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 ______________________ $$m/s.$$

In a metal forming operation when the material has just started yielding, the principal stresses are $${\sigma _1} = \,\, + 180\,\,MPa,\,\,\,$$ $${\sigma _2} = \,\, - 100\,\,MPa,\,\,\,$$ $${\sigma _3} = 0.$$ Following Von Mises' criterion, the yield stress is _____________ $$MPa.$$

In an arc welding process, welding speed is doubled. Assuming all other process parameters to be constant, the cross sectional area of the weld bead will

Two cutting tools with tool life equations given below are being compared:
$$\eqalign{ & Tool\,\,1:\,\,\,\,\,\,\,V{T^{0.1}} = 150 \cr & Tool\,\,2:\,\,\,\,\,\,\,V{T^{0.3}} = 300 \cr} $$
where $$V$$ is cutting speed in $$m/minute$$ and $$T$$ is tool life in minutes. The breakeven cutting speed beyond which Tool $$2$$ will have a higher tool life is _______________ $$m/minute$$.