Construction of an Optical Pyrometer

Figure 1.

The key components (see figure 1) of an optical pyrometer include:

1. Eyepiece: The observer uses the eyepiece to visually align the filament of the lamp with the target object.
2. Red Filter: A red filter is used to narrow the spectrum of light and enhance accuracy, allowing only specific wavelengths to pass through.
3. Lamp with Filament: A tungsten filament inside the lamp is used as a reference for brightness comparison. Its brightness changes with the current passing through it.
4. Absorption Filter: It ensures that the light entering the optical system matches the required wavelength range.
5. Rheostat (Variable Resistor): Adjusts the current passing through the filament to control its brightness.
6. Battery: Provides the power supply for the circuit.
7. Ammeter: Measures the current passing through the filament, which is used to calibrate the corresponding temperature.
8. Objective Lens: Focuses the radiation from the hot source onto the filament for better visibility.
9. Hot Source (Target): The object whose temperature is to be measured.

Working Principle of Operation

The optical pyrometer operates based on the disappearing filament principle. This principle states that when the brightness of the filament in the optical pyrometer matches the brightness of the target, the filament visually “disappears” against the background.

The operation relies on Planck’s radiation law, which describes how the intensity of radiation emitted by an object is related to its temperature and wavelength. Hotter objects emit more intense radiation, particularly at shorter wavelengths.

Working of an Optical Pyrometer

The working process involves the following steps:

Step 1: Focus the Target – The objective lens focuses the light emitted by the hot object onto the filament. This ensures a clear view through the eyepiece.

Step 2: Adjust the Filament Brightness – Using the rheostat, the observer adjusts the current through the filament to match the brightness of the target object.

Step 3: Visual Matching – The observer looks through the eyepiece to visually compare the filament’s brightness with the target.

• If the filament appears darker than the background, the current is too low.
• If the filament appears brighter, the current is too high.
• When the filament “disappears”, its brightness matches the target object’s brightness.

Step 4: Record the Current: The current passing through the filament at the point of brightness matching is measured using the ammeter.

Step 5: Determine the Temperature: The measured current corresponds to a specific temperature, which is calibrated and displayed on the pyrometer’s scale or calculated using known calibration equations.

(a) Low Current: The filament appears darker than the target because its temperature (and thus brightness) is lower than the target’s.

(b) Matched Brightness:  The filament “disappears” when its brightness matches the target, indicating that the current is exactly right for the corresponding temperature.

(c) High Current: The filament appears brighter than the target because its temperature (and brightness) exceeds the target’s.

Applications of Optical Pyrometers

Optical pyrometers are widely used in various industries due to their ability to measure high temperatures accurately and without contact. Some notable applications include:

1. Metal Industry: Measuring the temperature of molten metals, furnaces, and heated surfaces in steel and aluminum production.
2. Glass Industry: Monitoring the temperature of molten glass during manufacturing and processing.
3. Power Plants: Measuring boiler temperatures, turbine blades, and other high-temperature components.
4. Ceramics: Ensuring optimal temperatures during the firing and sintering processes in kilns.
5. Research and Development: Conducting experiments where high temperatures need precise measurement, such as combustion research or material testing.
6. Aerospace: Testing engines, turbines, and other components subjected to extreme heat.
7. Automotive: Analyzing engine performance and exhaust temperatures.

Advantages of Optical Pyrometers

1. Non-Contact Measurement: Allows temperature measurement of inaccessible or hazardous objects.
2. High-Temperature Range: Can measure temperatures beyond the capability of conventional thermometers (e.g., up to 3000°C).
3. Quick Response: Provides real-time temperature readings.
4. Durability: Can withstand harsh environments without compromising accuracy.
5. Wide Applicability: Suitable for industries requiring high-temperature measurements.

Limitations of Optical Pyrometers

1. Dependency on Visual Observation: Requires a skilled observer to match brightness, leading to potential errors.
2. Limited to Radiating Objects: Cannot measure the temperature of objects that do not emit sufficient radiation (e.g., low-temperature objects).
3. Influence of Ambient Light: Bright surroundings or poor contrast may affect accuracy.
4. Calibrated for Specific Wavelengths: The accuracy of measurements may depend on the type of material being measured due to its emissivity.
5. Manual Adjustment: Matching brightness can be time-consuming and subjective.

Calibration and Maintenance

Calibration

Regular calibration is necessary to maintain accuracy. This involves comparing the pyrometer readings with a known standard, such as a blackbody radiator.

Maintenance

Keep the optical components clean and free of dust or smudges. Inspect the filament and circuitry periodically to ensure proper functioning.

Types of Optical Pyrometers

Conclusion

The optical pyrometer remains an invaluable tool for measuring high temperatures in industrial and scientific applications. Its non-contact nature, wide temperature range, and precision make it indispensable in environments where conventional thermometers fail. Advances in optical and infrared technologies continue to enhance its accuracy, ease of use, and applicability in modern industries.

The post What is Optical Pyrometer? Working Principle, Diagram, Types, Construction & Applications appeared first on Electrical and Electronics Blog.

Figure 1: Block diagram of a function generator.

