We were
discussing the basic difference between orifice
and mouthpiece, classification of orifices
and mouthpieces and
also advantages and disadvantages of orifices in the subject of fluid
mechanics, in our recent posts. Now we will go ahead to find out the expression
for flow through an orifice.

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First we
will see here the basic concept of an orifice and after that we will find out
here the expression for flow through an orifice with the help of this post. So
let us come to the main topic, without wasting your time.

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**Orifice**

An orifice is basically a small opening
of any cross-section such as triangular, square or rectangular on the side or
at the bottom of tank, through which a fluid is flowing. Orifice is
basically used in order to determine the rate of flow of fluid.

As we have discussed above that orifice
will be a small opening of any cross-section, hence flow through the orifice
will be very small.

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**Flow through an orifice**

Let us consider one tank with a circular
orifice fitted at one side of the tank as displayed here in following figure.

Liquid flowing through the orifice is
developing a liquid jet whose cross-sectional area is smaller than the
cross-sectional area of the circular orifice. Area of liquid jet is decreasing
and area is minimum at section CC.

Section CC will be approximately at a
distance of half of diameter of the circular orifice. At section CC, the
streamlines are straight and parallel with each other and perpendicular to the
plane of the orifice. This section CC will be termed as Vena-contracta.

Beyond the section CC, liquid jet
diverges and will be attracted towards the downward direction due to gravity.

Image: Tank with a circular orifice

Let us consider that h is the head of
the liquid above the centre of orifice.

Let us consider two points 1 and 2 as
displayed in above figure. Point 1 is displayed inside the tank and point 2 is
shown at the Vena-contracta.

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**Assumption**

Let us consider that flow is steady and
at a constant differential head h.

p

_{1}= Pressure at point 1
v

_{1}= Velocity of fluid at point 1
p

_{2}= Pressure at point 2
v

_{2}= Velocity of fluid at point 2
Now we will apply the Bernoulli’s
equation at point 1 and 2.

Area of tank is quite large as compared
with area of liquid jet and therefore v

_{1}will be very small as compared with v_{2}. Therefore above expression for theoretical velocity could be re-expressed as mentioned here.
We must note it here that this is the theoretical velocity and actual velocity will be less than this value.

We will see various types of hydraulic co-efficients, in the subject of fluid mechanics, in our next post.

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

We will see various types of hydraulic co-efficients, in the subject of fluid mechanics, in our next post.

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**Reference: **

Fluid
Mechanics, By R. K. Bansal

Image
Courtesy: Google