Impact of power plant discharge on lake temperature Aquatic life is sensitive to water temperature. This lab involves under- standing the impact of cooling water discharge from a power plant into

a nearby lake on the lake temperature, as shown in Figure 1. It will make use of mass and energy balances to predict lake temperature as a function of time, which will be solved for numerically. Problem information The upstream (inflow) temperature is Tup = 18 °C, and it is constant at a flow rate of Qup=360,000 m³/h. The power plant discharge tempera- ture is at Tais = 40 °C, and it has a variable flow rate, Qas (m³/h), based on generation of 100 m³/h/MW of electricity generation. The flow out of the lake, Que (m³/h), is assumed as the sum of the upstream and dis- charge flow in this problem, and the lake temperature, Tuke (°C), is as- sumed the same as the outflow. power plant Quis T'dis lake zone Qup Tup {] Quake Tlake The demand of the power plant (MW) by hour of day is given as an Excel sheet on BBLearn, for you to use to calculate flows. For a given volume of lake (either 105 or 10 m³), calculate the lake temperature over that given day. You should gen- erate a figure that displays: Hour of day (0 to 24), on x-axis • Time varying solution using the Euler method with the two volumes (V1 and V2), on y-axis 1 Steady state solution (does not require the volume), on y-axis 1 • • MW demand in power plant, on y-axis 2 Solution procedure 1. Define open system (lake volume with mass inflows and outflow). Specify steady-state inflow and outflow rates, time-dependent inflow and outflow temperatures. Your unknown is the lake temperature. The lake temperature is assumed the same as the outflow temperature. 2. Write open system mass (steady-state) and energy (rate form) balance equations. 3. Relate terms in energy balance equation to unknown lake temperature and other inputs. 4. Specify inputs, flow properties, etc. and solve energy balance equation for unknown lake temperature, both from a time-varying and steady-state perspective (using Excel). For the Euler method, use the time step of the MW power change in the associated file (0.25 h). Deliverable Turn in a report that outlines the problem to be solved, your solution method (using Equation Editor in MS Word), the plot of your solution, and a discussion of the behavior shown on the plot. (An example plot is shown in the lecture notes for this section on BBLearn.)