Differential equations-Cengel 2.98 A spherical tank of radius R is initially filled with water. Now a...

Differential equations-Cengel 2.98
A spherical tank of radius R is initially filled with water. Now a hole of radius r is opened at the bottom of the tank and the water is let out. According to Torricelli's law, water comes out of the opening at a velocity v = (2gy) ^ 1/2, where y is the height of the water over the hole at a given moment, and g is the acceleration of gravity. Obtain a relation for the depth of the water with function of time t, and determine how long it takes to empty.
Explain your procedure

Expert Solution

`Hey,

Note: Brother in case of any queries, just comment in box I would be very happy to assist all your queries

Now integrate both sides So, t will go from 0 to t and h will go from 2R to h

So,

t=-((4*H^(3/2)*R)/3 - (16*2^(1/2)*R^(5/2))/15 - (2*H^(5/2))/5)*pi/(Cd*Ah*sqrt(2*g))

Where H is the water at time t in the tank

For H=0, time is

t=((16*2^(1/2)*R^(5/2))/15)*pi/(Cd*Ah*sqrt(2*g))

Kindly revert for any queries

Thanks.

Colby Messinger answered 2 years ago

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