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Venturimeter is used to measure the speed of flow of a fluid that is flowing through a pipe. It is a device made of 3 parts – a short converging part, a throat, and a diverging part. Venturimeter works on Bernaulli’s principle and has several applications.
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Key Terms: venturimeter uses, types of venturimeter, venturimeter installation, pressure, velocity, kinetic energy
What is a Venturimeter?
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A venturi meter is a device that is used to measure the speed flow of incompressible fluid through a pipe.
- The device converts pressure energy into kinetic energy and measures the rate of flow of liquid through pipes.
- It has a tube of broad diameter and a small constriction towards the middle.
- Venturi meter works on the principle of the Bernoulli equation such that the velocity of the fluid increases as the pressure decreases.
- The theory states that when the cross-sectional area of the flow decreases, a pressure difference is created between the different regions of the flow.
- This helps measure the difference under pressure which further helps to measure the discharge inflow.
Bernoulli’s Theorem Video Explanation
| Venturi meter – Related Topics | ||
|---|---|---|
| Different Properties of Fluids | Hydrostatic Pressure | Pascal’s Law |
| Hydraulic Machines | Viscosity | Unit of Viscosity |
Components of a Venturi Meter
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A Venturi meter is made up of the following components:
- Converging Part: The area of the cone decreases when water flows through it. Therefore, there is an increase in the speed of flowing water and a decrease in the pressure.
- Throat Diameter: The area remains constant in a throat diameter when water flows through it therefore the speed and pressure also remain constant.
- Diverging Part: The area increases when water flows through the cone and therefore the speed decreases and the pressure decreases.
Components of Venturi Meter
Working of a Venturi Meter
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The venturi meter works on the principle of Bernoulli’s equation which states that the pressure decreases as the velocity increases.
- The crosssection of the throat is less than that of the inlet pipe.
- As the crosssection from the inlet pipe to the throat of venturimeter decreases, the fluid velocity increases, and therefore the pressure decreases.
- Due to a decrease in the pressure, a pressure difference is created between the throat of the venturi meter and the inlet pipe.
- This is further measured by applying a differential manometer between the throat section and the inlet section. It can also be measured by using two gauges on the inlet section and throat.
- The pressure difference through the pipe is then calculated after obtaining the rate of flow.
Read More:
| Mechanical Properties of Fluids – Related Topics | ||
|---|---|---|
| Elastic Limit | Mechanical Properties of Fluids | Stokes’ Law |
| Pressure | Fluid Friction | Surface tension |
| Buoyant Force | Mechanical Properties of Solid | Poisson’s Ratio |
| Shearing Stress | Barometer | Reynolds Number |
| Surface Energy | Critical Velocity | Aristotle Fallacy |
Venturimeter Formula
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A Venturi Meter contains two tubes connected by a pipe at narrow ends. The venturi-meter is positioned horizontally and the liquid enters end 1 and passes through end 2. Let,
- P1 is the pressure in the inlet section
- P2 is the pressure in the throat section
- v1 is the velocity of the fluid passing through the inlet section
- v2 is the velocity of the fluid passing through the throat section
- ρ is the density of the liquid
- A1 and A2 be the area of the cross-section at the inlet section and throat section respectively.
Working of a Venturi Meter
By Equation of Continuity
A1v1 = A2v2.
By Bernoulli’s equation,
P1 + \({1 \over 2}\)v12 = P1 + \({1 \over 2}\)v22
So, P1 – P2 = \({1 \over 2}\)v22 – v12
P1 – P2 = \({1 \over 2}\)(\({A_1^2v_1^2 \over A2^2} - v_1^2\))
P1 – P2 = \({1 \over 2}\)v12(\({A_1^2- A_2^2 \over A2^2}\))
v1 = A2[\([{2(P_1 - P_2) \over (A1^2-A2^2)}]^{1/2}\)]
However, A1v1 = \(\triangle v\)
where \(\triangle v\) represents the volume that flows through a cross-section per second.
Therefore, ΔV = A1A2[\({2gh \over A_1^2 - A_2^2}\)]1/2
The venturi effect formula can be demonstrated as
\(p_1 - p_2 = \frac{\rho}{2} (v_2^2 - v_1^2)\)
p1 = pressure at position 1 before the narrowing of the pipe
p2 = pressure at position 2 after the narrowing of the pipe
\(\rho \) = density of the fluid traveling in pipe
v2 = velocity of the fluid at position 2
v1 = velocity of the fluid at position 1
The video below explains this:
Venturimeter Detailed Video Explanation:
Types of Venturi Meters
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There are normally three types of venturi meters:
- Horizontal Venturi Meter: In this venturimeter, the kinetic energy is the highest and the potential energy is the lowest
- Vertical Venturi Meter: In this, the potential energy is maximum and the kinetic energy is minimum
- Inclined Venturi Meter: It is a venturi meter that is inserted in an inclined pipeline in a vertical plane. It helps in measuring the flow rate through the pipe.
Read More: Stokes Theorem
Applications of a Venturi Meter
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A Venturi Meter has a number of applications in the practical world such as:
- It is used to determine the flow of chemicals in pipelines.
- Venturimeter can determine the flow rate of the fluid discharged through the pipe of the device.