What is Function Generator?

A function generator is a signal source that produces various waveforms, such as sine, square, triangular, sawtooth, and pulse signals. The frequency, amplitude, and waveform type can often be controlled, making it versatile for different applications. These waveforms can be adjusted to specific requirements, depending on the use case.

Block Diagram of a Function Generator

The block diagram (like the one provided in your image) typically consists of the following components:

1. Frequency Control Network: This stage determines the frequency of the output waveform, which can be controlled manually or externally. External frequency control enables precise adjustment for synchronization.
2. Upper and Lower Constant Current Sources: These sources are responsible for generating a current that charges or discharges a capacitor to produce ramp-like signals for triangular and sawtooth waveforms.
3. Integrator: Converts the current into a voltage signal. By controlling the charging and discharging rates, different waveform slopes can be achieved.
4. Voltage Comparator and Multivibrator: This block compares the voltage from the integrator with a reference voltage, converting it into square waveforms or pulse signals.
5. Resistance-Diode Shaping Circuit: Used to shape the triangular or square waves into sine waves through nonlinear distortion.
6. Output Amplifiers: Amplify the generated waveforms and provide multiple outputs for driving different devices.

Types of Function Generators

Function generators can be classified into various types based on technology and usage:

1. Analog Function Generators: These use analog circuitry to generate signals and include components like operational amplifiers, resistors, capacitors, and diodes. Analog generators are cost-effective and reliable for basic applications.
2. Digital Function Generators: Digital function generators use digital signal processing (DSP) techniques to create waveforms. They offer greater precision, programmability, and flexibility in generating arbitrary waveforms.
3. Arbitrary Waveform Generators (AWGs): AWGs are advanced versions of digital function generators. They allow users to generate custom waveforms stored as data points in memory, making them highly versatile for specialized applications.
4. RF Function Generators: These are designed to operate at high frequencies, typically in the radio frequency (RF) range, for applications like communication testing.

Advantages of Function Generators

1. Versatility: Capable of producing multiple waveform types and frequencies.
2. Ease of Use: User-friendly interfaces with precise control over frequency, amplitude, and phase.
3. Cost-Effective: Basic analog models are affordable for educational and general-purpose use.
4. Integration: Many modern function generators include features like frequency counters and arbitrary waveform generation.
5. Wide Range of Applications: Suitable for R&D, production testing, educational labs, and more.

Disadvantages of Function Generators

1. Accuracy Limitations: Analog function generators have limited accuracy compared to digital models.
2. Complexity in Arbitrary Waveform Generation: Designing custom waveforms on arbitrary waveform generators may require specialized knowledge.
3. Frequency Range Limitations: Certain function generators may not cover very high or very low frequencies.
4. Distortion: At extreme ranges, waveforms may become distorted, impacting accuracy.

Applications of Function Generators

Function generators are essential tools in many fields. Some key applications include:

1. Testing and Debugging: Used to test circuits by simulating input signals. Debugging faults in communication, audio, and control systems.
2. Signal Simulation: Mimics real-world signals in systems like sensors and transducers.
3. Education and Training: Found in physics and electronics labs to demonstrate waveform characteristics.
4. Calibration: Serves as a reference signal source for calibration of other equipment.
5. Research and Development: Generates complex waveforms for experimental analysis and prototyping.
6. Communications: Produces modulated signals for testing communication systems.

Working of a Function Generator

1. Signal Generation: The frequency control network sets the base frequency. Current sources generate charging and discharging cycles for capacitors, which are processed to produce triangular, sine, and square waves.
2. Shaping Circuits: The resistance-diode shaping circuit converts triangular signals to approximate sine waves by manipulating voltage curves.
3. Output Delivery: Amplified waveforms are sent to the output terminals for use in external circuits.

Difference between Analog and Digital Function Generators

Conclusion

Function generators play a critical role in modern electronics, providing the flexibility to create, modify, and analyze signals in various domains. Their versatility, coupled with continuous advancements in technology, ensures their relevance in scientific research, industrial applications, and education. Understanding their design and operation allows engineers and students to harness their full potential effectively.

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Construction of a pH Meter

A pH meter typically consists of the following components:

1. pH-Sensitive Electrode: The main sensor of the pH meter, usually made of glass, which responds to hydrogen ion activity. It has a pH-sensitive glass membrane at its tip that interacts with the solution being tested.
2. Reference Electrode: Contains a stable electrolyte solution (commonly potassium chloride) and serves as a reference point for the pH measurement. Includes a porous plug for ionic exchange with the test solution.
3. Silver Chloride Coated Silver Wires: Present inside both the pH-sensitive and reference electrodes for electrical connectivity.
4. Temperature Sensor: Measures the temperature of the solution since pH measurements are temperature-dependent.
5. Signal Conditioning and Output: Converts the small voltage generated by the electrodes into a readable pH value. The output is displayed on a digital or analog screen.
6. Electrolyte Solution: Maintains the ionic balance inside the electrodes to facilitate accurate readings.

Working Principle of a pH Meter

The working of a pH meter is based on the Nernst equation, which relates the electric potential generated by the pH-sensitive electrode to the hydrogen ion concentration in the solution.

