A sprue in a sand mould has a top diameter of $$20mm$$ and height of $$200mm.$$ The velocity of the molten metal at the entry of the sprue is $$0.5m/s.$$ Assume acceleration due to gravity as $$9.8\,\,m/{s^2}$$ and neglect all losses. If the mould is well ventilated, the velocity (upto $$3$$ decimal points accuracy) of the molten metal at the bottom of the sprue is ______________________ $$m/s.$$

Gray cast iron blocks of size $$100\,\,mm \times 50\,\,mm \times 10\,\,mm$$ with a central spherical cavity of diameter $$4$$ mm are sand cast. The shrinkage allowance for the pattern is $$3\% $$. The ratio of the volume of the pattern to volume of the casting is ___________________

Heat is removed from a molten metal of mass $$2$$ $$kg$$ at a constant rate of $$10$$ $$kW$$ till it is completely solidified. The cooling curve is shown in the figure.

Assuming uniform temperature throughout the volume of the metal during solidification, the latent heat of fusion of the metal (in $$kJ/kg$$) is ______________

A cylindrical job with diameter of $$200$$ $$mm$$ and height of $$100$$ $$mm$$ is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in $$mm$$) is