Flow measurement &vibration

Introduction The measurement of fluid flow is important in applications ranging from

measurements of blood-flow rates in human artery to the measurement of liquid oxygen in a rocket.

The selection of the proper instrument for a particular application is governed by many variables, including cost.

Flow-rate-measurement devices frequently require accurate pressure and temperature measurements in order to calculate the output of the instrument.

The most widely used flow metering principle involves placing a fixed area flow restriction of some type in the pipe or duct carrying the fluid. This flow restriction causes a pressure drop that varies with the flow rate.

Thus, measurement of the pressure drop by means of a suitable differential-pressure pick up allows flow rate measurement.

Principles of Fluid Flow in Pipes

The Bernoulli equation defines the relationship between fluid velocity (v), fluid pressure (p), and height (h) above some fixed point for a fluid flowing through a pipe of varying cross-section, and is the starting point for understanding the principle of the differential pressure flowmeter.

Bernoulli’s equation states that:

Bernoulli’s equation can be used to measure flow rate.Consider the pipe section shown in figure below. Since the pipe is horizontal, h 1 = h 2, and the equation reduces to:

Principles of Fluid Flow in Pipes

The conservation of mass principle requires that:

Flow meters

Devices used to measure flow rate:

Venturi meter (based on pressure difference)

Orifice meter (based on pressure difference)

Rotameter (based on drag forces)

Pitot tube

Turbine flow meter

The smooth design of the Venturi tube means that it is less sensitive to erosion than the orifice plate, and thus more suitable for use with dirty gases or liquids.

The Venturi tube is also less sensitive to upstream disturbances, and therefore needs shorter lengths of straight pipework upstream of the meter than the equivalent orifice plate or nozzle.

Like the orifice plate and nozzle, the design, installation, and use of the Venturi tube is covered by a number of international standards.

The disadvantages of the Venturi tube flowmeter are its size and cost.

The Venturi Tube

venturi meter

When a venture meter 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.

Venturimeter

The venturi flow meter is an obstruction flow meter due to which pressure drop occurs

Pressure drop is given by :

Discharge is given by:

C discharge co-efficient

Application of Venturimeter

Plumbing

Venturi meters are used in pipelines at wastewater collection systems and treatment plants.

The Flow of Chemicals in Pipelines

The temperatures and pressures of chemicals in a pipeline do not affect the accuracy of a Venturi flow meter and because of this they are used in crude oil pipelines. 

Carburetors

The venturi in carburetors is used to measure airflow in a car engine and to ensure that a correct amount of fuel is fed to the gas combustion engine when needed during driving. The air and fuel mixture must be evenly distributed to the engine in order for it to work properly. The temperatures of air and fuel are constantly changing due to the shift in temperatures that occur in an engine during idling, acceleration, high speeds, and low speeds.

Orifice Plate

An orifice plate is a device used for measuring the volumetric flow rate. It uses the same principle as a Venturi nozzle, namely Bernoulli’s principle which states that there is a relationship between the pressure of the fluid and the velocity of the fluid. When the velocity increases, the pressure decreases and vice versa.

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Orifice Plate Flowmeter

The orifice plate is a differential pressure flow meter (Primary element).

Based on the work of Daniel Bernoulli the relationship between the velocity of fluid passing through the orifice is proportional to the square root of the pressure loss across it.

To measure the differential pressure when the fluid is flowing, connections are made from the upstream and downstream pressure tappings to a secondary device known as a DP (Differential Pressure) cell.

Orifice Plate Flowmeter

Volume flowrate is given as:

Orifice Plates

Advantages:

Low cost, especially on large sizes

No need for recalibration

Widely accepted

Disadvantages:

Poor turndown (4:1 typical)

Long installations (20D to 30D)

Accuracy dependant on geometry.

