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A 1500 litre fuel storage tank initially contains 750 litres of liquid fuel with 20g of chemical (C) additive in it. Fuel flows into the tank at a rate of 30 litres/hour. The fuel flowing into the tank has a time dependent concentration of the above mention chemical of (2cos(t) + 1) g/litre, where t is time in seconds. Assuming a well-mixed solution leaves the tank at a rate of 15 litres/hour outline an ordinary differential equation (ODE) that relates how the amount the Chemical (C) varies with time (t). Solve this ODE analytically to find a relationship between C and t. Calculate C when t=30seconds. Plot graphs of your result.

A 1500 litre fuel storage tank initially contains 750 litres of liquid fuel with 20g of chemical (C) additive in it. Fuel flows into the tank at a rate of 30 litres/hour. The fuel flowing into the tank has a time dependent concentration of the above mention chemical of (2cos(t) + 1) g/litre, where t is time in seconds. Assuming a well-mixed solution leaves the tank at a rate of 15 litres/hour outline an ordinary differential equation (ODE) that relates how the amount the Chemical (C) varies with time (t). Solve this ODE analytically to find a relationship between C and t. Calculate C when t=30seconds. Plot graphs of your result.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A 1500 litre fuel storage tank initially contains 750 litres of liquid fuel with 20g of chemical (C) additive in it. Fuel flows into the tank at a rate of 30 litres/hour. The fuel flowing into the tank has a time dependent concentration of the above mention chemical of (2cos(t) + 1) g/litre, where t is time in seconds. Assuming a well-mixed solution leaves the tank at a rate of 15 litres/hour outline an ordinary differential equation (ODE) that relates how the amount the Chemical (C) varies with time (t). Solve this ODE analytically to find a relationship between C and t. Calculate C when t-30seconds. Plot graphs of your result.
Transcribed Image Text:A 1500 litre fuel storage tank initially contains 750 litres of liquid fuel with 20g of chemical (C) additive in it. Fuel flows into the tank at a rate of 30 litres/hour. The fuel flowing into the tank has a time dependent concentration of the above mention chemical of (2cos(t) + 1) g/litre, where t is time in seconds. Assuming a well-mixed solution leaves the tank at a rate of 15 litres/hour outline an ordinary differential equation (ODE) that relates how the amount the Chemical (C) varies with time (t). Solve this ODE analytically to find a relationship between C and t. Calculate C when t-30seconds. Plot graphs of your result.
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