1. Electrode Interaction: The pH-sensitive electrode interacts with hydrogen ions in the test solution. The reference electrode provides a stable voltage as a comparison point.
2. Voltage Generation: The difference in hydrogen ion concentration between the inner solution of the electrode and the external solution generates a small voltage.
3. Temperature Compensation: The temperature sensor adjusts the pH reading to account for the effect of temperature on the ion activity.
4. Signal Processing: The generated voltage is processed by the signal conditioning unit, which converts it into a pH value displayed on the meter.

Types of pH Meters

Advantages of pH Meters

1. High Precision: Offers accurate measurements with minimal errors.
2. User-Friendly: Easy to operate with digital displays and automatic calibration features.
3. Versatility: Applicable across various fields, including environmental science, biology, and industry.
4. Portability: Portable models allow for on-site testing.
5. Wide Range of Measurements: Suitable for acidic, neutral, and basic solutions.

Disadvantages of pH Meters

1. Calibration Requirement: Requires frequent calibration for accurate results.
2. Fragility: The glass electrode is delicate and prone to breakage.
3. Dependency on Temperature: Measurements can be affected by temperature changes if not compensated.
4. Maintenance: Electrodes need to be cleaned and stored properly to prevent contamination or damage.
5. Cost: High-quality pH meters can be expensive.

Applications of pH Meters

1. Environmental Monitoring: Testing the pH of water bodies to monitor pollution levels and aquatic health.
2. Agriculture: Soil pH testing to optimize crop growth and fertilizer application.
3. Food and Beverage Industry: Ensuring product quality by monitoring the pH of ingredients and final products.
4. Pharmaceuticals: Measuring the pH of solutions in drug formulations and quality control.
5. Chemical Industry: Monitoring reactions and ensuring the safety of chemical processes.
6. Wastewater Treatment: Controlling pH during the treatment process to comply with environmental regulations.
7. Biotechnology and Research: Maintaining appropriate pH levels in biological experiments and cell culture media.
8. Aquariums and Aquaculture: Ensuring suitable pH levels for aquatic organisms.

Conclusion

A pH meter is an indispensable tool in scientific and industrial applications for accurately determining the acidity or alkalinity of solutions. Despite its limitations, advancements in technology have made pH meters more robust, user-friendly, and versatile. Proper maintenance and calibration ensure their reliable performance across a wide range of applications.

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Construction of Energy Meter

Current Coil (1): A coil connected in series with the load, which produces a magnetic field proportional to the load current.

Voltage Coil (2): A coil connected in parallel with the supply, generating a magnetic field proportional to the supply voltage.

Worm Gear (3): This gear mechanism translates the rotational movement of the aluminum disc into the motion required for the registering mechanism.

Registering Mechanism (4): The counter or dial records the total energy consumed over time, in kilowatt-hours (kWh).

Permanent Magnet (5): Used to control the speed of the aluminum disc and provide damping to ensure smooth operation.

Aluminum Disc (6): Rotates due to the interaction of the magnetic fields produced by the current and voltage coils.

Supply Terminals (7): Points where the energy meter is connected to the electrical supply.

Load Terminals (8): Output terminals where the load is connected.

Working of Energy Meter

The induction-type energy meter works on the electromagnetic induction principle. Here’s the step-by-step working process:

1. Magnetic Field Generation: The current coil produces a magnetic field proportional to the current flowing through the load. The voltage coil generates another magnetic field proportional to the supply voltage.
2. Interaction of Magnetic Fields: The interaction of these magnetic fields produces eddy currents in the aluminum disc. These eddy currents interact with the magnetic fields, generating a torque that causes the aluminum disc to rotate.
3. Disc Rotation: The speed of the disc is proportional to the power consumed by the load (product of voltage and current). The permanent magnet provides damping by opposing the rotation, ensuring stable and accurate operation.
4. Energy Recording: The rotational movement is transmitted through the worm gear to the registering mechanism, which records the total energy consumed over time.

Advantages of Energy Meters

1. Accurate measurement of energy consumption.
2. Helps manage and reduce energy usage.
3. Essential for fair billing and load management.
4. Smart meters enable real-time monitoring and remote operation.

Applications of Energy Meter

1. Residential Applications:
   • To monitor electricity consumption in homes.
   • Used by utility companies for billing purposes.
2. Commercial Applications:
   • Energy monitoring in businesses, offices, and shopping complexes.
   • Helps in reducing energy costs by identifying high consumption areas.
3. Industrial Applications:
   • To measure and control energy usage in factories and large facilities.
   • Used in high-load systems like HVAC, motors, and production machinery.
4. Renewable Energy Systems:
   • In solar and wind power systems, energy meters are used to monitor energy generated, consumed, and exported to the grid (net metering).
5. Prepaid Systems:
   • Widely used in rental housing, hostels, and public utilities to manage energy consumption and payments.
6. Demand Management:
   • Smart meters assist in managing peak load demand and implementing demand response strategies.

