Figure shows the schematic for the measurement of velocity of air (density $$ = 1.2\,\,kg/{m^3}$$ ) through a constant -area duct using a Pilot tube and a water-tube manometer. The differential head of water (density $$ = 1000\,kg/{m^3}$$) in the two columns of the manometer is $$10$$ $$mm.$$ Take acceleration due to gravity as $$9.8$$ $$m/{s^2}.$$ The velocity of air in $$m/s$$

The ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness of flows of two fluids $$P$$ and $$Q$$ on a flat plate are $${1 \over 2}$$ and $$2$$ respectively. The Reynolds number based on the plate length for both the flows is $${10^4}.$$ The Prandtl and Nusselt numbers for $$P$$ are $${1 \over 8}$$ and $$35$$ respectively. The Prandtl and Nusselt number for $$Q$$ are respectively

In a condenser of a power plant, the steam condenses at a temperature of $${60^ \circ }C.$$ The cooling water enters at $${30^ \circ }C$$ and leaves at $${45^ \circ }C.$$ The logarithmic mean temperature difference $$(LMTD)$$ of the condenser is

A spherical steel ball of $$12mm$$ diameter is initially at $$100K.$$ It is slowly cooled in a surrounding of $$300K.$$ The heat transfer coefficient between the steel ball and the surrounding is $$5W/{m^2}K.$$ The thermal conductivity of steel is $$20$$ $$W/mK.$$ The temperature difference between the centre and the surface of steel ball is