We were
discussing the basic difference
between orifice and mouthpiece, classification
of orifices and mouthpieces, advantages
and disadvantages of orifices, hydraulic
coefficients and also experimental process to determine the hydraulic coefficients, in the subject of fluid mechanics, in our recent posts.

Now we
will go ahead to find out the flow through large orifices, in the subject of
fluid mechanics, with the help of this post.

First we
need to understand the basic concept and meaning of

*large orifice*.
If the
head of liquid is less than the five times the depth of orifice, orifice will
be termed as large orifice. Mathematically, we can write here the equation for
large orifice.

Head of liquid
< 5 x depth of the orifice

When we
talk about the small orifice, the velocity over the entire cross-section of the
jet will be constant and we can determine the flow or discharge through the
orifice by using the equation as mentioned here.

But in
case of large orifice, the velocity over the entire cross-section of the jet
will not be constant. Hence, we will not be able to determine the flow or
discharge through the orifice by using the above mentioned equation.

So how we
will find out the flow or discharge through a large orifice. Let us derive here
one expression for the flow or discharge through a large rectangular orifice.

###
**Flow or discharge through a large rectangular
orifice **

Let us
consider a tank filled with liquid and also fixed with a large rectangular
orifice. Let us think that rectangular orifice is fixed at one side of tank as
displayed here in following figure.

Let us
consider the following data from above figure.

H

_{1}= Height of liquid surface from the top edge of the rectangular orifice
H

_{2}= Height of liquid surface from the bottom edge of the rectangular orifice
Depth of
rectangular orifice = H

_{2}- H_{1}
b = Breadth
of the rectangular orifice

d = Depth
of rectangular orifice

d = H

_{2}- H_{1}
C

_{d}= Coefficient of discharge
Let us
consider one elementary horizontal strip of depth dh at a depth of h, below the
free surface of the liquid in the tank, in rectangular orifice as displayed in
above figure.

*Discharge through elementary horizontal strip*,

dQ = Coefficient
of discharge x Area of elementary horizontal strip x Velocity

In order
to secure the expression for the flow or discharge through the entire
rectangular orifice, we will integrate the above equation between the limits H

_{1}and H_{2}.
This is
the expression for the flow or discharge through the large rectangular orifice.

Now we
will go ahead to find out the method to determine the discharge through a fully submerged orifice, in the subject of fluid mechanics, in our next post.

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

###
**Reference:**

Fluid
mechanics, By R. K. Bansal

Image Courtesy:
Google