The lake is a closed system with one river input, precipitation input, and no ou
ID: 3148957 • Letter: T
Question
The lake is a closed system with one river input, precipitation input, and no outputs except evaporation. Using the first order feedback model, calculate the present volume of the lake based on change to the water input after the river water was diverted. Assume steady-state for the system.
Given data:
Residence time of water in lake: 25 years
Initial lake volume, pre-diversion: 8,660,000 acre-feet
Pre-River diversion Inputs: River, 330,000 acre-feet /year ; Precipitation: 14,600 acre-feet /year
Post-diversion inputs: River, 76,000 acre-feet /year ; Precipitation: 14,600 acre-feet / year
Time elapsed since diversion: 109 years
PLease show steps.
Explanation / Answer
RESIDECE TIME OF WATER = 25 YEARS RIVER INPUT = 330,000 ,PRECIPATION INPUT= 14600 HENCE PER YEAR TOTAL INPUT = 330,000 + 14600 = 344,600 ACRE-FEET/YEAR IN 25 YEARS TOTAL INPUT = 25X (344,600) = 8615000 , INITIAL LAKE VOLUME = 8,660,000 ,WHICH IS MORE THAN INTAKE SHOWING THAT NO EFFECT OF EVAPORATION.
NOW AFTER DIVERSION INTAKE (76000+14600)X109 = 9875400 (109 YEARS) TOTAL VOLUME = 8,660,000+9875400 = 18535400 ACRE-FEET
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