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)

Shown below are three tanks, tank $$1$$ without an orifice tube and tanks $$2$$ and $$3$$ with orifice tubes as shown. Neglecting losses and assuming the diameter of orifice to be much less than that of the tank, write expressions for the exit velocity in each of the three tanks.