We were discussing the various basic
concepts such asÂ Eulerâ€™s Equation of motion, Bernoulliâ€™s equation from Eulerâ€™s equation and derivation of discharge through venturimeter, in the subject of fluid mechanics, in our recent posts.Â

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

Â

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.

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**
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
ofÂ Bernoulliâ€™s equationÂ andÂ 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.

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**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

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**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.

d

_{1}Â = Diameter at section 1 (Inlet section)
P

_{1}Â = Pressure at section 1 (Inlet section)
v

_{1}Â = Velocity of fluid at section 1 (Inlet section)
A

_{1}Â = Area of pipe at section 1 (Inlet section)
d

_{2}Â = Diameter at section 2
P

_{2}Â = Pressure at section 2
v

_{2}Â = Velocity of fluid at section 2
A

_{2}Â = Area at section 2
Let us recall the Bernoulliâ€™s equation
and applying at section 1 and section 2.

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**According to Bernoulliâ€™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.

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**Assumptions**

Assumptions made for deriving the expressionÂ of discharge through the orifice meterÂ 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 Bernoulliâ€™s equation at section 1 and section 2.

Let A

_{0}is the area of the orifice
Co-efficient of contraction, C

_{C}= A_{2}/A_{0}
Let us recall the continuity equation
and we will have following equation

Thus we will use the value
of C

_{C}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,Â in the subject of fluid mechanics, in our next post.

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

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**Reference:**

Fluid mechanics, By R. K. Bansal

Image Courtesy: Google

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