ROTO METERS

 

A rotameter is a variable area type flow meter. It consists of a vertical tapered tube with a float which is free to move within the tube. The fluid goes from the bottom to the top. When no fluid flows, the float rests at the bottom of the tube. The float is made of such a diameter that it completely blocks the inlet. When flow starts in the pipeline and fluid reaches the float, the buoyant effect of fluid makes the float lighter. The float passage remains closed until the pressure of the flowing material plus the buoyance effect exceeds the downward pressure due to the float weight. Thus, depending on flow, the float assumes a position. Thus the float gives the reading of flow rate.

Advantages and Disadvantages

Advantages:

•  Pressure drop is constant

• No special fuel or external energy is required to pump

• Very easy to construct and we can use a wide variety of materials to construct.

Disadvantages:

• Due to its use of gravity, a rotameter must always be vertically oriented and right way up, with the fluid flowing upward.

• Rotameters normally require the use of glass (or other transparent material), otherwise the user cannot see the float. This limits their use in many industries to benign fluids, such as water.

• Rotameters are not easily adapted for reading by machine; although magnetic floats that drive a follower outside the tube are available.

Pitot Tube

Principle: “Transformation of kinetic energy of a liquid into potential energy in the form of a static head”.

Figure shows a pitot tube installed in a pipeline where it acts like a probe. The tube consists of two concentric tubes, the inner tube with its open ends ‘faces’ the liquid.

Pitot tube principle

outer tube has a closed end and has four to eight holes in its wall. The pressure in the outer tube is the static pressure in the line. Total pressure is sum of static pressure and the pressure due to the impact of fluid.

If PH -Pressure at inlet (Stagnation pressure)

PL - Static pressure

- Density, then

Velocity v = from which flow rate is determined.

Pitot tube

Applying Bernoulli's equation we get:

Now from above equation we get,

We can calculate the velocity and multiplying it with the area will give the flow rate

Turbine flow meter

The turbine flow meter translates the mechanical action of the turbine rotating in the liquid flow around an axis into a user-readable rate of flow. The turbine tends to have all the flow traveling around it.

The turbine wheel is set in the path of a fluid stream. The flowing fluid impinges on the turbine blades, imparting a force to the blade surface and setting the rotor in motion. When a steady rotation speed has been reached, the speed is proportional to fluid velocity.

Turbine flow meters are used for the measurement of natural gas and liquid flow.

Turbine Flow Meters

vibration

•Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road.

•Any motion that repeats itself after an interval of time is called vibration

Main Reasons of vibration

•Unbalanced centrifugal force in system ( This is caused by because of non-uniform material distribution in rotating machine element.)

•Elastic nature of the system.

•External excitation applied on the system.

•Wind may cause vibration of certain systems such as Electricity lines, telephone lines, etc.

Harmful effects of vibration.

•Excessive stresses in machine parts

•Undesirable noise

•Looseness of parts

•Partial or complete failure of parts

Use of vibration phenomenon

•Musical Instruments

•Vibrating Conveyors

•Shakers

•Stress Relieving instruments

Elimination or Reduction of undesirable vibration

•By removing the causes of vibration •By vibration isolation •By using shock absorbers •By installing dynamic vibration absorbers

Some

Important

Definitions

• Periodic motion:

A motion which

repeatsitself after equal intervals of

time.

Time Period: Time taken to complete one cycle

T = ( )/ ( . ) 𝒕 𝑻𝒊𝒎𝒆 𝒕𝒂𝒌𝒆𝒏 𝑵 𝑵𝒐 𝒐𝒇 𝒄𝒚𝒄𝒍𝒆 Frequency: Number of cycle per unit time

𝒇= / 𝟏 𝑻 Amplitude: The maximum displacement of vibrating

body from its equilibrium position

Natural frequency: When no external force acts on the system after giving it an initial displacement, the body vibrates. These vibrations are called free vibration and their frequency as natural frequency. It is expressed as radian/sec. or Hz.

Fundamental mode of vibration: The fundamental mode of vibration of a system is the mode having the lowest natural frequency

Resonance: When the frequency of external excitation is equal to the natural frequency of a vibrating body, the amplitude of vibration becomes excessively large. This concept is known as resonance

Resonance can also cause

damage to the system.

