In butt welding operation on plates, the heat input necessary is given by

$$Q = 8\,K\,{T_c}\,t\,\,\,\left[ {0.2 + {{Vb} \over {4\alpha }}} \right]$$
Where $$K=$$ thermal conductivity,
$${T_c} = $$ temp increases from room temp up to $$MP,$$
$$t=$$ thickness of plate,
$$V=$$ welding speed,
$$b=$$ width of weld,
$$\alpha = thermal diffusivity

Two alloy steel plates as shown in fig are to be welded using a power source rated at $$5$$ $$kVA$$ having a duty cycle of $$75\% .$$ Using the given data, determine the maximum welding speed for the job given in $$mm/s$$

Data : $$K = 45\,W/{m^0}C,\,\,{T_c} = {1450^ \circ }C,$$ and
$$\alpha = 1.2 \times {10^{ - 5}}\,\,{m^2}/s.$$

For butt welding $$40mm$$ thick steel plates, when the expected quantity of such jobs is $$5000$$ per month over a period of $$10$$ years, choose the best suitable welding process out of the following available alternatives.

In a particular mold design, the down sprue has an area of Cross section of $$6.45\,\,c{m^2}$$ where the pouring basin leads into the sprue. The sprue is $$20$$ $$cm$$ long. The required metal flow rate at the top section of the sprue is $$820$$ $$c{m^3}/s.$$ Determine the pouring height necessary above the sprue top. Also determine the area of $$C.S$$ of sprue at its bottom to avoid the aspiration of liquid molten metal.

Which of the following materials requires the largest shrinkage allowance, while making a pattern for casting?