## Sunday, 10 June 2018

We were discussing the various basic concepts such as Euler’s Equation of motion, Bernoulli’s equation from Euler’s equation and derivation of discharge through venturimeter, in the subject of fluid mechanics, in our recent posts.

We had already seen the application of Bernoulli’s equation in working principle of Venturimeter. Now we will go ahead to find out the other practical applications of Bernoulli’s equation, in the subject of fluid mechanics, with the help of this post.

Today we will see here the basic concept of Orifice meter and also the derivation of discharge through orifice meter with the help of this post.

### Orifice meter or Orifice plate

Orifice meter is basically defined as a device which is used for measuring the rate of flow of fluid flowing through a pipe. Orifice meter is also known as Orifice plate.

Orifice meter works on the principle of Bernoulli’s equation and continuity equation.

Orifice meter is less costly as compared to the venturimter. Venturimeter is also very reliable flow measuring device. There are some pressure losses in venturimeter and it is usually used in larger volume liquid and gas flows. Venturimeter is expensive due to complexity of its design. Therefore, in order to determine the rate of flow of fluid through small pipe lines, orifice meter is better to use as compared to venturimeter.

Orifice meter consists of one flat circular plate and this circular plate will have one circular sharp edge hole bored in it. The circular sharp edge hole is termed as orifice.

Diameter of orifice will be 0.5 times of diameter of pipe through which fluid is flowing, though it may vary from 0.4 to 0.8 times of diameter of pipe.

Orifice plate is installed in pipe between two flanges of pipe. Orifice will restrict the flow of fluid and will reduce the cross sectional area of flow passage. A differential pressure will be developed across the orifice plate. Due to creation of pressure difference, we will be able to determine the rate of fluid flow through the pipe.

### Types of Orifice meter

Orifices are usually of concentric types i.e. orifice will be concentric with the pipe line. But, there are few more designs available as mentioned here
1. Eccentric orifice plate
2. Sharp edge orifice plate
3. Segmental orifice plate
4. Conical orifice plate

### Derivation of rate of flow through Orifice meter

Let us consider one orifice meter fitted in a horizontal pipe as displayed here in following figure. Let us say that water is flowing through the horizontal pipe.

Let us consider two sections i.e. section 1 and section 2 as displayed here in following figure. A differential manometer will be connected as displayed in figure at section 1, which will be approximate 1.5 to 2 times the diameter of pipe upstream from the orifice, and at section 2, which will be approximate 0.5 times the diameter of the orifice on the downstream side from the orifice plate.
d1 = Diameter at section 1 (Inlet section)
P1 = Pressure at section 1 (Inlet section)
v1 = Velocity of fluid at section 1 (Inlet section)
A1 = Area of pipe at section 1 (Inlet section)
d2 = Diameter at section 2
P2 = Pressure at section 2
v2 = Velocity of fluid at section 2
A2 = Area at section 2

Let us recall the Bernoulli’s equation and applying at section 1 and section 2.

### According to Bernoulli’s theorem.....

In an incompressible, ideal fluid when the flow is steady and continuous, the sum of pressure energy, kinetic energy and potential energy will be constant along a stream line.

### Assumptions

Assumptions made for deriving the expression of discharge through the orifice meter is as mentioned here.
1. Fluid is ideal, i.e. inviscid and incompressible.
2. Fluid flow is steady and continuous
3. Fluid flow is irrotational
4. Frictionless inner surface

We will have following equation after applying Bernoulli’s equation at section 1 and section 2.
Let A0 is the area of the orifice
Co-efficient of contraction, CC = A2/A0
Let us recall the continuity equation and we will have following equation
Thus we will use the value of CC in above equation of discharge Q and we will have following result for rate of flow or discharge through orifice meter.
Co-efficient of discharge of the orifice meter will be quite small as compared to the co-efficient of discharge of the venturimeter.

We will now find out the Basic principle of Pitot-tube, 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