DISCHARGE THROUGH FULLY SUBMERGED 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 fully submerged orifices, in the subject of fluid mechanics, with the help of this post.

Fully submerged orifice is one which has its whole of the outlet side submerged under liquid so that it discharges a jet of liquid in to the liquid of the same kind.

Fully submerged orifice is also called as totally drowned orifice. Coefficient of contraction for fully submerged orifice will be equivalent to 1.

Let us consider the following figure displaying the fully submerged orifice. Let us consider two points i.e. 1 and 2. Point 1 will be in the reservoir on the upstream side of the orifice and point 2 will be at the vena-contracta as displayed here in following figure.

H₁ = Height of water above the top of the orifice on the upstream side

H₂ = Height of water above the bottom of the orifice

H = Difference in level of water

b = Width of the orifice

C_d = Coefficient of discharge

Height of water above the centre of orifice on upstream side

= H₁ + (H₂- H₁)/2

= (H₁+ H₂)/2

Height of water above the centre of orifice on downstream side

= (H₁+ H₂)/2 – H

Now we will apply the Bernoulli’s equation at 1 and 2.

Considering the term z₁ = z₂, we will have following equation as mentioned here

This is the expression for the flow or discharge through the fully submerged orifice.

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

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