Types of Energy Meters

Energy meters can be broadly categorized based on their working principle and application:

1. Based on Operation Principle:

1. Electromechanical (Induction-Type) Energy Meters:
   • Operate on the principle of electromagnetic induction.
   • Common in residential applications for measuring energy consumption.
   • Features rotating aluminum discs and mechanical counters.
2. Electronic (Digital) Energy Meters:
   • Use microcontrollers or microprocessors to measure energy.
   • Display readings digitally, often with additional features like real-time monitoring and remote reading.
   • High accuracy and low maintenance.
3. Smart Energy Meters:
   • Advanced digital meters with communication capabilities (e.g., IoT or GSM-based).
   • Allow remote monitoring, real-time data analysis, and demand-side management.
   • Enable two-way communication between the consumer and the utility provider.
4. Static Energy Meters:
   • Measure energy based on static devices like Hall-effect sensors.
   • Highly accurate and often used in commercial or industrial environments.

2. Based on Type of Current:

1. Single-Phase Energy Meter:
   • Used in homes or small businesses with single-phase supply (230V).
2. Three-Phase Energy Meter:
   • Used in industrial or large-scale commercial applications with three-phase supply (400V or higher).

3. Based on Usage:

1. Prepaid Energy Meter:
   • Consumers pay for electricity in advance, and the meter disconnects the load when the credit is exhausted.
   • Useful for controlling energy consumption.
2. Net Energy Meter:
   • Common in solar power systems.
   • Measures both the energy consumed from the grid and the energy exported to the grid.

Difference Between Energy Meter and Wattmeter

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Figure 1: Pitot Tube.

A Pitot tube is a device used to measure the velocity of fluid flow, commonly used in aerodynamics and fluid mechanics applications. It measures both the total (stagnation) pressure and static pressure of the fluid to calculate its dynamic pressure and subsequently the flow velocity.

Working Principle of Pitot Tube

The Pitot tube operates on the principle of Bernoulli’s equation, which relates pressure, velocity, and height in a steady flow of an incompressible fluid. When a fluid enters the Pitot tube, it comes to rest (stagnates) at the opening of the tube, converting the kinetic energy of the fluid into pressure energy. This enables the measurement of the fluid’s velocity by comparing the total pressure with the static pressure.

Construction of Pitot Tube

A typical Pitot tube, as shown in the figure 1, consists of the following parts:

Ellipsoidal nose: The front tip of the Pitot tube that faces the fluid flow.

Spacers: Used to maintain the position and alignment of the internal parts.

Static pressure holes: Small holes on the sides of the tube, away from the flow direction, to measure the static pressure of the fluid.

Supporting stem: The structure that holds the Pitot tube in position.

Alignment arm: Ensures proper orientation of the tube in the fluid flow.

Static and Total Pressure Connections: Tubes leading to a manometer or pressure measurement system.

Δh (Delta h): Represents the difference in pressure levels, which corresponds to the dynamic pressure.

Working of Pitot Tube

1. The Pitot tube is inserted into the fluid flow with its nose aligned to face the flow.
2. The fluid enters the open end, where its velocity reduces to zero (stagnates). The pressure at this point is the total pressure.
3. Static pressure is measured using the side holes, which are perpendicular to the flow and do not disturb it.
4. The total pressure and static pressure are recorded, and the difference between them gives the dynamic pressure.

Stagnation point

When the solid body is kept centrally and stationary, in the pipe line with fluid streaming down, the velocity of the fluid diminishes due to the presence of the body still it is reduced to zero in front of the body. This is what is known as stagnation point. The inner (stagnation) tube is open ended. It faces the incoming stream of fluid.

The fluid impinging this open end is brought to rest and its kinetic energy is converted into pressure head. This pressure head is called as “Velocity head”. Thus the pressure sensed by the stagnation tube (stagnation pressure) is greater than that in the free stream by velocity head.

Stagnation pressure consists of velocity head and the static pressure head of the free stem. The static tube is closed at the nose of the tube. It has ellipsoidal head at the nose of the tube. This is the facility is to avoid flow separations. Stream lines next to the nose are longer than in the undisturbed flow. This indicates increase in the velocity.

On the other hand right angled stem stagnates the flow. It tends to raise the static pressure in its vicinity. For an accurate result the pitot tube is moved across the entire diameter of the pipe to measure the velocity at different points so that average velocity is calculated.

Working Formula of Pitot Tube

The velocity of the fluid is calculated using the relationship:

Where:

\[ v = \sqrt{\frac{2 (\Delta P)}{\rho}} \]

• $v$: Fluid velocity (m/s)
• $\Delta$$P$: Dynamic pressure (Total pressure – Static pressure) in Pascals (Pa)
• $\rho$: Density of the fluid (kg/m³)

Advantages of Pitot Tube

1. Simple construction.
2. Less pressure loss.
3. Can be inserted in the pipe very easily.
4. Useful to check mean velocity of flow

Disadvantages of Pitot Tube

1. Accuracy is very less.
2. Not suitable for low velocity measurements (below 5 m/sec).
3. Sensitive to misalignment of the probe w.r.t free stream velocity.
4. Not suitable for measurement of fluctuating velocities.
5. Unsuitable for dirty, sticky fluids.
6. Use is limited to exploratory studies.
7. Not commonly used in industrial applications.

