How venturimeter is used for flow measuring? [with Pdf]

Hey friends, just now I have successfully performed flow measuring experiment on venturimeter setup in my college lab. Before performing this flow measurement practical I have done simple searches about the question “How venturimeter is used for flow measuring?” which I have mentioned below.

For the measurement of flow rate, the venturimeter is fitted between the pipe of which flow rate is to measure. The manometer attached before converging section and at the throat section shows the pressure difference between two section. Then by using Bernoulli’s equation and continuity equation we can easily calculate the flow rate through pipe.

What is the venturimeter ?

Venturimeter is the device which works on principle of Bernoulli’s equation to measure the flow rate of fluid. It generally consists of following four components.

  1. Converging section
  2. Throat section
  3. Diverging section
  4. U-tube manometer

Let’s know in detail what is the role of each component.

venturimeter working diagram
venturimeter

1) Converging section:-

Converging section means the reduction in cross section area in the direction of flow.
as the liquid pass through the converging section the pressure energy of liquid gets converted into kinetic energy.

Hence because of converging section the pressure of the liquid decreases and the velocity of liquid increases.

P1>P2 and V2>V1

2) Throat section:-

Throat section has the constant cross-sectional area equal to the exit area of converging section.
The pressure and velocity across the throat section remains constant.

3) Diverging section:-

The diverging section means gradual increase in cross sectional area in the direction of flow.
Hence as the liquid passes through the the diverging section the kinetic energy of liquid is again gets converted into the pressure energy.

It means pressure across the diverging section again increases and velocity decreases.

4) U-tube manometer:-

U-tube manometer is used in venturimeter to record the pressure difference between pipe cross section before converging section and throat cross section.

The one end of a U-tube manometer is connected at the section 1 before converging section and at section 2 (throat).

What is the Working principle of venturimeter?

  • The venturimeter is based on Bernoulli’s principle.
  • While passing through the venturimeter the fluid experience decrease in pressure energy in converging section and further it experience again increase in its pressure energy in divergent section.
  • This change in pressure can be measured using U-tube manometer and then by using Bernoulli’s and continuity equation we can easily obtain value of flow rate.

How venturimeter is used for flow measuring?

1) As shown in figure, liquid enters into the device at section-1 with initial velocity V1 and pressure P1.

2) While passing through the converging section some amount of pressure energy of fluid gets converted into kinetic energy.

3) Hence the velocity of liquid increase to the V2 and pressure decreases to P2.

4) In throat section there is no change in the velocity and pressure of liquid.

5) The U-tube manometer measures the pressure difference between two sections.

6) Further when liquid passes through the divergent section, the pressure of liquid gradually increases and velocity again reaches to its initial value.

7) Now as we have values of the inlet and throat area of Venturi meter and pressure difference we can easily calculate the flow rate using Bernoulli’s and continuity equation.

How to calculate flow through venturimeter?

The notations to be used in venturimeter experiment are,

A1 = Area at section 1
A2= Area at section 2
P1= Inlet pressure at section 1
P2= Pressure at throat section
V1= Inlet velocity
V2= Velocity at throat section
h = Pressure head between two sections

By applying Bernoulli’s theorem across the section 1 and 2

`\frac{P_{1}}{\rho g}+\frac{V_{1}^{2}}{2g}+Z_{1}= \frac{P_{2}}{\rho g}+\frac{V_{2}^{2}}{2g}+Z_{2}`

For the horizontally mounted venturimeter,

`Z_{1}=Z_{2}`

Now the equation will become,

`\frac{P_{1}}{\rho g}+\frac{V_{1}^{2}}{2g}= \frac{P_{2}}{\rho g}+\frac{V_{2}^{2}}{2g}`

`\frac{P_{1}-P_{2}}{\rho g}= \frac{V_{2}^{2}-V_{1}^{2}}{2g}`

`\frac{\Delta P}{\rho g}= \frac{V_{2}^{2}-V_{1}^{2}}{2g}`

`h= \frac{V_{2}^{2}-V_{1}^{2}}{2g}`

`2gh=V_{2}^{2}-V_{1}^{2}`

………..Equation 1

By continuity equation,

`A_{1}V_{1}=A_{2}V_{2}`

`V_{1}=\frac{A_{2}}{A_{1}}\times V_{2}`

Now by putting this value the equation 1 become,

`2gh=V_{2}^{2}- ( \frac{A_{2}}{A_{1}}\times V_{2} )^{2}`

`2gh=[ 1-(\frac{A_{2}}{A_{1}})^{2} ]\times V_{2}^{2}`

`2gh=\frac{A_{1}^{2}-A_{2}^{2}}{A_{1}^{2}}\times V_{2}^{2}`

`V_{2}=\frac{A_{1}}{\sqrt{A_{1}^{2}-A_{2}^{2}}}\times \sqrt{2gh}`

Now, Flow rate is given by

`Q=A_{2}V_{2}=\frac{A_{1}\times A_{2}}{\sqrt{A_{1}^{2}-A_{2}^{2}}}\times \sqrt{2gh}`

`Q=\frac{A_{1}\times A_{2}}{\sqrt{A_{1}^{2}-A_{2}^{2}}}\times \sqrt{2gh}`

This is the required equation for the flowrate through horizontally mounted venturimeter.

Where we can use venturimeter?

The venturimeter is generally used in following applications

1) In industrial pipes to measure flow rate of liquid and slurry.
2) it gives higher accuracy and hence it is generally used where higher accuracy is required.
3) it is used in applications where high pressure recovery is necessary.
4) it can also use for slurry and dirt water.
5) Also used for incompressible as well as compressible fluids.

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