of rectangular cross-section, which has a width of 88.7 ft and depth of 41.2 ft. The water flows through this channel at 12.4 mph. The power plant claims a planned efficiency of 36.10% for its new power plant design. Based on this information, what is the maximum power that the power plant can output without endangering the river smelt? Number MW Based on your results, which advice would you offer city planners about the proposed upgrade? The power plant should be able to deliver 689 MW of power without endangering the smelt. O The smelt population will be endangered if the power plant increases its delivered power to 689 MW.

Answer 1

given
initial power output, Pi = 242 MW
Pf = 689 MW

width of river, w = 212 ft

dimensions of channel axb = 88.7 ft x 41.2 ft = 3654.44 ft^2 = 339.5 m^2
v = 12.4 mph = 5.588 m/s
hence mass flow rate = rho*axb*v
rho = 1000 kg/m^3 ( density of water)
m' = 18997126 kg/s

efficiency = 37.3 %
power output = P
Wasted power = Pw
then
e = P/(P + Pw)
1/e = 1 + Pw/P
Pw = (1/e - 1)*P

now Pw = m'cdT
c = 4186 J/kg K ( heat capacity of water)
dT = 3.44 K or C
hence
Pw = 27318310859.84 W = 27318.31 MW
P = 42751.66 MW

Power transmitted = P -Pw = 15433.35 MW
hence the plant can increase power output to 15433.35+242 = 15675 MW without endangering the smelt.

The power plant should be able to deliver 689 MW of power without endangering the smelt.