VenturimeterPresented by-

Bibhuti Bhushan Bhardwaj

(CIB-09-016)

Dept. of Civil Engg., Tezpur University, Napaam- 784028, Assam

Contents:

1. Definition of Venturimeter 2. Parts of a Venturimeter3. Principle involved in it4. Expression for rate of flow5. Disadvantages of Venturimeter

Picture of a VENTURIMETER

Definition and different parts of a venturimeter: Venturimeter device used for measuring the rate of flow of a fluid flowing through a pipe

It consists of three parts:

(i) Converging part (ii) Throat (iii) Diverging part

Principle involved

• Venturimeter is based on the principle of Burnoulli’s equation

(2) (1)

Some assumptions taken

• Burnoulli’s equation is

applicable only in case of an incompressible fluid.

• The fluid flowing is incompressible

• The inner surfaces are frictionless

• The flow is steady and irrotational

DIAGRAM FOR VENTURIMETER

(1) (2)

Expression for rate of flow through a venturimeter :

• Let’s consider a venturimeter fitted in a horizontal pipe through which a fluid is flowing

• Let,

• D1= diameter at section (1)

• P1= pressure at section (1)

• v1 = velocity at section (1)

• a1 = area at section (1)

• Similarly,

• D2, P2, v2, a2 are the respective diameter,

pressure, velocity, area at section (2)

• Applying Burnoulli’s theorem in section (1) and (2)

• ( p1/Þg )+( v12/2g )+z1 = ( p2/Þg )+( v2

2/2g )+z2

• As the pipe is horizontal, hence z1=z2

• ( p1/Þg )+( v12/2g ) = ( p2/Þg )+( v2

2/2g )

• ( p1 - p2 )/Þg = (v22/2g) – (v1

2/2g)

• But, ( p1 – p2 )/Þg is the difference of pressure

heads at sections (1) and (2) and it is equal to h.

• i.e.

• ( p1 – p2 )/Þg = h

• Substituting the value of ( p1 – p2 )/Þg in the

previous equation , we get ,

h = (v22/2g) – (v1

2/2g) -----------(1)

• Now, applying continuity equation in section 1 and 2,

• a1v1 = a2v2

Or, v1 = ( a2v2/a1 )

Substituting this value of v1 in equation (1)

h = (v22/2g) – (a2

2v22/a1

22g)

= (v22/2g)[1- (a2

2/a12)]

= (v22/2g)[(a2

2-a12)/a1

2]

• v22 = (2gha1

2)/(a12 - a2

2)

• v2 = [a1/{a12 – a2

2}1/2][2gh]1/2

Therefore, Q = a2v2

• Q = [a1a2][2gh]1/2/[a12 – a2

2]1/2---------(2)

Q is the ideal discharge & less than real discharge Qact

• Qact = Cd a1a2(2gh)1/2/(a12 – a2

2)

• Where, Cd = Co-efficient of venturimeter

and its value is less than 1.

•

Value of “ h ” given by differential manometer :CASE I :

Differential manometer contains a liquid which

is heavier than the liquid flowing through the

pipe. Let,

Sh = Specific gravity of the heavier liquid

S0 = Specific gravity of the liquid flowing

through pipe

x = Difference of the heavier liquid column

in U - tube

h = x [ (Sh/S0) – 1]

CASE II :

If the differential manometer contains a liquid

which is lighter than the liquid flowing through

pipe then

h = x [1 - (Sl/S0) ]

where,

Sl = Specific gravity of lighter liquid

in U – tube

S0 = Specific gravity of fluid flowing

through pipe

x = Difference of the lighter liquid

columns in U - tube

Inclined Venturimeter with Differential U-tube manometer :

CASE III :

Inclined venturimeter having differential

U-tube manometer. Differential

manometer contains heavier liquid

h = {(p1/Þg}+z1} – {(p2/Þg}+z2}

= x [ (Sh/S0) – 1]

• CASE IV:

• Inclined venturimeter in which

differential manometer contains a liquid

lighter than the liquid flowing through the

pipe

h = {(p1/Þg}+z1} – {(p2/Þg}+z2}

• = x [1 - (Sl/S0) ]

Disadvantages of Venturimeter:

• Highly expensive

•Occupies considerable space

•Cannot be altered for measuring

pressure beyond a maximum

velocity 

 

Thank you