A stream is rushing from a boiler through a conical pipe, the diameters of the ends of which are D and d. If V and v be the corresponding velocities of the stream and if the motion is assumed to be steady and diverging from the vertex of the cone, then prove that \frac{V}{v} = \frac{D^2}{d^2} e^{(v^2 - V^2)/2K}, where K is the pressure divided by the density and is constant.

3Medium15 marks

A plane passes through a fixed point (a, b, c) and cuts the axes at the points A, B, C respectively. Find the locus of the centre of the sphere which passes through the origin O and A, B, C.

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