consider a 1 m 3 Storage tank filled with a liquid with a density of 1000 kg/m 3

Question

consider a 1 m3 Storage tank filled with a liquid with a density of 1000 kg/m3. At a particulate instant, an inlet valve is opened and a fluid density of 900 kg/m3 flows into the tank at a rate of 0.1 m3/min. at this same time, an outlet valve is opened and adjusted such that the liquid level in the tank is maintained at constant elevation. A Mixer is also turned on to ensure that the liquid in the tank is well mixed. After these valves are opened the mixer is turned on.

A. How long will it take the density of the liquid in tank to decline from 1000 kg/m3 to 950 kg/m3?

Explanation / Answer

Let's solve this problem interms of mass-time

We have 1000 kg of liquid initially, then we want to make it to 950 Kg.

Instantaneous density of the liquid will be

D(t) = 1000 + 90t - D(t)*0.1*t/ 1

Hence, D(t) = 1000+ 90t/ 1+ 0.1 t

Now we need to make D(t) = 950

Hence t will be ,

950 * (1 + .1t ) = 1000 + 90t

t = 10 min

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