Applications of Pitot Tube

1. Useful in gas flow measurements.
2. Measurements of flow through large pipes and ducts.
3. Stream measurement where accuracy is not that important.

The post What is Pitot Tube? Working Principle, Diagram, Construction, Advantages & Applications appeared first on Electrical and Electronics Blog.

Figure 1: Turbine Flow Meter.

Working Principle of Turbine Flow Meter

The turbine flow meter is based on Faraday’s Law of Electromagnetic Induction. As the liquid flows through the pipe, it rotates the rotor. The rotor’s blades are equipped with permanent magnets, which create a magnetic field.

When fluid flows through the pipe, the rotor starts to rotate due to the kinetic energy of the flowing liquid. The speed of rotation of the rotor is proportional to the flow rate of the liquid.

As the rotor rotates, the magnetic poles (N and S) of the magnets pass near the coil. This induces voltage pulses in the coil.

The frequency of the voltage pulses corresponds to the rotational speed of the rotor. By counting these pulses, the flow rate of the liquid can be determined.

Construction of Turbine Flow Meter

Pipe (1): Through which the liquid or gas flows.

Rotor (Turbine) (2): Inside the pipe, a rotor or turbine with small permanent magnets is mounted on a shaft. The rotor blades are angled to make the turbine rotates as fluid flows through it.

Shaft (3): The rotor is connected to a shaft that holds it in place and allows free rotation.

Coil (4): A magnetic pickup coil is placed outside the pipe. It senses the magnetic field changes caused by the rotating rotor.

Working of Turbine Flow Meter

At the centre of pipe line a shaft is supported in the bearing. Turbine blades NS, NS, NS pairs are fitted on the shaft. Rate of rotation of rotor is proportional to the rate of flow of liquid through the pipe. At the surface of the pipe a coil having no. of turns is fitted firmly. Now rotor blades rotate as fluid flow is impinged on them. Rotor blades are alternately N-pole, S-pole and hence a magnetic field is around the poles.

When the rotor rotates the magnetic field produced by them also rotates. It is a rotating magnetic field. This flux is cut by the number of turns of the coil fitted on the surface of pipe. As per Faraday’s law therefore EMF i.e. voltage is produced in the coil. Value of this voltage depends on the rotational speed of rotor and rotation is due to the flow of liquid.

Voltage ∝ fluid flow rate

The scale is calibrated such that this voltage indicates the fluid flow rate.

Advantages of Turbine Flow Meter

1. Better accuracy.
2. Allows low pressure drop.
3. It provides excellent repeatability and rangeability.
4. Low maintenance.
5. Easy installation.
6. It gives good temperature and pressure ratings.
7. Accuracy range is from ± 0.25% to ± 0.50%.
8. Repeatability ranging is from ±0.25% to ± 0.02%.
9. Available in sizes from 6.25 mm to 60 mm.
10. Liquid flow rate from 0.1 to 50,000 gallons/minute.

Disadvantages of Turbine Flow Meter

1. Very costly.
2. Creates problems for non-lubricating fluids.

Applications of Turbine Flow Meter

1. For measurements of liquid, gas.
2. Measuring low flow rates.
3. In military operations.
4. Useful in blending system for petroleum industries.
5. Useful in airborne applications for energy fuel and cryogenic (liquid, Oxygen and Nitrogen) flow measurement.

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Figure 1: Venturimeter.

A venturimeter is a device used to measure the flow rate of a fluid (liquid or gas) through a pipe. It is based on the principle of Bernoulli’s equation, which relates the pressure, velocity, and elevation of a fluid in steady flow.

Working Principle of Venturimeter

The venturimeter operates on the principle of the Venturi effect, which states that when a fluid flows through a constricted section of a pipe, its velocity increases while the pressure decreases. By measuring the pressure difference between the wider section and the constricted throat, the flow rate can be determined.

Main Parts of Venturimeter

1. U-tube manometer
2. High pressure tap
3. Low pressure tap
4. Diameter at inlet section (D)
5. Diameter at throat section (d)
6. α₁ inclined angle (19 to 23°)
7. α₂ inclined angIe (5° to 15°)

Construction of Venturimeter

1. Inlet Section:
   • A large-diameter section where the fluid enters.
   • It is connected to a high-pressure tap for pressure measurement.
2. Converging Section:
   • A gradually tapering section reduces the pipe diameter.
   • This accelerates the fluid, increasing its velocity and lowering the pressure.
3. Throat Section:
   • The narrowest section where the fluid velocity is at its maximum, and the pressure is at its minimum.
   • A low-pressure tap is placed here.
4. Diverging Section:
   • A gradually expanding section that slows down the fluid, recovering some of the pressure.
   • Ensures the flow returns to normal conditions downstream.
5. Pressure Taps:
   • High-pressure and low-pressure taps connected to a U-tube manometer.
   • Measures the pressure difference (Δ$h)$ between the inlet and throat.

