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

A composite wall, having unit length normal to the plane of paper, is insulated at the top and bottom as shown in the figure. It is comprised of four different materials $$A, B, C$$ and $$D.$$
Dimensions are $$$\eqalign{ & {H_A} = {H_D} = 3cm, \cr & {H_B} = {H_C} = 1.5cm, \cr & {L_1} = {L_3} = 0.05m,\,\,\,\,\,\,\,\,\,\,{L_2} = 0.1m \cr} $$$

Thermal conductivity of the materials are $$$\eqalign{ & {K_A} = {K_D} = 50\,\,\,W/mK, \cr & {K_B} = 10\,\,W/mK,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{K_C} = 1\,\,W/mK \cr} $$$
The fluid temps and $$HTC$$(see fig) are $$$\eqalign{ & {T_1} = {200^ \circ }C,\,\,\,\,{h_1} = 50\,\,W/{m^2}K, \cr & T{}_2 = {25^ \circ }C,\,\,\,\,{h_2} = 10\,\,W/{m^2}K, \cr} $$$

Assuming one dimensional heat transfer condition. Determine the rate of heat transfer through the wall.