A cylindrical body of cross - sectional area A, height $$H$$ and density $${\rho _s},$$ is immersed to a depth $$h$$ in a liquid of density $$\rho ,$$ and tied to the bottom with a string. The tension in the string is

Air flows through a venture and into atmosphere. Air density is $$\rho $$; atmospheric pressure is $$'\,{P_a}';$$ throat diameter is exit diameter is $$'{D_t}';$$ and exit velocity is $$U.$$ the throat is connected to a cylinder containing a frictionless piston attached to a spring. The spring constant is $$'k'.$$ the bottom surface of the piston is exposed to atmosphere. Due to the flow, the piston moves by distance $$x.$$ assuming incompressible frictionless flow, $$x$$ is

A plate having $$10\,\,c{m^2}$$ area each side is hanging in the middle of a room of $$100\,\,{m^2}$$ total surface area. The plate temperature and emissivity are respectively $$800$$ $$K$$ and $$0.6.$$

The temperature and emissivity values for the surfaces of the room are $$300$$ $$K$$ and $$0.3$$ respectively. Boltzmannn constant $$\sigma = 5.67 \times {10^{ - 8}}\,\,W/{m^2}{K^4}.$$ The total heat loss from the two surfaces of the plate is

In a counter flow heat exchanger, for the hot fluid the heat capacity $$= 2kJ/kg$$ $$K,$$ mass flow rate $$= 5 kg/s,$$ inlet temperature $$ = {150^ \circ }C$$, outlet temperature $$ = {100^ \circ }C$$. For the cold fluid, heat capacity $$= 4 kJ/kg$$ $$K,$$ mass flow rate $$= 10 kg/s,$$ inlet temperature=$$ = {20^ \circ }C$$. Neglecting heat transfer to the surroundings, the outlet temperature of the cold fluid in $$ = {^ \circ }C$$ is