A tank of large base area is filled with water up to a height of `5 m`. A hole of `2 cm^(2)` cross section in the bottom allows the water to drain out in continuous streams. For this situation, mark out the correct statement(s) (take `rho_("water")=1000kg//m^(3),g=10ms^(-2))`

Options

A. The cross-sectional area of the emerging stream of water decreases as it falls down
B. The cross-sectional area of the emerging stream of water increases as it falls down
C. At a distance of 5 m below the bottom of the tank, the cross-sectional area of the stream is ` 1.414 cm ^ 2 `
D. At a distance of 5 m below the bottom of the tank, the cross-sectional area of the stream is ` 2.86 cm ^2`

Answer

A, C

Explanation

`v=sqrt(2gh)=sqrt(2xx10xx5)=10m//s`. Also, using equation of continuity, Av = constant
Using Bernoulli’s Theorem
`P_(0)+(rhov^2)/(2)+0=P_(0)+(rhov_(1)^(2))/(2)-rhogh` (Just outside the hole and 5 m below the bottom of tank)
`Rightarrow(rhov_(1)^(2))/(2)=(rhov^(2))/(2)+rhoghRightarrowv_(1)=10sqrt(2)m//s`. As Av = constant `RightarrowA_(1)=sqrt(2)=1.414cm^(2)`