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A tank shaped like a vertical cylinder initially contains water to a depth of 9m. The bottom plug is pulled at time t = 0. After 1h, the depth has dropped to 4m. The rate of change of depth of water in the cylinder, y, is described by: ce dt the extinder OFFI AW The differential equation in the above can be derived using the Bernouli Equation and the Mass Continuity Equation. Bernouli Equation: P/p+0.5v² + gz=0 Mass Continuity Equation Mass in-Mass out + Generation - Consumption = accumulatio where y is the depth of the water in the cylinder (m) t is the time (hr) k is a constant Derive the Differential Equation Fice √y express b) k in terms of the properties of the system.

A tank shaped like a vertical cylinder initially contains water to a depth of 9m. The bottom plug is pulled at time t = 0. After 1h, the depth has dropped to 4m. The rate of change of depth of water in the cylinder, y, is described by: ce dt the extinder OFFI AW The differential equation in the above can be derived using the Bernouli Equation and the Mass Continuity Equation. Bernouli Equation: P/p+0.5v² + gz=0 Mass Continuity Equation Mass in-Mass out + Generation - Consumption = accumulatio where y is the depth of the water in the cylinder (m) t is the time (hr) k is a constant Derive the Differential Equation Fice √y express b) k in terms of the properties of the system.

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Can someone help explain clearly and use the Bernouli Equation and Mass Continuity Equation to a) derive the differential equation and b) express k in terms of the properties of the system?
A tank shaped like a vertical cylinder initially contains water to a depth of 9m. The bottom plug is pulled at time t = 0. After 1h, the depth has dropped to 4m. The rate of change of depth of water in the cylinder, y, is described by: Fice dy dt where y is the depth of the water in the cylinder (m) t is the time (hr) k is a constant Office The differential equation in the above can be derived using the Bernouli Equation and the Mass Continuity Equation. Bernouli Equation: a) Derive the Differential Equation P/p+ 0.5v² + gz = 0 Mass Continuity Equation Mass in - Mass out + Generation - Consumption = accumulation. dy dt Fice =-k√y express b) k in terms of the properties of the system.
Transcribed Image Text:A tank shaped like a vertical cylinder initially contains water to a depth of 9m. The bottom plug is pulled at time t = 0. After 1h, the depth has dropped to 4m. The rate of change of depth of water in the cylinder, y, is described by: Fice dy dt where y is the depth of the water in the cylinder (m) t is the time (hr) k is a constant Office The differential equation in the above can be derived using the Bernouli Equation and the Mass Continuity Equation. Bernouli Equation: a) Derive the Differential Equation P/p+ 0.5v² + gz = 0 Mass Continuity Equation Mass in - Mass out + Generation - Consumption = accumulation. dy dt Fice =-k√y express b) k in terms of the properties of the system.
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