## Saturday, 23 June 2018

We were discussing the various basic concepts such as Euler’s Equation of motionMoment of momentum equationBernoulli’s equation from Euler’s equationderivation of discharge through venturimeter, derivation of discharge through Orifice meter and Pitot tube as well as 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.

Let us see the following figure of jet at point A, coming out from a nozzle, as displayed here in following figure.
Let us consider the following data from above figure.
U = Velocity of free jet coming out from nozzle
θ = Angle made by jet at point A with the horizontal direction
U Cos θ = Horizontal component of velocity (U) of free jet at point A
U Sin θ = 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 θ) X t
x = U t Cos θ

#### Vertical distance travelled the fluid particle

y = Velocity component in y-direction X Time of travelling – (1/2) gt2
y = U t Sin θ– (1/2) gt2

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 θ)

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. Difference between orifice and mouthpiece.

#### Reference:

Fluid mechanics, By R. K. Bansal