Question

The diagram (fig.) shows a venturimeter, through which water is flowing. The speed of water at X is 2 cm/sec. The speed of water at Y (taking g = 1000cm/$se{c}^2$)is -

• A. 23 cm/sec
• B. 32 cm/sec
• C. 101 cm/sec
• D. 1024 cm/sec

Answer 1

The correct option is B 32 cm/sec

The speed of water at $x$, let $v_x=2cm/$ sec

let Speed at $y$ is $V_y$

let length of verticle column at $x$ and $y$

are $l_x$ and $l_y$ respectively.

let $density$=$\rho$

$atm=p_0$

according to Barnouli's equation at $X$ and $Y$

$P_0+{\rho gl}_x+\frac{1}{2}\rho v_x^2=P_0+\rho g{l}_y+\frac{1}{2}\rho v_y^2$

or

$\rho g(l_x-l_y)+\frac{1}{2}\rho v_x^2=\frac{1}{2}\rho v_y^2$

$1000\times \frac{5\cdot 1}{10}+\frac{4}{2}=\frac{1}{2}{v}_y^2\therefore (l_x-ly)=5.1mn$

or

$512=\frac{v_y^2}{2}$

or $v_y^2=1024$

or

$V_y=32cm/sec$

Speed of water at Y is $v_y$ =32 m/s

Correct option is $\left(B\right)$