Abstract

Citation

Researchers should cite this work as follows:

• Winkel, B. (2022). 1-052-SaltWaterTanks-ModelingScenario. SIMIODE, QUBES Educational Resources. doi:10.25334/GCQ6-7T80

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Article Context

Description

As an example, consider SITUATION 1: At time t = 0 a tank contains Q₀ lb of salt dissolved in 100 gal of water. Assume that water containing 0.25 lb of salt per gallon is entering the tank at a rate of 3 gal/mm, and that the well-stirred solution is leaving the tank at the same rate.

(a) Describe what you think will happen to the amount of salt in the tank over time, perhaps with a verbal description or a plot.

(b) Describe the rate at which the salt water is being added to the tank and "subtracted" from the tank as a function of time t in s.

(c) Write out a differential equation with initial condition which describes the rate of change of salt in the tank, i.e. Q'(t).

(d) Find an expression for the amount of salt Q(t) in the tank at time t.

(e) Describe the long term behavior of the amount of salt in the tank. Tell why this makes sense.

(f) Determine the maximum or maximum possible amount of salt in the tank over time.

g) Determine the time when the amount of salt in the tank is at 75% of the maximum possible in (e).