Here are the steps to solve this problem: 1. Given: Inlet diameter (d1) = 200 mm = 0.2 m Throat diameter (d2) = 100 mm = 0.1 m Specific gravity of oil (Sf) = 0.9 2. Calculate the areas: Inlet area (A1) = πr12 = π(0.1)2 = 0.0314 m2 Throat area (A2) = πr22 = π(0.05)2 = 0.00785 m2 3. Use the venturimeter discharge equation: Q = Cd * A1*

1. VENTURIMETER
●WORKING PRINCIPLE
●CONSTRUCTION
●PRINCIPLE
●NUMERICALS

5. ●It is a device used to measure the speed and flow rate or discharge
of fluid through a pipe.” Venturimeter is work on Bernoulli’s
equation.
●Its basic principle also depend on Bernoulli’s equation and
continuity equation. Velocity increases pressure decreases.

6. ●Simple meaning is “When cross sectional area of the flow is
reduces it creates pressure difference between the different areas of
flow. This difference in pressure is measured with the help of
manometer and helps in determining rate of fluid flow or other
discharge from the pipe line.”
●History:- The principle of venture meter is firstly developed by
G.B. Venturi in 1797 but this principle comes into consideration
with the help of C. Herschel in 1887.

8. VENTURIMETER

9. WORKING PRINCIPLE
●PRINCIPLE:
The principle of venturimeter is that when a fluid flows through
the venturimeter,
it accelerates in the convergent section and decelerates in the diverg
resulting in a drop in the static pressure followed by a pressure reco
in the flow direction.

10. USE OF VENTURIMETER
●A venturi meter is also called a venturi flow meter.
●It is used to calculate the velocity of fluids in running through a
pipeline.
● The fluid may be a liquid or a gas. ...
● The venturi meter calculates velocity by measuring the pressure
head at both points before and after the narrowed throat.

11. PRINCIPLE BASED ON
BERNOULLI’S PRINCIPLE
●Principle of Venturimeter
●The working of venturimeter is based on the principle
of Bernoulli’s equation.
●Bernoulli’s Statement: It states that in a steady, ideal
flow of an incompressible fluid, the total energy at
any point of the fluid is constant. The total energy
consists of pressure energy, kinetic energy and
potential energy or datum energy

12. Mathematically
●PRESSURE ENERGY+KINETIC ENERGY+POTIENTAL
ENERGY=CONSTANT
●Here all the energies are taken per unit weight of the
fluid.
●The Bernoulli’s equation for the fluid passing through
the section 1 and 2 are given by

13. ●Bernoulli’s equation for the fluid passing through the
section 1 and 2 are given by
●p/(rho)*g+v2
/2*g+z=contant
●p1/(rho)*g+v1
2
/2*g+z1=p2/(rho)*g+v2
2
/2*g+z2

14. CONSTRUCTION

15. ●A venturimeter is a device used for measuring the rate of flow of a
fluid flowing through a pipe.
●The main parts of a venturimeter are:

16. ●Main parts of Venturimeter:-
●1. Converging part
●2. Throat
●3. Diverging Part

17. CONVERGENT PART
●It is starting section of venturimeter which attached at inlet pipe.
●The cross sectional area of this cone starts to decrease and the
converging angle is 20 degree.
● Its length is 2.7(D-d). Here (D) is the diameter of inlet section and
(d) is the diameter of throat.
● Other end of converging is attached with throat.
●A short converging part: It is that portion of the venturi where the
fluid gets converges.

18. ●The function of the converging portion is to increase the velocity of
the fluid and temporarily lower its static pressure. The pressure
difference between inlet and throat is developed.

21. ●In this meter the fluid is accelerated by its passage through a
converging cone of angle 15-20deg
●The fluid is then retarded in a cone of smaller angle
● (5-7degree in which large proportion of kinetic energy is converted
back to pressure energy. .

22. THROAT
●Throat is middle portion of venturimeter and its cross sectional area
is too small.
● At this point pressure is decreases and velocity is increases.
● One end is connected with converging part and other end is
attached with diverging part. Diameter of throat is ¼ to ¾ of the
diameter of the inlet pipe, but mostly it is ½ of the diameter of the
pipe.

23. DIVERGENT PART
●Diverging part is last part of venturimeter and its cross sectional
area is increases continually.
●Angle of diverging part is 5 to 15 degree. Its cross sectional area
continuously increases.
● One end is connected to throat and other end is connected to outlet
pipe.
●The main reason behind the low diverging angle is to avoid the
formation of eddies because flow separation and eddies formation
will results in large amount of loss in energy

24. WORKING
●Venturimeter is work on Bernoulli’s equation and its simple
principle is when velocity increases pressure decreases.
●Cross sectional area of throat section is smaller than inlet section
due to this the velocity of flow at throat section is higher than
velocity at inlet section, this happen according to continuity
equation.
● The increases in velocity at the throat result in decreases in
pressure at this section , due to this pressure difference is developed
between inlet valve and throat of the venturimeter.

