The head loss for a laminar incompressible flow through a horizontal circular pipe is $${h_1}$$. Pipe length and fluid remaining the same, if the average flow velocity doubles and the pipe diameter reduces to half its previous value, the head loss is $${h_2}.$$ The ratio $${h_2}/{h_1}$$ is

Within a boundary layer for a steady incompressible flow, the Bernoulli equation

If a foam insulation is added to a $$4cm$$ outer diameter pipe as shown as figure, the critical radius of insulation (in $$cm$$) is ________.

A cylindrical uranium fuel rod of radius 5 mm in a nuclear reactor is generating heat at the rate of $$4 \times {10^7}\,\,W/{m^3}.$$ The rod is cooled by a liquid (convective heat transfer coefficient $$1000W/{m^2}$$-$$K$$) at $${25^ \circ }C$$. At steady state, the surface temperature (in $$K$$) of the rod is