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

A $$4$$ $$mm$$ thick sheet is rolled with $$300$$ $$mm$$ diameter rolls to reduce thickness without any change in its width. The friction coefficient at the work-roll interface is $$0.1.$$ The minimum possible thickness of the sheet that can be produced in a single pass is

In a wire drawing operation, diameter of a steel wire is reduced from $$10$$ $$mm$$ to $$8$$ $$mm.$$ the mean flow stress of the material is $$400$$ $$MPa.$$ The ideal force required for drawing ignoring friction and redundant work is:

In arc welding process, the voltage and current are $$25V$$ and $$300A$$ respectively. The arc heat transfer efficiency is $$0.85$$ and welding speed is $$8$$ $$mm/sec$$. The net heat input (in $$J/mm$$) is