Carbon Reservoir calculations! Please help! Oceanography 310!?

Posted on 2015-12-02 06:46:00 in Engineering by SHAYLA

The analogy of a bath tub can be used to describe the
atmospheric carbon reservoir and its associated input and output
fluxes, with the input flux represented by water flowing into the tub,
and the output flux represented by water flowing out of the tub.
Consider the example of a large tub of water that includes a negative
feedback: outflow rate (flux) is proportional to total reservoir volume.
In this example, reservoir size is measured in volume (rather than
mass, which is used for the carbon cycle).

(a). A reservoir of water at steady state has a volume Vres = 7500 L
and an outflow rate Fout = 25 L min-1
. The outflow rate is directly
proportional to the reservoir size; i.e., Fout = kVres, where k is a
proportionality constant. Calculate the residence time (?res) of water,
and also the value of k for this reservoir. What is the relationship
between ?res and k?

(b). Imagine that all water is emptied from the reservoir, then it
begins to fill with constant inflow rate Fin, while maintaining outflow
rate Fout = kVres. On the graph below, qualitatively sketch how Vres will
change as a function of time (hint: initially, with little water in the
reservoir, outflow will be small and Vres will increase almost linearly
with time. However, as Vres increases, so will Fout, such that the rate
of increase in Vres will decrease to almost zero as the reservoir
approaches its steady state volume).

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