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

The following figure was generated from experimental data relating spectral black body emissive power to wave length at three temperatures $${T_1},{T_2}$$ and $${T_3}\left( {{T_1} > {T_2} > {T_3}} \right).$$

The conclusion is that the measurements are

Hot oil is cooled from $${80^ \circ }C$$ to $${50^ \circ }C$$ in an oil cooler which uses air as the coolant. The air temperature rises from $${30^ \circ }C$$ to $${40^ \circ }C$$. the designer uses a $$LMTD$$ value of $${26^ \circ }C$$. the type of heat exchanger is