## Free Jet Liquid

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# Free Jet Liquid

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 at

Displacement in x-direction

S

x = u-cos θ t t = x / u cos θ

displacement in y-direction

S

y = u sin θ. t - gt

Substituting the value f ‘t’ from

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

y = x tan θ - gt

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

At maximum height, velocity u-direction becomes zero

v

h = u

Displacement in y-direction

s

y = u sin θ t - 1/2 gt

0 = u sin θ t - gt

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

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

s = ut + 1/2 at

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

R = u

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

sin 2θ = 1 sin 90 = 1

2θ = 90 θ = 45

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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 at

^{2}Displacement in x-direction

S

_{x }= u_{x }+ 1/2a_{x}t^{2}a_{x}= 0x = u-cos θ t t = x / u cos θ

displacement in y-direction

S

_{y }= u_{x}t + 1/2 a_{y}t^{2 }a_{y}= - gy = u sin θ. t - gt

^{2}/ 2Substituting the value f ‘t’ from

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

^{2}y = x tan θ - gt

^{2}/ 2u sec^{2}θThis is the equation f free liquid jet and it is parabolic.

**Maximum Height:**At maximum height, velocity u-direction becomes zero

v

^{2}y = u_{y}^{2}+ 2a_{y}^{3 }0 = u^{2}sin^{2}θ-2g (h)h = u

^{2}sin^{2 }θ / 2g**Time of flight:**Displacement in y-direction

s

_{y}= u_{y }+ 1/2 a_{y}t^{2}y = u sin θ t - 1/2 gt

^{2}0 = u sin θ t - gt

^{2}/ 2 t = 2u sin θ / g

Time to reached the highest point: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:Range:

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

s = ut + 1/2 at

^{2}ax = 0R = u cos θ. t = u cos θ ( 2u sin θ / g)

R = u

^{2}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 = 45

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