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 ____________

Match the following pairs:

The velocity field on an incompressible flow is given by
$$V = \left( {{a_1}x + {a_2}y + {a_3}z} \right)i + \left( {{b_1}x + {b_2}y + {b_3}z} \right)j$$ $$$ + \left( {{c_1}x + {c_2}y + {c_3}z} \right)k,$$$

Where $${a_1} = 2$$ and $${c_3} = - 4.$$ The value of $${b_2}$$ 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