We were discussing the various basic concepts such
asÂ Eulerâ€™s
Equation of motion,Â Moment of momentum equation,Â Bernoulliâ€™s
equation from Eulerâ€™s equation,Â derivation
of discharge through venturimeter, derivation of discharge throughÂ Orifice
meterÂ andÂ Pitot
tubeÂ as well asÂ resultant force exerted by flowing fluid
on a pipe bend, in the subject of fluid mechanics, in our recent posts.

Today we will see here the basic concept of free
liquid jets, in the subject of fluid mechanics, with the help of this post.

###
**Free
Liquid jets **

Free liquid jet is basically defined as the jet of
water coming out from nozzle in atmosphere. Path followed by the free jet will
be parabolic.Â

Let us see the following figure of jet at point A,
coming out from a nozzle, as displayed here in following figure.Â

Let us consider the following data from above figure.

U = Velocity of free jet coming out from nozzle

Î¸ = Angle made by jet at point A with the horizontal
direction

U Cos Î¸ = Horizontal component of velocity (U) of
free jet at point A

U Sin Î¸ = Vertical component of velocity (U) of free
jet at point A

Let us consider one point P at the path followed by
the free liquid jet. Co-ordinate of P is (x, y) and it is displayed above in
figure.

u = Velocity of free jet at point P

v = Velocity of free jet at point P

t = Time taken by a liquid particle to reach from
point A to point P

#### Horizontal distance travelled by the fluid particle

x = Velocity component in x-direction X Time of
travelling

x = (U Cos Î¸) X t

x = U t Cos Î¸

#### Vertical distance travelled the fluid particle

y = Velocity component in y-direction X Time of
travelling â€“ (1/2) gt

^{2}
y = U t Sin Î¸â€“ (1/2) gt

^{2}
We can secure the value of time t from equation of
horizontal distance travelled the fluid particle and we will have following
value of time t as mentioned here.

t = x/ (U Cos Î¸)

Now we will use the value time t in above equation
of vertical distance travelled the fluid particle.

Above equation shows that path followed by the free
jet in atmosphere is parabolic.

### Let us consider the following formula which will be used in analysis of problems related with free liquid jet

*Maximum height attained by the jet*

*Time of flight*

*Time to reach highest point*

*Horizontal range of the jet*

*Value of angle for the maximum range*

Do you have any suggestions? Please write in comment
box.

We will find out the next post i.e.Â Difference between orifice and mouthpiece.

####
**Reference:
**

Fluid mechanics, By R. K. BansalÂ

Image Courtesy: GoogleÂ

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