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VENTURYMETER TUBE ApliCAtion of Bernoulli’s lAw

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VENTURYMETER TUBEApliCAtion of Bernoulli’s lAw

CP

H

IS

I

VenturImeter

Venturimeter is an instrument used to

measure fluid flow velocity in the

pipeline

This tool works based on ventury effect

Venturimeter

Venturimeter With

Manometer

Venturimeter Without

Manometer

Venturimeter With Manometer

Venturimeter the manometer is a joint application between venturimeter and pitottubes. Its function is to measure the rate of fluid.

The Formula of Venturimeter With Manometer

From Bernouli’s law equation :

Because the cylinder is horizontal

so, h1=h2 :

With Used hidrostatic pressure will get :

From kontinuitas equation it will be :

So, if the formula subtitued into the first equation,

it become :P1 + ρv1² + ρgh1 = P2 + ρv2² + ρgh2

1

2

1

2

P1 + ρv1² = P2 + ρv2²1

2

1

2

P1+ ρgh = P2 + ρ’gh

P1 = P2 + (ρ’- ρ)gh

A1. v1 = A2. v2 v2 = A1. v1

A2

P2+ (ρ’- ρ)gh + ρv1² = P2 + ρ1

2

1

2

A1. v1

A2[

(ρ’- ρ)gh = ρv1² 11

2

A1²

A2²[ ]v1² =

(ρ’- ρ)gh

1

A1²

A2²[ ]1

v1 = 2(ρ’- ρ)gh

ρ A1²

A2²[ ]1

]2

v1 = 2(ρ’- ρ)gh

ρ(A1² - A2²)

A2

(ρ’- ρ)gh = ρ ρv1²1

2

A1. v1

A2[ ]

21

2

Sample of QuestionPipes Venturi meter has a cross of each 8 × 10 ¯ ² m² and 5 × 10 ¯ ³ ² is used to measure the

speed of the water. If the height difference in the two mercury manometer is 0.2 m and g = 10

m / s ², find the speed of the water (ρ mercury = 13,600 kg / m³, water ρ = 1000 kg / m³).

Known : A1 = 8 10¯² m², A2 = 5 10¯³ m², h = 0,2 m, and g = 10 m/s².

v1 = 2(ρ’- ρ)gh

ρ(A1² - A2²) A2

= 5 10¯³ 2 (13.600 – 1000) (10) (0.2)

1000 [(8 10¯²)² - (5 10¯³)²]

v1 = 0,44 m/s

Venturimeter Without Manometer

Working Principle Venturimeter withoutmanometer is based on the Bernoulli principle,which reads: In the horizontal pipe (horizontal),fluid pressure is greatest at the smallest lag itsflow, and pressure is at least part of its flowspeed of most.

The Formula of Venturimeter Without Manometers

From Bernouli’s law equation :

Based on kontinuitas equation :

So,its obtained :

P1 + ρv1² + ρgh1 = P2 + ρv2² + ρgh21

2

1

2P1 + ρv1² = P2 + ρv2²

1

2

1

2P1 – P2 = ρ (v2² – v1²)1

2

A1. v1 = A2. v2 v2 = A1. v1

A2

P1 – P2 = ρ ( )² – v1²1

2A1. v1

A2[ ]

[ ]P1 – P2 = ρv1² ( )² – 11

2A1

A2

Difference P1 and P2 together with the hydrostatic

pressure of the liquid height h is:

So that :

P1 – P2 = ρgh

[ ]ρgh = ρv1² ( )² – 11

2A1

A2

v1² = 2gh

A1²

A2²1

v1 = 2gh

A1

A2

1[ ]2

Sample of Question

A venturi meter tool used to measure avelocity of water flow in pipes. Apparently the difference between high waterthe large cross-section of the large and smallpipe 10 cm. ifcomparative cross-sectional arealarge and small is 3:1.What is the speed of water flowthe large cross sectionand small?

Completion :v1 = 2gh

A1

A2

1[ ]2

v1 = 2.10.0,1

3 1

1[ ]2

v1 = 2

8

v1 = 12

m/s

Kontinuitas equation :

v2 = A1. v1

A2

v2 = 12

31

x

v2 = 32

m/s

Uses and Applications

Smokestacks

Calculating flow rate of fluid in a tube

Setting the flow of gasoline in the ignition system of a motor vehicle

In the field of medicine, has also designed venturi meter is used to measure the rate of blood flow in the arteries

Application of Venturimeter

1. Mining Installation

2. Lab Test Equipment

Mechanism Work of Smokestacks

First, the smoke of burning has high temperature heat. Due to hightemperatures,so the density of air is small. If the air wich have aSmall density, it’s easy float moves up. The reasonnot just this, from Bernoulli's Principle is also involved in thismatter.Second, Bernoulli’s principle says that if the air flow rate is highthen the pressure becomes low, otherwise if the air flow rate islow, the pressure is high. Remember that the top chimneys areoutdoors. There is a wind blowing at the top of the chimney, so thatthe air pressure surrounding smaller. In the closed room no windblowing, so the air pressure greater. So, the smoke dribbled outthrough the chimney. (air moving from a high-pressure air to a lowair pressure).

Conclusion

Venturimeter is an instrument used tomeasure fluid flow velocity in the pipeline

The formula of venturimeter without manometer are :

The formula of venturimeter with manometer are :

v1 = 2(ρ’- ρ)gh

ρ(A1² - A2²)

A2

v1 = 2gh

A1

A2

1[ ]2