26. Expression for the rate of flow through
venturimeter:-
●Let d1, p1, v1 & a1, are the diameter at the inlet, pressure at the
inlet, velocity at the inlet and area at the cross section 1.
●And d2, p2, v2 and a2 are the corresponding values at section 2.
●p1/(rho)*g+v1
2/2*g+z1=p2/(rho)*g+v2
2/2*g+z2

27. ●As the pipe is horizontal, so z1 = z2
●p1/(rho)*g+v1
2/2*g=p2/(rho)*g+v2
2/2*g
●p1-p2/(rho)*g=v2
2-v1
2/2*g ...............................1
(p1 – p2)/ρg is the difference of pressure heads at section 1 and 2
and it is equal to h. So
h=(p1-p2)/(rho)*g ..................................................2

28. ●Substituting this value of h (2) in equation (1), we get
●h=v2
2-v1
2/2*g ...........................3
●Applying Continuity Equation:
●a1*v1=a2*v2
●v1=a2*v2/a1 ......................................4
●Substituting this value of v1 in equation (2) and solving, we get
●v2=a1/sqrt(a1
2-a2
2)*sqrt(2*g*h)

29. ●Since Q=a2*v2
●Q={(a1*a2)√(a1
2-a2
2)}*√(2*g*h)
●Q is the theoretical discharge under ideal conditions. Actual
discharge will be less than the theoretical discharge. The actual
discharge is given by the formula
●Qth=(a1*a2/√a1
2
-a2
2
)*(√2*g*h)
●Qact=Cd *[{a1*a2/)√(a1
2-a2
2)}*√(2*g*h)]
●Where cd is less than 1 =coefficent of discharge.

30. ●Value of ‘h’ is given by differential manometer
●Case I: Let differential Manometer contains liquid which is
heavier than liquid flowing through pipe
●Sh= Specific gravity of heavier liquid
●So=specific gravity of light liquid flowing through pipe
●x=difference of heavier liquid in column
●h=x[Sh/So-1]

31. ●Case II :If differential Manometer contains liquid lighter than liquid
flowing through pipe:
●h=x[1-Sl/So]
●Where
●Sl=Specific Gravity of lighter liquid
●So=Specific gravity of liquid flowing through pipe

32. APPLICATION: Carburettor
●The carburetor works on Bernoulli's principle: the faster air moves,
the lower its static pressure, and higher the dynamic pressure is. The
throttle (accelerator) linkage does not directly control the flow of
liquid fuel. ... Later engines used an early form of fuel injection
known as a pressure carburetor.
●Venturi in carburettor is to determine air flow in a car engine and to
ensure correct amount of fuel to feed to gas combustion engine
when needed during driving.

33. PLUMBING:
●Venturi meters are used in pipelines at wastewater collection
systems and treatment plants. They are used in wastewater pipes
because their overall design structure allows for solids to pass
through it instead of collecting in front of it.
● Less build up in the pipes allows for more accurate readings of the
pressure of the wastewater and thus its velocity

34. Advantages
●Less chance of getting stuck with sediment.
●The discharge coefficient is high.
●Its behaviour can be predicted perfectly.
●It can be installed vertically, horizontally, inclined.
●They are more precise and can be used for a wide range of flows.
●About 90% of the pressure drop can be recovered.

35. Dis advantages
●They are large in size and, therefore, where space is limited, they
can not be used.
●Initial costs, installation and expensive maintenance.
●Requires a long placement length. ...
●It can not be used in pipes of less than 7.5 cm in diameter.
●Maintenance is not easy

36. Problems:
●A horizontal Venturimeter with inlet and throat diameter
30cm,15cm respectively is used to measure the flow of water .the
readings of differential manometer connected to inlet and throat is
20cm of Mercury .Determine rate of flow. take Cd =0.98.
●Solution:
●d1=30cm a1=0.07065m2
●d2=15cm a2=0.0176m2
●x=20cm=0.2m

37. ●As differential manometer contains heavy liquid
●h=x[Sh/So-1]=0.2[13.6/1-1]
●Specific gravity of heavy liquid Sh=13.6,So=1
●h=0.2[12.6]=2.52m
●Rate of flow:
●Q=Cd*{[a1*a2/√a1
2-a2
2]*√2-g*h}
● =0.98{[0.07065*0.0176/√0.070652
-0.01762
]*√2*9.81*2.52
●=0.6055 m3/sec

38. ●An oil of specific gravity 0.8 is flowing through venturimeter
having inlet diameter 20cm and throat diameter 10cm.The oil -
mercury differential Manometer shows a reading of
0.25m.Calculater discharge of oil through a horizontal venturimeter.
Take Cd=0.98
●Data:
●d1=20cm=0.2m a1=0.0314m2
●d2=10cm=0.1m a2=0.00785m2
●X=0.25m
●Soil=0.8 Cd=0.98

39. ●Since x=0.25m
●h=x{1-Soill/Shg}
● =0.25{1-0.8/13.6}
● =4m
●Rate of discharge:
●Q=Cd[*a1*a2//√a1
2-a2
2]*√2*g*h
● = 0.98*[0.0314*0.0078/√0.03142-0.007852]*√2*g*h
●

40. MQP
●Q)State the purpose of a Venturimeter?
●A)Venturi meters are flow measurement instruments which use a
converging section of pipe to give an increase in the flow velocity
and a corresponding pressure drop from which the flow rate can be
deduced. They have been in common use for many years, especially
in the water supply industry.

