allons/minute (gpm) into the tank. Water discharges through an outlet in the tank, but this only occurs when the volume V is greater than 200 gallons. When above this level, the rate at which water leaves the tank (in gpm) depends on the volume in the tank according to the following relationship: ???? =(0.05/minute)*(V-200) If the tank starts off empty, develop a mathematical model for V versus the time t, then solve for the time that it will take to fill up the tank to 800 gallons. (Hint: the model can be a discontinuous function, so use mass balances for V both before and after water begins exiting
A 1000-gallon water tank is used for experiments in the field. Water is pumped
from a local creek at a rate of Qin = 40 gallons/minute (gpm) into the tank. Water discharges
through an outlet in the tank, but this only occurs when the volume V is greater than 200
gallons. When above this level, the rate at which water leaves the tank (in gpm) depends on
the volume in the tank according to the following relationship:
???? =(0.05/minute)*(V-200)
If the tank starts off empty, develop a mathematical model for V versus the time t, then solve
for the time that it will take to fill up the tank to 800 gallons. (Hint: the model can be a
discontinuous function, so use mass balances for V both before and after water begins exiting
the tank).
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