Question:
A 2m × 2m tank of 3 m height has inflow, outflow and stirring mechanisms. Initially, the tank was half-filled with fresh water. At t = 0, an inflow of a salt solution of concentration 5 g/m3 at the rate of 2 litre/s and an outflow of the well stirred mixture at the rate of 1 litre/s are initiated. This process can be modelled using the following differential equation:
\(\frac {dm}{dt}+\frac {m}{6000+t}=0.01\)
where m is the mass (grams) of the salt at time t (seconds). The mass of the salt (in grams) in the tank at 75% of its capacity is _____ (rounded off to 2 decimal places).
A 2m × 2m tank of 3 m height has inflow, outflow and stirring mechanisms. Initially, the tank was half-filled with fresh water. At t = 0, an inflow of a salt solution of concentration 5 g/m3 at the rate of 2 litre/s and an outflow of the well stirred mixture at the rate of 1 litre/s are initiated. This process can be modelled using the following differential equation:
\(\frac {dm}{dt}+\frac {m}{6000+t}=0.01\)
where m is the mass (grams) of the salt at time t (seconds). The mass of the salt (in grams) in the tank at 75% of its capacity is _____ (rounded off to 2 decimal places).
\(\frac {dm}{dt}+\frac {m}{6000+t}=0.01\)
where m is the mass (grams) of the salt at time t (seconds). The mass of the salt (in grams) in the tank at 75% of its capacity is _____ (rounded off to 2 decimal places).
Updated On: Dec 13, 2024
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Correct Answer: 24.5
Solution and Explanation
The answer is: 24.50 or 25.50 (approx.)
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