Consider steady flow of water in a situation where two pipe lines (pipe $$1$$ and pipe $$2$$) combine into a single pipe line $$(pipe-3)$$ as shown in the figure. The cross-sectional areas of all three pipelines are constant. The following data is given :

Assuming the water properties and the velocities to be uniform across the cross section of the inlets and the outlet, the exit velocity (in $$m/s$$) in pipe $$3$$ is

The pressure drop for laminar flow of a liquid in a smooth pipe at normal temperature and pressure is

Heat is being transferred convectively from a cylindrical nuclear reactor fuel rod of $$50mm$$ diameter to water at $${70^ \circ }C$$, under steady state condition, the rate of heat generation within the fuel element is $$50 \times {10^6}\,\,W/{m^3}$$ and the convective heat transfer coefficient is $$1$$ $$kW/{m^2}K.$$ The outer surface temperature of the fuel element would be

Autogeneous gas tungsten arc welding of a steel plate is carried out with welding current of $$500A,$$ voltage of $$20V,$$ and weld speed of $$20mm/min.$$ Consider the heat transfer efficiency from the arc to the weld pool as $$90\% $$. The heat input per unit length (in $$kJ/mm$$) is