Consider fully developed flow in a circular pipe with negligible entrance length effects. Assuming the mass flow rate, density and friction factor to be constant, if the length of the pipe is doubled and the diameter is halved, the head loss due to friction will increase by a factor of

Air ( $${\rho = 1.2\,\,kg/{m^3}}$$ and kinematic viscosity, $${v = 2 \times {{10}^{ - 5}}{m^2}/s}$$ ) with a velocity of $$2m/s$$ flows over the top surface of a flat plate of length $$2.5m.$$ If the average value of friction coefficient is $${C_f} = {{1.328} \over {\sqrt {{{{\mathop{\rm Re}\nolimits} }_x}} }},\,\,$$ the total drag force (in $$N$$) per unit width of the plate is ____________

A $$10$$ $$mm$$ diameter electrical conductor is covered by an insulation of $$2$$ $$mm$$ thickness. The conductivity of the insulation is $$0.08$$ $$W/m$$-$$K$$ and the convection coefficient at the insulation surface is $$10$$ $$W/{m^2}$$ -$$K.$$ Addition of further insulation of the same material will

The Blasius equation related to boundary layer theory is a