## Measurement of Various Quantities

These study notes on measurement of various quantities include the following important topics:

- Flow Measurement
- Pressure Measurement

## Flow Measurement

Flow measurement is a critical aspect of measurement of various quantities, where the accurate quantification of fluid movement is necessary for monitoring and controlling operations. Various flow measurement techniques are employed based on the specific requirements of the application.

- Velocity refers to both the direction and speed of an object's motion. In the context of fluids, velocity describes the rate at which fluid particles move within a pipe or conduit. The velocity of various particles can change across the flow.
- Laminar flow occurs when the average velocity of liquid is relatively low, resulting in fluid particles moving smoothly in well-defined layers. The velocity of the particles have a parabolic shape with different layers that slide past each other.
- In contrast, turbulent flow arises when velocity flow is high, causing the fluid particles to move erratically and no longer smoothly in distinct layers. This leads to turbulence within the fluid flow, characterized by swirling and mixing.
- Viscosity refers to the property of gasses or liquids that measures its resistance towards motion or flow. Viscous liquids, like syrup, have significantly higher viscosity compared to water. Similarly, viscosity of water is higher than air, which means it flows more easily.
- The Reynolds number is a dimensionless quantity used in fluid mechanics to predict the flow regime of a fluid (liquid or gas) around an object or through a conduit. It is derived through the relationship combining viscosity and density with flow velocity and the cross-sectional dimensions of the flow. It determines whether the flow is laminar or turbulent

** R= VDρ/μ**

where

V = average fluid velocity

D = diameter of the pipe

r = density of the liquid

μ = absolute viscosity

### Flow Formulas

The continuity equation expresses the principle of conservation of mass in fluid dynamics. It states that if the overall flow rate in a system remains constant over time, then the flow rate in any specific part of the system will also remain constant. Mathematically, the continuity equation can be expressed as:

** Q = VA **

where Q = flow rate

V = average velocity

A = cross-sectional area of the pipe

If liquids are flowing in a tube with different cross section areas, i.e., A1 and A2, the continuity equation gives

** Q = V1A1 = V2A2**

This equation shows that when the cross-sectional area of a pipe or channel decreases, the fluid velocity increases to maintain a constant flow rate. Conversely, if the cross-sectional area increases, the velocity decreases accordingly. The continuity equation is a fundamental principle in fluid mechanics and is widely used in the analysis and design of fluid systems.

**Flow Measurement Instruments**

Flow measurement instruments can be categorized into different groups based on the type of flow being measured: flow rate, total flow, mass flow, open channel flow, and electromagnetic flow measurement. Here are some commonly used instruments in each category:

### Flow Rate Measurement

- Orifice Plate: A simple metal diaphragm with a constricting hole, clamped between pipe flanges.
- Venturi Tube: Uses the differential pressure principle, with the advantage of handling large amounts of suspended solids and creating less turbulence.
- Flow Nozzle: Offers a good compromise between cost and accuracy for clean liquids, commonly used for steam flow measurement.
- Dall Tube: Has the lowest insertion loss but not suitable for use with slurries.

The orifice is the simplest, cheapest, and easiest to replace flow measurement instrument, but it is less accurate, more prone to damage and erosion, and has the highest pressure loss. The Venturi tube, although more expensive and difficult to replace, offers the highest accuracy, better tolerance to damage and erosion, and the lowest pressure losses. The flow nozzle provides a compromise between the orifice and Venturi tube. The Dall tube has the advantage of the lowest insertion loss but is not suitable for slurries.

- Elbow Meter: Utilizes an elbow as a differential flow meter, good for handling particulates in solution.
- Variable-Area Meters: Variable-Area Meters like a Rotameter consists of a vertical tapered tube with a T-shaped weight, providing a direct visual indicator for flow rate measurements.

**Total Flow Measurement**

Total Flow Measurement refers to the measurement of the total quantity or volume of fluid that has passed through a system or process. It is important in various industries and applications to accurately determine the cumulative flow of fluids over a given period.

- Positive Displacement Meters: Use containers of known size to measure the total flow volume, such as piston flow meters and nutating disc flow meters.
- Totalizers: are electronic devices that integrate flow rate measurements over time to calculate the total flow. These devices can receive inputs from flow sensors and provide a cumulative total flow value, often displayed on a digital screen.

**Mass Flow Measurement**

Mass Flow Measurement is a method of measuring the mass rate of fluid flow, which is the amount of mass passing through a point in a given time. It is an important parameter in various industries where the mass of a fluid, rather than its volume, is of primary interest. Mass flow measurement is commonly used in applications such as chemical processes, pharmaceutical production, food and beverage manufacturing, and environmental monitoring.

- Anemometer: An anemometer is an instrument used to measure the speed or velocity of air or other gases. It is commonly employed in meteorology, environmental monitoring, and various industrial applications where airflow measurement is essential.
- Coriolis Flow Meters: These meters utilize the Coriolis effect, where a fluid flowing through a vibrating tube causes a phase shift in the vibration. This phase shift is directly proportional to the mass flow rate, allowing for accurate mass flow measurement.
- Thermal Mass Flow Meters: These meters measure the mass flow rate by using the principle of heat transfer. The meter measures the cooling effect of a fluid passing over a heated element, and this cooling effect is proportional to the mass flow rate.
- Weighing Systems: In some applications, the mass flow rate is determined by weighing the fluid as it flows through a container or vessel. The change in weight over time gives the mass flow rate.
- Density Measurement: By combining flow rate measurement with density measurement, the mass flow rate can be determined. This is often done using density meters or sensors in conjunction with flow meters.

