Consider steady, incompressible and irrotational flow through a reducer in a horizontal pipe where the diameter is reduced from $$20cm$$ to $$10cm.$$ The pressure in the $$20cm$$ pipe just upstream of the reducer is $$150kPa.$$ The fluid has a vapour pressure of $$50kPa$$ and a specific weight of $$5\,\,kN/{m^3}.$$ Neglecting frictional effects, the maximum discharge (in $${m^3}/s$$) that can pass through the reducer without causing cavitation is

Consider steady-state heat conduction across the thickness in a plane composite wall as shown in fig exposed to convection conditions on both sides.

Assuming negligible contact resistance between the wall surfaces, the interface temp $$T(C)$$ of the two walls will be

Radiative heat transfer is intended between the inner surfaces of two very largen isothermal parallel metal plates. While the upper plate (designated as plate $$1$$) is a black surface and is the warmer one being maintained at $${727^ \circ }C,$$ the lower plate (plate $$2$$) is a diffuse and gray surface with an emissivity of $$0.7$$ and is kept at $${27^ \circ }C.$$ Assume that the surfaces are sufficiently large to form a two-surface enclosure and steady state conditions to exist. Stefan Boltzmann constant is given as
$$5.67 \times {10^{ - 8}}\,W/{m^2}{K^4}$$

If plate is also a diffuse gray surface with an emisivity value of $$0.8,$$ the net radiant heat exchange (in $$kW/{m^2}$$) between plate $$1$$ and plate $$2$$

In a parallel flow heat exchanger operating under steady state, the heat capacity rates (product of specific heat at constant pressure and mass flow rate) of the hot and cold fluid are equal. The hot fluid, flowing at $$1kg/sec$$ with $$sp.$$ heat $$= 4kJ/kgK,$$ enters the heat exchanger at $${102^ \circ }C$$ while the cold fluid has an inlet temperature of $${15^ \circ }C$$. The overall heat transfer coefficient for the heat exchanger is estimated to be $$1\,\,kW/{m^2}K$$ and the corresponding heat transfer surface area is $$5{m^2}$$. Neglect heat transfer between the heat exchanger and the ambient.

The heat exchanger is characterized by the following relation $$2\varepsilon = 1 - Exp\left( { - 2NTU} \right).$$ The exit temp (in $$^ \circ C$$) for the cold fluid is