The $$2$$ - $$D$$ flow with, velocity $$\overrightarrow v = \left( {x + 2y + 2} \right)\overrightarrow i + \left( {4 - y} \right)\overrightarrow j $$ is

The horizontal and vertical hydrostatic forces $${F_x}$$ and $${F_y}$$ on the semi-circular gate, having a width $$'w'$$ into the plane of figure, are

Water $$\left( {\rho = 1000\,\,kg/{m^3}} \right)$$ flows horizontally through a nozzle into the atmosphere under the conditions given below. (assume steady state flow).

At inlet: $$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$ At outlet:
$${A_1} = {10^{ - 3}}{m^2};\,$$ $$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$ $${A_2} = {10^{ - 4}}{m^2};$$
$${V_1} = 2\,m/\sec ;$$ $$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$ $${P_2} = {P_{atm}}$$
$${P_1} = 3 \times {10^5}\,Pa\,(gauge)$$

Determine the external horizontal force needed to keep the nozzle

In descending order of magnitude, the thermal conductivity of $$(a)$$ Pure iron, $$(b)$$ liquid water, $$(c)$$ saturated water vapour, and $$(d)$$ aluminum can be arranged as