This article provides an overview of how to measure discharge using an orifice? in fluid mechanics, covering fundamental principles and practical applications.
An orifice is described as a small opening of any cross-section provided on the side or bottom of a tank through which a fluid can flow easily. Orifices are used to measure the rate of flow of a fluid.
The continuous stream of fluid that flows out of an orifice is called a jet of water. An orifice can have a rectangular, circular, or triangular shape.
This guide covers the classification and determination of the rate of flow through an orifice.
Flow Through an Orifice
Consider a tank with a rectangular orifice fitted at the surface as shown in Figure-2. Let the head of the liquid above the center of the orifice be ‘H’. The liquid that comes out of the orifice forms a jet of liquid that possesses an area of cross-section less than that of the orifice. The area of the cross-section of this liquid jet goes on decreasing and attains a minimum value in section 1-1.
At section 1-1, the area of cross-section (Ac) is minimum, the streamlines are straight and they are parallel to each other. The streamlines are hence perpendicular to the plane of the orifice. This section is called as vena-contracta. Usually, vena-contracta is located at a distance equal to the radius of the orifice.
If the velocity of liquid at vena-contracta can be expressed as “v”, then the theoretical velocity of flow at vena-contracta can be expressed as:
Classification of Orifice
Orifices are classified based on the following categories:
1. Based on Size
Orifice can be classified as small or large orifice based on the size and the head of fluid in the orifice.
1.1. Small Orifice
If the head of fluid is greater than 5 times the depth of the orifice, then it is categorized as small orifice. In the case of small orifice, the jet of fluid possesses a constant velocity throughout the cross-section. Hence, the discharge is calculated as:
Where, a= area of orifice, Cd is a hydraulic coefficient named as coefficient of discharge and g= acceleration because of gravity. The value of Cd varies from 0.61 to 0.65.
1.2. Large Orifice
If the head of fluid is less than 5 times the depth of the orifice, then it is categorized as a large orifice. Here, the velocity over the entire cross-section of the jet of fluid is not constant, hence discharge cannot be determined by Equation-2. Hence,
The total discharge of fluid for a large orifice can be expressed as:
Q = Cd.b. [ H23/2 – H13/2]
Equation-3
2. Based on Shape
Based on shape or cross-section of an orifice, they are classified as:
- Rectangular orifice
- Circular orifice
- Triangular orifice
- Square orifice
3. Based on Nature of Discharge Through Orifice
Based on the nature of discharge of the fluid, an orifice can be classified as:
3.1 Fully-Submerged Orifice
A full-submerged orifice is one whose outlet is fully submerged under liquid.
The actual discharge through fully-submerged orifice is:
Where,
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 water level
b = width of orifice
Cd = Coefficient of discharge
3.2. Partially Submerged Orifice
Partially submerged orifice is one whose outlet side is partially submerged in the fluid as shown in Figure-4 below.
The actual discharge through partially submerged orifice is:
Where,
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 water level
b = width of orifice
Cd = Coefficient of discharge
4. Based on Upstream Edge of Orifice
Based on the upstream edge of the orifice, it is classified as:
- Sharp-edged orifice
- Bell-mounted orifice