A syringe with a frictionless plunger contains water and has at its end a $$100$$ $$mm$$ long needle of $$1$$ $$mm$$ diameter. The internal diameter of the syringe is $$10$$ $$mm.$$ Water density is $$1000\,\,kg/{m^3}.$$ . The plunger is pushed in at $$10$$ $$mm/s$$ and the water comes out as a jet.

Neglect losses in the cylinder and assume fully developed laminar viscous flow throughout the needle; the Darcy friction factor is $${64/R_e}$$. Where $${R_e}$$ is the Reynolds number. Given that the viscosity of water is $$1.0 \times {10^{ - 3}}\,\,kg/m\,\,\,s,$$ the force $$F$$ in newtons required on the plunger 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

Consider a laminar boundary layer over a heated flat plate. The free stream velocity is $${U_\infty }.$$ At some distance $$x$$ from the leading edge the velocity boundary layer thickness is $${\delta _v}$$ and the thermal boundary layer is $${\delta _r}.$$ If the Prandtl number is greater than $$1,$$ then