A reservoir has an inflow of 15 m³/s and an outflow of 10 m³/s. If its surface area is 2 km² and evaporation is 0.5 cm/day, what is the net change in storage volume over 24 hours, excluding precipitation?

The net change in storage volume of a reservoir over a specific period is determined by the water balance equation, which accounts for all water entering the reservoir and subtracting all water leaving it during that time. For this calculation, the inputs include inflow, and the outputs include outflow and evaporation, with precipitation being explicitly excluded. A positive net change indicates an increase in the reservoir's stored water, while a negative change indicates a decrease.

To calculate the net change, all units must first be made consistent. The given time period is 24 hours. There are 86,400 seconds in 24 hours (24 hours multiplied by 60 minutes per hour, then multiplied by 60 seconds per minute). The reservoir's surface area is 2 square kilometers (km²), which is equivalent to 2,000,000 square meters (m²) because 1 kilometer equals 1,000 meters, so 1 km² equals 1,000,000 m². The evaporation rate is 0.5 centimeters per day, which converts to 0.005 meters per day (0.5 centimeters divided by 100 centimeters per meter).

Next, the total volume for each component over the 24-hour period is calculated. Inflow is the volume of water entering the reservoir, typically from rivers or streams. With an inflow rate of 15 cubic meters per second (m³/s), the total inflow volume over 24 hours is calculated by multiplying the rate by the time in seconds: 15 m³/s multiplied by 86,400 seconds, which equals 1,296,000 m³. Outflow is the volume of water leaving the reservoir, usually through structures like a dam or spillway. With an outflow rate of 10 cubic meters per second (m³/s), the total outflow volume over 24 hours is 10 m³/s multiplied by 86,400 seconds, which equals 864,000 m³. Evaporation is the process where liquid water on the reservoir's surface transforms into water vapor and rises into the atmosphere, representing a loss of water from the reservoir. The volume of water lost due to evaporation is determined by multiplying the evaporation depth by the surface area. Over 24 hours (one day), with an evaporation rate of 0.005 meters per day and a surface area of 2,000,000 m², the total evaporation volume is 0.005 m/day multiplied by 2,000,000 m², which equals 10,000 m³.

Finally, the net change in storage volume is calculated by subtracting the total water leaving the reservoir from the total water entering it. The formula is: Net change in storage volume = Inflow Volume - Outflow Volume - Evaporation Volume. Substituting the calculated values: Net change = 1,296,000 m³ - 864,000 m³ - 10,000 m³. Performing the subtractions, 1,296,000 m³ minus 864,000 m³ equals 432,000 m³. Then, 432,000 m³ minus 10,000 m³ equals 422,000 m³. Therefore, the net change in storage volume over 24 hours is 422,000 cubic meters.