A $$U$$-tube manometer with a small quantity of mercury is used to measure the static pressure difference between two locations $$A$$ and $$B$$ in a conical section through which an incompressible fluid flows. At a particular flow rate, the mercury column appears as shown in the figure. The density of mercury is $$13600$$ $$kg/{m^3}$$ and $$g = 9.81$$ $$m/{s^2}.$$ Which of the following is correct?

A venturimeter of $$20$$ $$mm$$ throat diameter is used to measure the velocity of water in a horizontal pipe of $$40$$ $$mm$$ diameter. If the pressure difference between the pipe and throat sections is found to be $$30$$ $$kPa$$ then, neglecting frictional losses, the flow velocity is

A leaf is caught in a whirlpool. At a given instant, the leaf is at a distance of $$120$$ $$m$$ from the centre of the whirlpool. The whirlpool can be described by the following velocitry distribution ;
$${V_r} = - \left( {{{60 \times {{10}^3}} \over {2\pi r}}} \right)m/s$$
and $${V_\theta } = - \left( {{{300 \times {{10}^3}} \over {2\pi r}}} \right)m/s.$$

Where $$r$$ (in meters) is the distance from the centre of the whirlpool . What will be the distance of the leaf from the centre when it has moved through half a revolution?

The velocity components in the $$x$$ and $$y$$ directions of a two dimensional potential flow are $$u$$ and $$v$$, respectively. Then $${{\partial u} \over {\partial y}}$$ is equal to