The stepped cylindrical tank shown is initially filled with liquid water at STP

Question

The stepped cylindrical tank shown is initially filled with liquid water at STP to a height H1. Subsequently, a plug at the bottom of the tank is removed to allow water to flow from the small hole of diameter d. The velocity v of the flowing water can be related to the instantaneous height of the water above it h(t) based on an adjusted mechanical energy conservation relationship; 1/2mv^2 = 0.96mgh . Develop an expression for the time to drain the tank based on given parameters and then evaluate the time to drain if D1=60cm, D2=35cm, H1=70cm, H2=30cm and d=6mm. (sorry, i can't post the picture. If you need a picture, please let me know the email, then i will send to you, thanks)

Explanation / Answer

let at any instant the height of water in the tank be x.... from the adjusted energy conservation equation... v=sqrt(2 * 0.96 *g*x)... dx/dt=4.34 sqrt(x)... t=0.46(sqrt(H2)-sqrt(H1))....

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