Working of Venturimeter

Fluid enters the venturimeter through the inlet, where the pressure is measured using the high-pressure tap. As the fluid passes through the converging section, its velocity increases, and the pressure decreases due to the reduced cross-sectional area. At the throat, the velocity is at its maximum, and the pressure is at its minimum. The low-pressure tap measures the pressure at this point. The U-tube manometer measures the pressure difference between the inlet and the throat. The height difference (Δ$h$) in the manometer corresponds to the pressure difference. The fluid slows down as it flows through the diverging section, recovering some pressure while avoiding flow separation.

Liquid flow route

Flow comes from pipe of diameter ‘D’ and introduces inside, then passed through throat of less diameter ‘d’ then comes in the diverging section of inclination of angle α₂.

Location of pressure taps from where the manometer tube is introduced – One tap at inlet section and second at middle of throat section. This arrangement provided to measure the pressure difference (P₁ – P₂) by manometer u-tube.

Derivation of Flow Rate for a Venturimeter

The derivation involves applying Bernoulli’s equation and the continuity equation.

From Bernoulli’s Equation

\[P_1 + \frac{1}{2} \rho v_1^2 = P_2 + \frac{1}{2} \rho v_2^2\]

Rearranging to find the pressure difference:

\[P_1 – P_2 = \frac{1}{2} \rho \left( v_2^2 – v_1^2 \right)\]

The continuity equation is:

\[A_1 v_1 = A_2 v_2\]

From this, the velocity at the inlet (\(v_1\)) is expressed as:

\[v_1 = \frac{A_2}{A_1} v_2\]

Substituting \(v_1 = \frac{A_2}{A_1} v_2\) into the Bernoulli’s equation for pressure difference

\[P_1 – P_2 = \frac{1}{2} \rho \left( v_2^2 – \left( \frac{A_2}{A_1} v_2 \right)^2 \right)\]

Also

\[P_1 – P_2 = \frac{1}{2} \rho v_2^2 \left( 1 – \left( \frac{A_2}{A_1} \right)^2 \right)\]

The pressure difference (\(\Delta P\)) is

\[\Delta P = P_1 – P_2 = \frac{1}{2} \rho v_2^2 \left( 1 – \left( \frac{A_2}{A_1} \right)^2 \right)\]

Rearranging for \(v_2\)

\[v_2 = \sqrt{\frac{2 \Delta P}{\rho \left( 1 – \left( \frac{A_2}{A_1} \right)^2 \right)}}\]

The volumetric flow rate (\(Q\)) is

\[Q = A_2 v_2\]

Substitute \(v_2\)

\[Q = A_2 \sqrt{\frac{2 \Delta P}{\rho \left( 1 – \left( \frac{A_2}{A_1} \right)^2 \right)}}\]

The final flow rate equation is

\[Q = A_2 \sqrt{\frac{2 \Delta P}{\rho \left( 1 – \left( \frac{A_2}{A_1} \right)^2 \right)}}\]

where,

A₁, A₂​: Cross-sectional areas of the inlet and throat.

ΔP = (P₁ – P₂) : Pressure difference.

$\rho$: Fluid density.

Advantages of Venturimeter

1. Accurate measurement of flow rate.
2. Low energy loss compared to orifice meters.
3. Suitable for large-diameter pipes.
4. Good characteristics.
5. Suitable for flow of suspended fluids.
6. More accurate.
7. Low permanent loss.
8. Suitable for high flow rate.
9. No tear or wear as surface is smooth.

Disadvantages of Venturimeter

1. Large size so occupies more space.
2. Higher cost.
3. Not easy for inspection.
4. It cannot be used for small pipe diameters.

Applications of Venturimeter

1. Used in water supply systems, oil pipelines, and chemical industries.
2. For measurements, liquids, slurries, dirty fluids etc.

Features of Venturimeter

1. The main venturi tube is of cast iron or steel.
2. Flow coefficients = 0.984.
3. Accuracy much more ± 0.25 to ± 3%.
4. Sizes 100 mm to 813 mm.

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Figure 1: Orifice Meter.

An orifice meter is a device used to measure the flow rate of a fluid (liquid or gas) through a pipeline. Orifice meter is a thin plate with a central narrow aperture which is introduced in a pipeline. Thus, when a fluid stream passes through the narrow constriction of the orifice, the velocity (i.e., kinetic energy) of the fluid at the orifice plate increases in comparison with its velocity at the entry of the pipe. Thus, the corresponding pressure energy decreases. The reduction in pressure can be measured by the manometer.

Working Principle of Orifice Meter

According to the Bernoulli’s theorem, the increase in the velocity head with the decrease in pressure head can be correlated between the two points i.e., where the manometer is arranged in a pipeline. The velocity of the fluid at the point (before entering the orifice) can be neglected due to the smaller diameter of the orifice than pipe diameter. In such a case, the velocity of the fluid is directly read from the manometer. The velocity of the fluid at the orifice can be calculated from the following formula.

\[{{u}_{0}}=\sqrt{2{{g}_{c}}\Delta H}……(1)\]

Where,

u₀ = Fluid velocity at the point of orifice

C₀ = Constant of orifice meter

ΔH = Difference in pressure head, m.

