DISCHARGE THROUGH A LARGE RECTANGULAR ORIFICE

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.

H₁ = Height of liquid surface from the top edge of the rectangular orifice

H₂ = Height of liquid surface from the bottom edge of the rectangular orifice

Depth of rectangular orifice = H₂- H₁

b = Breadth of the rectangular orifice

d = Depth of rectangular orifice

d = H₂- H₁

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 H₁ and H₂.

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.

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