A cylinder of $$150mm$$ diameter & $$200mm$$ height is to be cast with out any riser. The cylinder is moulded entirely in the drag of a green sand flask & is top gated. The cope of the flask is $$200mm$$ height & the height of the metal during pouring is $$50mm$$ above the cope. A tapered sprue is employed & the gating ratio is $$1:1.5:2$$. The time taken (in seconds) to fill the casting cavity neglecting energy losses, if the in-gate area is $$400sq.mm$$

A casting of $$200\,\,mm\,\, \times \,\,100\,\,mm \times 70\,\,mm$$ size solidifies in ten minutes. Estimate solidification time for a $$200\,\,mm\,\, \times \,\,100\,\,mm \times 10\,\,mm$$ casting under similar conditions?

If the freezing ratio equal to (casting area/casting volume)/(riser area/riser volume) & the volumetric ratio equal to riser volume/casting volume, for a disc casting of $$20cm$$ diameter and $$10$$ $$cm$$ thick are $$1.4$$ and $$0.8$$ respectively. The corresponding values for a square disc of $$20$$ $$cm$$ side and $$10$$ $$cm$$ thick if the same cylindrical riser with a height to diameter ratio of unity is used in both cases.

Molten aluminium was poured in a sand mold and the thickness of solid skin formed after $$20$$ seconds and $$50$$ seconds were fond to be $$3mm$$ and $$4.5mm$$ respectively. What would be the thickness of the solid skin at the end of $$100$$ seconds after pouring?