41. ●Q)List down Assumptions of Bernoullis Theorem
●A)The following assumptions must be met for this Bernoulli
equation to apply:
●the flow must be steady, i.e. the flow parameters (velocity, density,
etc...) at any point cannot change with time,
●the flow must be incompressible – even though pressure varies, the
density must remain constant along a streamline;

42. ●Q) Write down the usage of Venturimeter in a pipe flow and list out
its parts
●A)Venturi Meter is a device in which pressure energy is converted
into kinetic energy and it is used for measuring the rate of flow of
liquid through pipes.
● It is invented by an American Engineer Clemans Herchel and
named by the Italian physicist Giovanni Venturi.
● It works on the basic principle of Bernoulli’s Equation.

43. ●A Venturi Meter is consisted of:
●Converging cone or Diameter (the area is decreasing).
●Throat Diameter (the area is constant).
●Diverging cone (the area is increasing).
●let’s consider a pipe in which there is a venturi meter is fixed. In the
pipe, fluid is flowing so first it enters into a converging cone then
Thorat and then Diverging Cone.

44. ●Converging Cone:
●When water flowing through this cone the area is decreasing,
therefore, the speed of flowing water increases and pressure
decreases.
●Throat Diameter:When water flowing through this cone the area
remains constant therefore the speed of flowing water and pressure
remains constant.
●Diverging Cone:When water flowing through this cone the area is
increasing, therefore, the speed of flowing water decreases and
pressure decreases.

46. Working Principle of Venturi Meter:
● Thee quantity of liquid v1 enter to the pipe, as per continuity
equation volume flow rate at the inlet (Q1), is equal to discharge at
the outlet (Q2), so if v1 amount of water enters to the inlet of the
venturi meter the same amount of water should be discharged at the
outlet, that means at unit second v1/t1= v2/t2.
●As the area of section 1 (according to the above diagram) is more
than the area of section 2, that means due to the decrease area the
pressure at throttling section is decreased and velocity will be
increased to maintain the flow (Q1=Q2).

47. ●In the throat position, the velocity of flow is maximum and
pressure is minimum.
●
●After throttling there again a diverging cone (diffuser) which
restores the pressure as nearly possible to the actual value.

48. ●By this, we can easily determine the volume flow rate with the help
of the U-Tube Manometer which is shown in the above diagram, by
finding the pressure difference between section 1 (converging
section) and section 2 which is throat.
●DERIVATION SIMILAR IN SLIDE 28,slide 29,slide 30,slide 31
slide 32,slide 33

49. Problems:
●A horizontal Venturimeter with inlet diameter 20cm and throat
10cm is used to measure the flow of specific gravity 0.8.The
discharge of oil through venturimeter is 60l/s..Find reading of oil
mercury differential manometer .Cd=0.981
●Data:
●d1=20cm a1=314cm2
●d2=10cm a2=78.5cm2
●Sf=0.8 Q=60litres/sec h=
●Cd=0.98

50. ●Rate of discharge
●Q=Cid*a1*a2*√√2*g*h/√a12-a22
●On subsituting:
●h=289.98cm
●Since h=x[Sh/Sf-1]
●X=18.12cm

51. ●A horizontal venturimeter with inlet diameter 20cm,throat diameter
10cm is used to measure the flow of water. The pressure at inlet is
17.658N/cm2 and vaccum pressure at throat is 30cm of
mercury.Find discharge of water through venturimeter.Take
Cd=0.98
●Data:d1=20cm a1=0.0314m2
● d2=10cm a2=0.00785m2
●P1=17.658N/cm2
=17.658*104
N/m2
●Pressure head P1/(ρ*g)=17.658*104/1000*9.81=18m of water
●P2=-30 cm of hg=-30*13.6=-4.08m of water

52. ●h=(P1/ρ*g)-(P2/ρ*g)
● =18-(-4.08)
● =22.08m
●Q=Cd*a1*a2*√√2*g*h/√a12
-a22
●On subsituting
●Q=0.15639m3/sec

53. To be solved in notes
●1)An oil of Specific gravity 0.9 is flowing through Venturimeter
having inlet diameter 200mmand throat diameter 100mm.The oil-
mercury differential manometer shows a reading of
200mm.Claculate discharge of oil through horizontal Venturimeter
.Take Cd=0.98
●2)In a lab experiment it had bee recorded that discharge of water in
a pipe connected with 100mm*60mm Venturimeter was 22.5 lires of
water /sec .U tube differential connected to Venturimeter with
Mercury as Manometeric liquid showed a level differennce of
300mm .Claculate Coefficent of discharge .

54. ●Thank u