A bent tube is lowered into the stream as shown in the figure below. The velocity of the stream relative to the tube equal to v. The closed upper end of the tube located at the light `h_(0)`. To what height h will the water jet spurt ?

Options

A. `(v^(2))/(2g)`
B. `(v^(2))/(2g)+h_(0)`
C. `(v^(2))/(2g)-h_(0)`
D. `(v^(2))/(4g)-h_(0)`

Answer

C

Explanation

Let tube's entrance be a depth y below the surface. Take point 1 at entry, 2 at the maximum height of the fountain.
Applying Bernoulli's theorem,
`p_(1)+rho gh_(1)+(1)/(2)rhov_(1)^(2)=p_(2)+rho gh_(2)+(1)/(2)rhov_(2)^(2)`
Taking, `h_(1)=0, h_(2)=(y+h_(0)+h),v_(1)=v,v_(2)=0`
substituting, `p_(0)+rho gy+(1)/(rho)v^(2)=p_(0)+rho g(y+h_(0)+h)`
`implies (1)/(2) rho v^(2)=rho g(h_(0)+h)`
`implies h=((v^(2))/(2g)-h_(0))`