Free jet liquid is the jet of liquid coming out from the nozzle in atmosphere. The path traveled by the free jet is parabolic is called as Projectile.


Consider a point P (x, y) on the centre-line of the jet let u is the velocity of jet from nozzle at an angle of 'θ' w.r.t x - axis.

Using equation of motion

S = ut + 1/2 at²

Displacement in x-direction

S_x = u_x + 1/2a_x t²                           a_x = 0

x = u-cos θ t                                   t = x / u cos θ

displacement in y-direction

S_y = u_x t + 1/2 a_y t²                      a_y = - g

y = u sin θ. t - gt² / 2

Substituting the value f ‘t’ from

y = u sin θ ( x / u cos θ ) - g/2 ( x / u cos θ )²

y = x tan θ - gt² / 2u sec² θ

This is the equation f free liquid jet and it is parabolic.

Maximum Height:

At maximum height, velocity u-direction becomes zero

v²y  = u_y² + 2a_y³             0 = u² sin² θ-2g (h)

h = u² sin² θ / 2g

Time of flight:

Displacement in y-direction

s_y  = u_y + 1/2 a_y t²

y  = u sin θ t - 1/2 gt²

0  = u sin θ t - gt² / 2                t = 2u sin θ / g

Time to reached the highest point:

The time to reached highest point is has the time of flight.
Let T be the time to reach highest point

T = t / 2 = 2u sin θ / g          T = u sin θ / g

Range:

The horizontal distance traveled by the fluid particle is called as horizontal range,

s  = ut + 1/2 at²         ax = 0

R  = u cos θ. t = u cos θ  ( 2u sin θ / g)

R  = u² sin2θ / g

Value of θ for maximum range:

The range R will be maximum for a given velocity project, when 2θ as maximum,

sin 2θ = 1                             sin 90 = 1

2θ  = 90                                     θ = 45⁰

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