Because of the effect of

resonance army do not

march on the bridge.

Elementary parts of vibratory system

A vibratory system basically consists of three elements, namely

1)Mass (inertia) = m

2)Spring (stiffness) = k

3)Damper = c

Energy stored in mass:

𝐾. .=12 2 𝐸 𝑚𝑥

Energy stored in spring:

P. .=12 2 𝐸 𝑘𝑥

Energy dissipated in the damper in the form of heat which oppose the motion of the system.

General equation o motion of vibratory system

It can be written as:

𝑚𝑥 + + = 𝑐𝑥 𝑘𝑥 𝑜

Where,

𝑐𝑥 = Damping force

𝑚𝑥 = inertia force and

𝑘𝑥 = spring force

( = displacement 𝑥

𝑥 = d /dt = velocity and 𝑥

𝑥 = d /dt = acceleration) 𝑥

Vibrometer• Let us consider equation

• Let us assume ω/ωn=r in the above eqn

• Characteristics of this equation is plotted as shown in fig.

From figure, it can be seenthat for large values of ω/ωn=r , the ratio Z/B

approaches unity for every value of damping.

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The phase angle plot shown below indicates the phaselag of the seismic mass with respect to vibrating baseof machine

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Vibrometer (Contd..)

consider equation

assume ω/ωn=r in the above eqn

Let us

Let us

When the value of r is very high (more than 3), the aboveequation can be written as

(as 2εr is very small term, so it is neglected for a widerange of damping factors)

• So the relative amplitude Z is shown equal to the amplitude

of vibrating body B on the screen.• Though Z and B are not in the same phase but B being in single harmonic, will result in the output signal as true reproduction of input quantity.

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• The instrument shown in figureVibrometerworks as a vibrometer

large value of r.for very (Contd..)

• Vibrometer (also known as lowfrequency transducer) is used to measure the high frequency ω of a vibrating body.Since the ratio r is very high, so•the natural frequency of theinstrument is low.

• Low natural frequency means heavy mass of the body of the instrument which makes its rare application in practice specially in systems which require much sophistication.

• The frequency range of a vibrometer depends upon several factors such as damping, its natural frequency, etc.

• It may have natural frequency 1 Hz to 5 Hz.10

Accelerometer• An accelerometer is used to measure the acceleration of a

vibrating body.• If the natural frequency ωn of the instrument is very high

compared to the frequency ω which is to be measured, the ratio ω/ωn is very small. i.e., ω/ωn=<< 1

• The range of frequency measurement is shown in figure. Since

the natural frequency of the instrument is high so it is very lightin construction.

From figure, it can be seenthat for large values of ω/ωn=r , the ratio Z/B

approaches unity for every value of damping.

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Accelerometer (Contd..)

• With the help of electronics integration devices, it displays velocity and displacement both.

• Because of its small size and usefulness for determining velocity and displacement besides acceleration, it is very widely used as a vibration measuring device and is termed as high frequency transducer.

• The voltage signals obtained from an accelerometer are usually very small which can be pre-amplified to see them bigger in size on oscilloscope.

• For getting velocity and displacement double integration device may be used and the results are obtained on screen.

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Again considering equation

assuming ω/ωn=<< 1

where f is a factor whichrange of accelerometer.

Where

remains constant for the useful

In this equation ω2B, the acceleration of the vibrating body. It isωn

2clearly seen that the acceleration is multiplied by a factor (1/To keep the value of factor f equal to 1 for very high range ofω/ωn, ratio, ε should be high in value.

).

The amplitude Z becomes proportional to the accelerationprovided the natural frequency remains constant.Thus Z is treated proportional to the amplitude of acceleration to be measured

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THANK YOU

Submitted By:HIMANSHU KUMAR (2012EME43)SHAILENDRA THAUR (2012EME46)SHAMBHOO VISHWAKARMA (2012EME47)JAYLENDRA PRASAD (2012EME48)