VENTURI METER

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BASIC TERMS

Flow Rate(v) •Velocity of fluid which passes through a given area per second (m/s).

Volumetric Flow Rate(Q)

•Volume of the fluid travelled through a cross sectional area per second (m3/s).

Conduit •Shape of path of the fluid.

Vena Contracta

•point in a fluid stream where the diameter of the stream is the least, and fluid velocity is at its maximum.

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Turbulent Flow Fluid undergoes irregular fluctuations,

discontinues.Laminar Flow No disturbances in the flow,

continues.

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DEFINITION & MAIN PARTS

Venturimeter device used for measuring the rate of flow of a fluid flowing through a pipe.

It consist of three parts,

•Converging part•Throat•Diverging part

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WORKING PRINCIPLE

Venturi meter works under the principle of Bernoulli's

equation and Continuity equation.

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•Bernaulli’s Equation PV = a constant•Continuity Equation ρ1A1V1 = ρ2A2V2

Where, P Pressure V Velocity ρ1 Density of converging fluid ρ2 Density of throat fluid A1 Pipe area A2 Throat area V1 Velocity of converging fluid V2 Velocity of throat

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TYPES OF VENTURIMETER

•Horizontal venturimeter

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•Inclined venturimeter • Vertical venturimeter

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SOME ASSUMPTIONS TAKEN

Incompressible fluids

Frictionless inner surfaces

Steady and irrotational flow

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EXPRESSION FOR RATE OF FLOW

•A(m1,ρ1,p1,v1)

•B(m2,ρ2,p2,v2)

Z1Z2

DatumAt pt:-A

P.E = g.z1

V.E = ½ v12

Pre.E = P1/ρ

At pt:-B

P.E = g.z2

V.E = ½ v22

Pre.E = P2/ρ

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g(Z1-Z2)+1/2(V12+V22)=(P2-P1)/ρ

Energy equation (horizontal arrangement)

If Z1=Z2½(v12-v22)= (P2-P1)/ρ ----- (1)

As per law at continuity

A1V1=A2V2 (since density is constant)

V1=(A2/A1)V2 & V2=(A1/A2)V1

Sub V1 value in (1)

½[(A2/A1)*V22-V22]=∆P/ρ

V22=(A12/A2

2-A12) * 2∆P/ρ

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Q2=A2.V2= A1.A2 * √2∆P/ρ

(√A22-A12)

Q α √2∆P

Q2=M.√(2∆Pg)/ωTheoretical--

Original-- Q2=CdE M√(2∆P)/ρ

M- velocity approach factor

Q-over all volumetric flow rate

Cd-coefficient of discharge

E- thermal expansion factor

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Q2=Cd . E . M . A2 √2g{hm[(wm/w )-1]-(Zx-Zy)}

Q2=Cd.E.M.A2√2g {hm(sg-1)-(Zx-Zy)}

Q2 in terms of specific weight

Q2 in terms of specific gravity

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VENTURI METER V/S FLOW

When a venturimeter is placed in a pipe carrying the fluid whose flow rate is to be measured, a pressure drop occurs between the entrance and throat of the venturimeter. This pressure drop is measured using a differential pressure sensor and when calibrated this pressure drop becomes a measure of flow rate.

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CONSTRUCTION

The entry of the venture is cylindrical in shape to match the size of the pipe through which fluid flows. This enables the venture to be fitted to the pipe.After the entry, there is a converging conical section with an included angle of 19’ to 23’.Following the converging section, there is a cylindrical section with minimum area called as the throat.After the throat, there is a diverging conical section with an included angle of 5’ to 15’.Openings are provided at the entry and throat of the venturi meter for attaching a differential pressure sensor.

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MANOMETER

The differential pressure sensor used here is Manometer.Manometer is a device to measure pressure. A common simple manometer consists of a U shaped tube of glass filled with some liquid.Manometers measure a pressure difference by balancing the weight of a fluid column between the two pressures of interest. Large pressure differences are measured with heavy fluids, such as mercury (high density).Small pressure differences, such as those experienced in experimental wind tunnels or venturi flowmeters are measured by lighter fluids such as water .

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OPERATION

The fluid whose flow rate is to be measured enters the entry section of the venturi meter with a pressure P1.

As the fluid flows into the converging section, its pressure keeps on reducing and attains a minimum value P2 when it enters the throat. That is, in the throat, the fluid pressure P2 will be minimum.

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The Manometer attached between the entry and throat section of the venturi meter records the pressure difference(P1-P2) which becomes an indication of the flow rate of the fluid through the pipe when calibrated.

The diverging section has been provided to enable the fluid to regain its pressure and hence its kinetic energy. Lesser the angle of the diverging section, greater is the recovery.

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• P1• High angle

converging

• p2• P1-p2

throat

• P ses• Less

angle

divergin

g

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SAMPLE PROBLEM

A horizontal venturimeter with 15 cm inlet . 7.5 cm throat is used for measurement of flow of water .The differential pressure between inlet and throat is 17.5 cm, when measured using U-TUBE manometer. Make the calculations for the water flow rate where Cd for venturi is 0.97. Specific gravity =13.6.

Q2= Cd . E . M . A2 √2g{ hm [(ρm/ρ )-1]}

M=A1/√A12-A22

A1=π*d2/4=π*152/4=176.71 , A2=π*d2/4=π*7.52/4=44.178

M= 1.03

Q2=0.97 * 1* 1.03* 44.178√2*9.8*17.5(13.6-1)

=0.02901 m3/sec

Sol:

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PRESSURE IN PIPELINE

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APPLICATIONS

1 •used where high pressure recovery is required.

2 •measuring flow rates of water, gases, suspended solids, slurries and dirty liquids.

3 •measure high flow rates in pipes having diameters in a few meters.

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ADVANTAGES

1 •Less chances of getting clogged with sediments.

2 •Coefficient of discharge is high.

3 •Its behaviour can be predicted perfectly.

4 •Can be installed vertically, horizontally or inclinded.

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DISADVANTAGES

1 •Highly expensive

2 •Occupies considerable space

3 •Cannot be altered for measuring pressure beyond a maximum velocity

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THANK YOU