The shape of an ancient water clock jug is such that water level descends at a constant rate at all time. If the water level falls by 4cm every hour, determine the shape of the jar, i.e. specify x as a function of y. The radius of drain hole in 2mm and can be assumed to be very small compared to x.

The shape of an ancient water clock jug is such that water level desce

1.	The shape of an ancient water clock jug is such that water level descends at a constant rate at all time. If the water level falls by 4cm every hour, determine the shape of the jar, i.e. specify x as a function of y. The radius of drain hole in 2mm and can be assumed to be very small compared to x.
Answer» Solution :`a sqrt(2gy)=pix^(2)(-(dy)/(DT))` Here, `-(dy)/(dt)=(4XX10^(-2))/(3600)=1.11xx10^(-5) m//s` `a=pir^(2)=pi (2XX10^(-3))^(2)` `=1.26xx10^(-5)m^(2)` substituting these values in Eq, (i) we have `(1.26xx10^(-5))sqrt(2xx9.8xxy)=pi (1.11xx10^(-5))x^(2)` or, `y=0.4x^(4)` This is the desired x-y relation.