A falk consisting of a cope and drag has the following dimensions: length $$300mm,$$ width $$200mm,$$ and total septh $$200mm$$ (cope height $$50mm$$).
A $$150mm\,\, \times \,100mm\,\, \times 50mm$$ cast iron block is to be cast. If the specific weight of cast iron is $$78\,\,kN/{m^3}$$ and that of the mold sand $$16\,\,kN/{m^3}$$, find lifting force on the cope created by buoyant force, weight of sand in the cope, the net force at the liquid-sand interface and additional weight to be kept on the cope.

A strip of thickness $$T$$ $$mm$$ is rolled in a $$2$$ high single pass rolling mill, having roll diameter $$D$$ $$mm,$$ to a final thickness of $$\left( {T - 2\Delta T} \right)mm.$$ If the friction coefficient between the roll and strip is $$\mu ,$$ calculate the maximum reduction $$2\Delta T$$ possible in this operation. Using this relation, for $$D=300mm,$$ $$T=40mm$$ and friction coefficient is $$0.3,$$ calculate the outgoing thickness of the strip. If the inlet velocity is $$5m/s,$$ what is the outgoing strip velocity?.

For gas welding a particular job using a neutral oxy-acetylene flame the acetylene consumption was $$10$$ ltrs. The oxygen consumption from the cylinder in liters will be