This is the simplest and widely used pressure differential flow meter. It consists of a thin plate with a central narrow aperture, which is smaller in diameter than the pipeline in which it is introduced. To measure the pressure difference, the manometer is connected to the pipe. The orifice meter can be placed in the side or bottom of the pipeline.

Working of Orifice Meter

When the fluid is introduced in the pipe, it passes through the narrow constriction of the orifice meter. Two points A and B are chosen in the orifice meter to demonstrate the velocity of the fluid flowing through the orifice. The fluid leaves the constriction of the orifice meter at point B with a velocity higher than the velocity at point A. Thus, the corresponding pressure head at point B is less than the pressure head at point A. The pressure difference (ΔH) is read from the manometer which is arranged at the points A and B.

The Bernoulli’s equation is applied for the two points A and B in the orifice meter as follows,

\[\sqrt{u_{0}^{2}-u_{A}^{2}}={{C}_{0}}\sqrt{2{{g}_{c}}.\Delta H}\]

Where,

u₀ = Fluid velocity at the point of orifice meter, m/s

u_A = Fluid velocity at the point A, m/s

C₀ = Constant

ΔH = Pressure difference, m.

When the diameter of the orifice is very less compared to the diameter of the pipe, then velocity of the fluid at point A (u_A) is less compared to the velocity of the fluid at the constriction (u₀). Hence, u_A is ignored.

Thus, equation (1) becomes

\[\sqrt{u_{0}^{2}}={{C}_{0}}\sqrt{2{{g}_{c}}.\Delta H}\]

\[{{u}_{0}}={{C}_{0}}\sqrt{2{{g}_{c}}.\Delta H}……(2)\]

The value of ‘ΔH’ is read from the manometer and substituted in equation (2) to calculate the velocity of the fluid flowing through the orifice meter, provided that the cross section of the pipe is known. The volume of the fluid flowing per hour is calculated.

In the above stated experimental conditions, the Bernoulli’s theorem is applied as follows.

\[{{X}_{A}}+\frac{u_{A}^{2}}{2{{g}_{c}}}+\frac{{{P}_{A}}}{g{{\rho }_{A}}}-F+W={{X}_{B}}+\frac{u_{B}^{2}}{2{{g}_{c}}}+\frac{{{P}_{B}}}{g{{\rho }_{B}}}……(3)\]

In the above equation, the following assumptions can be made to the orifice meter.

1. X_A = X_B because the heights of the points A and B are same and hence the terms get cancelled.
2. F = 0, friction losses are not appreciable and considered negligible.
3. ρ_A = ρ_B = ρ, because the fluid flowing through the orifice is the same.
4. W = 0, no work is done by the liquid.

The equation (3) is reduced to,

\[\frac{u_{A}^{2}}{2{{g}_{c}}}+\frac{{{P}_{A}}}{g\rho }=\frac{u_{B}^{2}}{2{{g}_{c}}}+\frac{{{P}_{B}}}{g\rho }\]

\[\frac{u_{B}^{2}}{2{{g}_{c}}}-\frac{u_{A}^{2}}{2{{g}_{c}}}=\frac{{{P}_{A}}}{g\rho }-\frac{{{P}_{B}}}{g\rho }\]

\[\frac{1}{2{{g}_{c}}}(u_{B}^{2}-u_{A}^{2})=\frac{1}{u_{B}^{2}}({{P}_{A}}-{{P}_{B}})\]

\[u_{B}^{2}-u_{A}^{2}=\frac{2{{g}_{c}}}{g\rho }({{P}_{A}}-{{P}_{B}})\]

\[u_{B}^{2}-u_{A}^{2}=\frac{2{{g}_{c}}}{g\rho }.\Delta P\text{          }\left[ {{P}_{A}}-{{P}_{B}}=\Delta P\text{ } \right]\]

\[u_{B}^{2}-u_{A}^{2}=2{{g}_{c}}.\Delta H\text{           }\left[ \frac{\Delta P}{g\rho }=\Delta H\text{ } \right]\]

To nullify the differences between the velocities at orifice and at vena contracta (point B) a constant, C₀ is included.

\[\sqrt{u_{B}^{2}-u_{A}^{2}}={{C}_{0}}\sqrt{2{{g}_{c}}.\Delta H\text{ }}\]

The velocity through the orifice is u₀.

\[\sqrt{u_{0}^{2}-u_{A}^{2}}={{C}_{0}}\sqrt{2{{g}_{c}}.\Delta H\text{ }}\]

u_A, is negligible as the orifice diameter is 1/5 th of the pipe diameter or less.

\[{{u}_{0}}={{C}_{0}}\sqrt{2{{g}_{c}}.\Delta H\text{ }}\]

Advantages of Orifice Meter

1. It is a simple machine having low cost.
2. It requires less space.
3. Easy to install and interchange.
4. Adjustable orifices are available.

Disadvantages of Orifice Meter

1. Permanent loss of pressure.
2. When the ratio of orifice to pipe diameter is above 0.75, the results are not accurate.
3. If the fluid contains solid particles, it may obstruct the orifice.
4. The orifice meter is not recommended above 1000 psi at 800ºF.