**Open Channel Flow Measurement**

Open Channel Flow Measurement is a technique in measurement of various quantities used to measure the flow of liquids in open channels, such as rivers, canals, channels, and streams, where the fluid is not confined within pipes. It is essential for water resource management, irrigation systems, flood control, and environmental monitoring.

- Weir: Used to measure open channel flow.
- Parshall Flume: Similar in shape to a Venturi tube, used for open channel flow measurement.
- Paddle Wheel or Open Flow Nozzle: Alternative methods for measuring open channel flow rates.

**Electromagnetic Flow Measurement**

Electromagnetic Flow Measurement is a method used to measure the volumetric flow rate of conductive fluids, such as liquids or slurries, using electromagnetic principles. It is a widely utilized and accurate technique for flow measurement of various quantities.

- Electromagnetic Flow Meters (EMF): Measure the volume flow of conductive liquids, slurries, sludges, and pastes. Based on Faraday's Law of Induction.
- Induction (Electro-Magnetic) Flowmeter: Analogous to Hall Transducer.
- Induction (Magnetic) Flowmeter: Construction with saddle-backed coils.
- Induction (Magnetic) Flowmeter-Immersion Type: Designed for immersion in the liquid being measured.

These instruments are commonly used in various industries for accurate and reliable flow measurement in different applications.

## Pressure Measurement

Pressure measurement is an essential aspect of measurement of various quantities, and it is important to understand the different terms and methods associated with pressure measurement. Here are the six terms commonly used in pressure measurements:

- Total Vacuum: This term refers to zero pressure or the absence of pressure, similar to the conditions experienced in outer space.
- Vacuum: Vacuum measurements are made between total vacuum and normal atmospheric pressure. It represents pressures lower than atmospheric pressure, often expressed in units such as pounds per square inch (psi).
- Atmospheric Pressure: Atmospheric pressure is the pressure exerted by the weight of the gases in the Earth's atmosphere on its surface. At sea level, it is typically expressed as 14.7 psi or 101.36 kilopascals (kPa).
- Absolute Pressure: Absolute pressure is the pressure measured relative to a vacuum reference point. It is typically expressed in pounds per square inch absolute (psi) and includes both atmospheric pressure and any additional pressure.
- Gauge Pressure: Gauge pressure is the pressure measured relative to atmospheric pressure. It is commonly expressed in pounds per square inch gauge (psi) and indicates the pressure above or below atmospheric pressure.
- Differential Pressure: Differential pressure refers to the pressure measured with respect to another pressure value. It represents the difference between two pressure points and is typically expressed as the numerical gap between the two values.

Understanding these pressure measurement terms is crucial in selecting the appropriate pressure measurement method and interpreting pressure readings accurately in various industrial applications.

### Pressure Formulas

Hydrostatic pressure refers to the pressure exerted by a liquid and is influenced by the depth within the liquid. The pressure increases with greater depth due to the weight of the fluid above the measurement point. The hydrostatic pressure can be calculated using the following formula:

** p = gh**

where:

p represents the pressure, measured in pounds per unit area or pascals.

g is the specific weight of the liquid, expressed in pounds per cubic foot (lb/ft³) for English units or newtons per cubic meter (N/m³) for SI units.

h denotes the distance from the liquid's surface to the measurement point, expressed in compatible units such as feet (ft), inches (in), centimeters (cm), meters (m), etc.

By applying this formula, one can determine the hydrostatic pressure in a liquid based on its specific weight and the depth at a particular location.

**Measuring Instrument for Pressure**

There are various measuring instruments available for measuring pressure in different applications. Here are some commonly used instruments:

- Manometers: Manometers are simple devices that use a column of liquid, such as mercury or water, to measure pressure. The height difference of the liquid column indicates the pressure being measured.

- Diaphragms, capsules, and bellows

- Bourdon tubes: Bourdon tubes are mechanical devices used in pressure measuring instruments, such as pressure gauges. They are one of the most common types of pressure sensing elements.

- Pressure Sensors: Pressure sensors are electronic devices that directly measure pressure and provide an electrical output signal. They can be based on various sensing technologies, including piezoresistive, capacitive, or piezoelectric principles.
- Barometers are instruments used for measuring atmospheric pressure. The traditional mercury barometer, although less commonly used nowadays due to its fragility and the toxicity of mercury, is one example. Instead, other types of barometers are preferred for direct reading and electrical outputs.
- Aneroid barometer: It operates without a fluid. It utilizes a bellows or a helical Bourdon tube as a pressure sensing element, allowing for direct reading of atmospheric pressure.
- Solid-state absolute pressure sensor: Provides electrical outputs. This sensor employs solid-state technology to measure pressure accurately and reliably.
- Piezoelectric pressure gauges: utilize piezoelectric crystals that generate a voltage when subjected to force or pressure. This voltage can be amplified and used as a pressure sensing mechanism.
- Capacitive devices: are another type of pressure sensor that measures pressure by detecting changes in capacitance between a sensing diaphragm and a fixed plate.

These various types of pressure measuring instruments offer different advantages and are selected based on factors such as accuracy requirements, sensitivity, environmental considerations, and the specific application at hand.

In conclusion, the measurement of various quantities, including flow and pressure, remains a fundamental aspect of modern industrial processes. As technology continues to evolve, so too will the methods and instruments used for measurement, leading to greater accuracy, reliability, and efficiency in a wide range of applications.

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