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 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 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.

Assuming ideal flow, the force $$F$$ in Newton’s required on the plunger to push out the water 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