Applications of Orifice Meter

The velocity of the fluid at the two points (A and B) can be calculated. The volume of the fluid flowing per hour can be determined provided that the velocity of the fluid at point A (u_A) and cross-section of the pipe are known. Orifice meters are used in industries like oil and gas, water treatment, power, and HVAC for measuring fluid and gas flow. Applications include natural gas pipelines, boiler feed water, steam, chemical processing, slurry flow, and air systems. They’re cost-effective, reliable, and versatile for diverse industrial and commercial flow measurement needs.

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Figure 1: Resistance Temperature Detector.

Working Principle of Resistance Temperature Detector (RTD)

Resistance Thermometers or Resistance Temperature Detector (RTD) works on the principle of positive temperature coefficient of resistance. i.e. as temperature increases, resistance offered by thermometer also increases.

Working & Construction of Resistance Temperature Detector (RTD)

Figure 2.

Various methods are employed for construction of resistance thermometers, depending on the application. Two common types are shown in Figs. 1 and 2.  The resistance of wire at tºC is given by

R_t = R₀ [ 1 + α₀t ]

Where,

R_t = Resistance at t°c

R₀ = Resistance at 0°C

α₀ = Resistance temperature coefficient

t = Change in temperature.

Modern platinum resistance thermometer.

It consists of pure, well-annealed platinum wire wound on thin strip of insulting mica or ceramic and placed in porcelain sheath. Free ends of platinum wire are attached to long lead low resistance copper wires (see Figure 1).

To measure the change in resistance bridge network is used. The resistance thermometer is connected to one of the arm of Wheatstone bridge circuit when resistance thermometer is subjected to temperature variation, the Wheatstone bridge gets unbalanced.

The galvanometer deflection can be directly calibrated to give temperature.  The unknown temperature t is given as,

\[t=\frac{{{R}_{t}-{R}_{0}}}{{{{R}_{100}-{R}_{0}}}}\times 100\]

Where,

R_t Resistance of wire at temperature t

R₀ = Resistance of wire at 0°C

R₁₀₀ = Resistance of wire at 100°C

Measurement of the change in resistance is usually made using a wheatstone bridge. The pyrometer coil is made one arm of the bridge as shown in Fig. 2. The resistance R₃ is adjusted until the meter G shown no current. Then it can be shown that,

\[\frac{{{R}_{1}}}{{{{R}_{2}}}}=\frac{{{R}_{3}}}{{{T}}}\]

For industrial use the resistance is unchanged and changes in the pyrometer resistance T cause an out of balance current to now through the meter G.

Advantages of Resistance Temperature Detector (RTD)

1. The response time compared to thermocouples is very fast. In the order of fractions of a second.
2. An RTD will not experience drift problems because it is not self-powered.
3. Within its range it is more accurate and has higher sensitivity than a thermocouple.
4. In an installation where long leads are required, the
5. RTD does not require special extension cable.
6. Unlike thermocouples, radioactive radiation (beta, gamma and neutrons) has minimal effect on RTDs since the parameter measured is resistance, not voltage.

Disadvantages of Resistance Temperature Detector (RTD)

1. Because the metal used for a RTD must be in its purest form, they are much more expensive than thermocouples.
2. In general, an RTD is not capable of measuring as wide a temperature range as a thermocouple.  A power supply failure can cause erroneous readings.
3. Small changes in resistance are being measured, thus all connections must be tight and free of corrosion, which will create errors.

Applications of Resistance Temperature Detector (RTD)

1. Among the many uses in a nuclear station, RTDs can be found in the reactor area temperature measurement and fuel channel coolant temperature.

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Figure 1: McLeod Gauge.

Working Principle of McLeod Gauge

It operates on the principle of compressing a known volume of low pressure gas to a higher pressure and measuring the resulting change in volume by a mercury manometer.

Construction and Working of McLeod Gauge

The construction of McLeod gauge is shown in Fig. 1. McLeod gauge comprises a system of glass tubing made of tough glass and mercury is used to trap the known volume of gas. The gauge is connected to the unknown gas whose pressure is to be measured.  The plunger moves up, lowers the mercury level to the cut off positions, entering the gas at unknown pressure through the tube.

This gas fills the tubes down to the cut off position of mercury level. Here the pressure is equal throughout the tubes.

Now the plunger is moved down to rise the mercury above the cut-off and traps the gas inside the bulb and measuring capillary.

Further pushing of plunger compresses the gas in the measuring capillary and mercury in the reference capillary reaches to zero reference line.

The pressure in the measuring capillary is higher than the measured pressure in the reference capillary. This difference in pressure causes the difference in mercury level in two tubes.

This difference in height represents the rise in gas pressure and unknown pressure is calculated.

Advantages of McLeod Gauge

1. It is very simple in use.
2. Measurement is independent of gas composition and it is related to physical dimensions of gauge.
3. It is a very accurate pressure measuring device.
4. It can be used as a standard to calibrate other low pressure gauges.

Disadvantages of McLeod Gauge

1. If the gas contains the vapour, it may not give correct result.
2. It is applicable to those systems where mercury is tolerable.
3. It does not give continuous output.

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