Question: A 1-m-diameter tank (empty at time zero) is being filled by liquid water flowing through a 0.025-m-diameter pipe at an average velocity of 30 m/s

A 1-m-diameter tank (empty at time zero) is being filled by liquid water flowing through a 0.025-m-diameter pipe at an average velocity of 30 m/s with a temperature of 100C. Evaporation is negligible.

A. Derive a differential equation relating the water level z in the tank to the time t.

B. Integrate this differential equation to determine the water level (m) in the tank at the end of 2 minutes.

C. Discuss any assumptions you made regarding the water density.

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