Laplace transform of $$sin$$ $$ht$$ is

Two pipes of uniform section but different diameters carry water at the same volumetric flow rate. Water properties are the same in the two pipes. The Reynolds number, based on the pipe diameter,

Oil is being pumped through a straight pipe, the pipe length, diameter and volumetric flow rate are all doubled in a new arrangement. The pipe friction factor, however, remains constant. The ratio of pipe frictional losses in the new arrangement to that in the original configuration would be

Two pipes of inner diameter $$100mm$$ and outer diameter $$110mm$$ each are joined by flash butt welding using $$30V$$ power supply. At the interface, $$1mm$$ of material melts from each pipe which has a resistance of $$42$$ Ohms.If the unit melt energy is $$64.4$$ $$MJ/{m^3}$$, then time required for welding (in $$S$$) is