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

The discharge velocity at the pipe exit in figure is

Fluid is flowing with an average velocity of $$V$$ through a pipe of diameter $$d.$$ over a length of $$L,$$ the “head” loss is given by $${{fL{V^2}} \over {2gD}}.$$ The friction factor, $$f,$$ for laminar flow in terms of Reynolds number ($$Re$$) is ______________ (fill the blank)