- It is used a lot in the waste treatment process in which large diameter pipes are used.
- It is used in the industrial sector to determine the pressure and the quantity of gas and liquid that flows inside the pipe.
- Venturimeter is also used in the medical sector to measure the rate of flow of blood in arteries.
- Recovery of high pressure is carried out by venturi meters.
Also Read: Water Pressure Formula
Advantages and Disadvantages of a Venturi Meter
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The advantages and disadvantages of a venturimeter are as discussed below –
Advantages of a Venturi Meter
Some major advantages of a Venturi meter are given below:
- They have high accuracy over wide flow ranges.
- They are easy to operate.
- They consume less energy and power.
- Venturimeters have high reproducibility.
- The coefficient of discharge is high.
- They can be used for compressible and incompressible fluid.
- Venturi meters are widely for a high flow rate or discharge.
Disadvantages of a Venturi Meter
Some of the disadvantages of a venturi meter are:
- High installation cost
- Not usable for pipes with a small diameter like 76.2 mm
- They are non-linear
- Expensive and slightly bulky
Read More: Unit of Pressure
Things to Remember
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- Venturi effect shows a reduction in fluid pressure which is the output of fluid flows through a constricted section of a pipe.
- Venturi meter is used for calculation of the velocity of fluids running through a pipeline. This fluid can be a liquid or a gas.
- In principle, the homogeneous model can be used with horizontally and vertically oriented Venturis.
- Pressure loss in the venturi meter is 10% while in orifice meter, pressure loss is 50-60%.
Read More: Kinetic Theory
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Sample Questions
Ques: Figures (a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect? Why? (4 marks)
Ans: Figure (a) is incorrect. Take the case given in figure (b).
Where,
A1 Area of pipe1
A2 = Area of pipe 2
V1 = Speed of the fluid in pipe1
V2 = Speed of the fluid in pipe 2
From the law of continuity, we have:
A1V1=A2V2.
When the area of cross-section in the middle of the venturimeter is small, the speed of the flow of liquid through this part is more. According to Bernoulli's principle, if speed is more, then pressure is less.
Pressure is directly proportional to height. Hence, the level of water in pipe 2 is less.
Therefore, figure (a) is not possible.
Ques: Give the principle of Working of venturimeter. Obtain an expression for the volume of liquid flowing through the tube per second. (4 marks)
Ans: Venturi Meter works on the principle of Bernoulli’s equation.
Let, P1 is the pressure in the inlet section, P2 is the pressure in the throat section, v1 is the velocity of the fluid passing through the inlet section, v2 is the velocity of the fluid passing through the throat section, ρ is the density of the liquid and A1 and A2 be the area of the cross-section at inlet section and throat section respectively.
According to Bernoulli's equation, this increase in speed is accompanied by a decrease in the fluid pressure P2 at the narrow region of section 2. Therefore, the pressure difference between section 1 and 2 is noted by measuring the height difference between the surfaces of the manometer liquid.
(ΔP = P1 – P2 )
By Equation of Continuity
A1v1= av2
v2=(A1/a)v1 ...Eq (1)
By Bernoulli’s equation,
P1 + ρ\(\frac{v_1^2}{2}\) = P2 + ρ\(\frac{v_2^2}{2}\) = P2 + ρ\(\frac{1}{2}\)(\(\frac{A}{a}\)v1)2
As there is a pressure difference the level of the fluid in the U-tube changes.
ΔP = P1 – P2 = ρ\(\frac{v_1^2(A^2-a^2)}{a^2}\)
So, the volume of the liquid flowing out per second is
V = Av1 = A\(\sqrt{\frac{2({\triangle}P)a^2}{{\rho}(A^2-a^2)}}\)= aA\(\sqrt{\frac{2({\triangle}P)}{{\rho}(A^2-a^2)}}\)
Ques: The flow of blood in a large artery of an anesthetized dog is diverted through a Venturimeter. The wider part of the meter has a cross-sectional area equal to that of the artery, A = 8 mm2. The narrow part has an area, a = 4 mm2. The pressure drop in the artery is 24 Pa. What is the speed of the blood in the artery? (Given: density of blood = 1.06 × 103 kg m-3). (4 marks)
Ans: We know that P1 – P2 = 1/2ρ (v22 – v12)
Also, a1v1 = a2v2
v2 = a1 x v1/a2
P1 – P2 = 1/2ρv12 (v22/v12 – 1)
= 1/2ρv12 ((a1/v2)2 – 1)
or v12 = \(\frac{2(P_1-P_2)}{{\rho}[{(\frac{a_1}{a_2})}^2-1]}\)
= \(\frac{2 * 24}{1.06*10^3[{(\frac{8}{4})}^2-1]}\) = \(\frac{2 * 24}{3*1060}\)
= v1 = \(\sqrt{\frac{48}{3180}}\) = 0.123 m/s
Ques: How is the length of the convergent cone in a venturi meter calculated? (1 marks)
Ans: The length of the convergent cone of a venturi meter is found with formula D-d where D= Diameter of inlet section and d= diameter of the throat.
Ques: What is the included angle of a venturi meter’s divergent cone? (1 marks)
Ans: The included angle of a venturi meter’s divergent cone is 5 degrees to 15 degrees (preferably about 6 degrees).
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