Torricelli's theorem

 Consider a vessel which is filled with water, at the surface of water P1 pressure is applied and the velocity of water is zero (V1 = 0). Let a hole is made at a point b from which water is coming out with velocity V & at that point the pressure is P2 .

 Let ‘H’ is the height from surface to the bottom of the vessel & ‘h’ is the height from the surface to the hole. Then the remaining height is

(H – h).  

 According to Pascal's law -

     P1 = P2 = P

     V1 = 0

According to Bernoulli's theorem-

P1 + ½ ρv12 + ρgh1 = P2 + ½ ρv22 + ρgh2

P + ½ ρv12 + ρgH = P+ ½ ρv22 + ρg(H – h)

½ ρ(0)2 + ρgH =  ½ ρv2 + ρg(H – h)

       ρgH =  ½ ρv2 + ρgH - ρgh

       ½ ρv2 = ρgh

       v2 = 2gh

        v = √2gh

Hence the speed of e-flux is  v = √2gh.

 Note: a) velocity of e-flux is independent on the nature of liquid, quantity of liquid in the vessel and area of orffice.

b) Path of liquid will be parabola.

c) Greater is the distance of the hole from the free surface greater will be the velocity.

  

                                                                                     https://youtu.be/O3D2belxKBs