A $$200$$ $$mm$$ long down sprue has an area of cross section of $$650$$ $$m{m^2}$$ where the pouring basin meets the down sprue (i.e. at the beginning of the down sprue). A constant head of molten metal is maintaining by the pouring basin. The molten metal flow rate is $$6.5 \times {10^5}\,\,\,m{m^3}/s.$$ considering the end of down sprue to be open to atmosphere and an acceleration due to gravity of $${10^4}mm/{s^2},$$ the area of the down sprue in $$m{m^2}$$ at its end (avoiding aspiration effects) should be

In a sand casting operation, the total liquid head is maintained constant such that it is equal to the mould height. The time taken to fill the mould with a top gate is $${t_A}.$$ If the same mould is filed with a bottom gate, then the time taken is $${t_B}.$$ Ignore the time required to fill the runner and frictional effects. Assume atmospheric pressure at the top molten metal surfaces. The relation between the $${t_A}$$ and $${t_B}$$ is

Match List - $${\rm I}$$ (products) with List - $${\rm II}$$ (casting process) and select the correct answer using the codes given below the lists

A mould has a downsprue whose length is $$20$$ $$cm$$ and the cross sectional area at the base of the down sprue is $$1\,\,c{m^2}.$$ The down sprue feeds a horizontal runner leading into the mould cavity of volume $$1000\,\,c{m^3}.$$ The time required to fill the mould cavity will be