The figure shows the commonly observed decrease in diameter of a water stream as it falls from a tap. The tap has internal diameter `D_(0)` and is connected toa large tank of water. The surface of the water is at a height `b` above the end of the tap.
By considering the dynamics of a thin "cylinder" of water in the steam answer the following: (ignore any reistance to the flow and any effects of surface tansion, given `rho_(w) =` density of water)

Equation for the flow rate, i.e. the mass of water flowing through a given point in the stream per unit time, as funcation of the water speed `v` will be

Options

A. `vrho_(w)piD^(2)//4`
B. `vrho_(w)(piD^(2)//4 - piD_(0)^(2)//4)`
C. `vrho_(w)piD^(2)2`
D. `vrho_(w)piD_(0^(2))//4`

Answer

A

Explanation

`(A)` As, `dm = Arhom vdt`
`rArr (dm)/(dt) = Arhow^(v) rArr (dm)/(dt) = Vrho_(W)pi (D^(2))/(4)` where `'D'` is the diameter of stream.