Measurement of various quantities (Flow and Pressure) Notes for Instrumentation Engineering

By Rahul Singh|Updated : August 20th, 2017

In this article, you will find the study notes on Measurement of Various Quantities which will cover the topics such as flow (differential pressure, variable area, electromagnetic, ultrasonic, turbine and open channel flow meters), pressure (including low pressure).


  • Velocity is a measure of speed and direction of an object. When related to fluids it is the rate of flow of fluid particles in a pipe. The speed of particles in a fluid flow varies across the flow.
  • Laminar flow of a liquid occurs when its average velocity is comparatively low and the fluid particles tend to move smoothly in layers, The velocity of the particles across the liquid takes a parabolic shape.
  • Turbulent flow occurs when the flow velocity is high and the particles no longer flow smoothly in layers and turbulence or a rolling effect occurs.
  • Viscosity is a property of a gas or liquid that is a measure of its resistance to motion or flow. A viscous liquid such as syrup has a much higher viscosity than water and water has a higher viscosity than air.
  • The Reynolds number R is a derived relationship combining the density and viscosity of a liquid with its velocity of flow and the cross-sectional dimensions of the flow and takes the form.


                      R= VDρ/μ


    V = average fluid velocity
    D = diameter of the pipe
     r = density of the liquid
    μ = absolute viscosity

Flow Formula:
Continuity equation The continuity equation states that if the overall flow rate in a system is not changing with time , the flow rate in any part of the system is constant.
From which we get the following equation:
Q = VA 
where Q = flow rate
V = average velocity
A = cross-sectional area of the pipe
The units on both sides of the equation must be compatible, i.e., English units or metric units.


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

Q = V1A1 = V2A2

Flow Measurement Instruments

Flow measurements can be divided into the following groups: flow rate, total flow, and mass flow.

Flow rate: Differential pressure measurements can be made for flow rate determination when a fluid flows through a restriction. The restriction produces an increase
in pressure which can be directly related to flow rate.Examples of commonly used restrictions

 (a) Orifice plate The orifice plate is normally a simple metal diaphragm with a constricting hole. The diaphragm is normally clamped between pipe flanges to give easy access,

 (b) Venturi tube The Venturi tube  uses the same differential pressure principle as the orifice plate. The advantages of the Venturi tube are its ability to handle
large amounts of suspended solids, it creates less turbulence and hence less insertion loss than the orifice plate.

 (c) flow nozzle The flow nozzle is a good compromise on the cost and accuracy between the orifice plate and the Venturi tube for clean liquids. It is not normally used with suspended particles. Its main use is the measurement of steam flow.

 (d) Dall tube The Dall tube has the lowest insertion loss but is not suitable for use with slurries.

To summarize, the orifice is the simplest, cheapest, easiest to replace, least accurate, more subject to damage and erosion, and has the highest loss. The Venturi tube is more difficult to replace, most expensive, most accurate, has high tolerance to damage and erosion, and the lowest losses of all the three tubes. The flow nozzle is intermediate between the other two and offers a good compromise. The Dall tube has the advantage of having the lowest insertion loss but cannot be used with slurries.

  (e) The elbow can be used as a differential flow meter.The elbow meter is good for handling particulates in solution, with good wear and erosion resistance characteristics but has low sensitivity.

  (f) Variable-area meters, such as the rotameter  are often used as a direct visual indicator for flow rate measurements. The rotameter is a vertical tapered tube with a T (or similar) shaped weight.

Total flow: Includes devices used to measure the total quantity of fluid flowing or the volume of liquid in a flow.

  • Positive displacement meters use containers of known size, which are filled and emptied for a known number of times in a given time period to give the total flow volume.Two of the more common instruments for measuring total flow are the piston flow meter and the nutating disc flow meter.

Mass flow:  By measuring the flow and knowing the density of a fluid, the mass of the flow can be measured. Mass flow instruments include constant speed impeller turbine wheel-spring combinations that relate the spring force to mass flow and devices that relate heat transfer to mass flow.

  •  Anemometer is an instrument that can be used to measure gas flow rates. 

Open channel flow: Open channel flow occurs when the fluid flowing is not contained as in a pipe but is in an open channel.

  • A Weir used to meaasure open channel flow.
  • A Parshall flume is also used for open channel flow measurement,which is similar in shape to a Venturi tube.
  • A Paddle wheel or open flow nozzle are alternative methods of measuring open channel flow rates.

Ultrasonic Transducers: They can be used for single point or continuous level measurement of a liquid or a solid. A single ultrasonic transmitter and receiver can be arranged with a gap to give single-point measurement.

Electromagnetic Flow measurement

  • Electromagnetic flow meters (EMF) can measure the volume flow of liquids, slurries,sludges and pastes in almost any industry. The only prerequisite to use an EMF is that the product being measured must have minimum electrical conductivity.
  • Electromagnetic flow measurement is based on Faraday's Law of Induction.The law states that voltage is induced across a conductor moving through a magnetic field. The functional principle of electromagnetic measuring devices is also based on this law of nature.

Measuring Instrument for Electromagnetic Flow

  • Induction (Electro-Magnetic) flowmeter: Analogous to Hall Transducer
  • Induction (Magnetic) flowmeter: Construction of flowmeter with saddle backed coils 
  • Induction (Magnetic) flowmeter-Immersion type


 Pressure measurements and become familiar with the most common methods of using the various pressure measurement standards. There are six terms applied to pressure measurements. They are as follows:

  • Total vacuum–which is zero pressure or lack of pressure, as would be experienced in outer space.
  • Vacuum is a pressure measurement made between total vacuum and normal atmospheric pressure (14.7 psi).
  • Atmospheric pressure is the pressure on the earth’s surface due to the weight of the gases in the earth’s atmosphere and is normally expressed at sea levelas 14.7 psi or 101.36 kPa. 
  • Absolute pressure is the pressure measured with respect to a vacuum and is expressed in pounds per square inch absolute (psi).
  • Gauge pressure is the pressure measured with respect to atmospheric pressure and is normally expressed in pounds per square inch gauge (psi). 
  • Differential pressure is the pressure measured with respect to another pressure and is expressed as the difference between the two values. 

byjusexamprepPressure Formulas Hydrostatic pressure is the pressure in a liquid. The pressure increases as the depth in a liquid increases. This increase is due to the weight of the fluid above the measurement point. The pressure is given by
  p = gh

where p = pressure in pounds per unit area or pascals
g = the specific weight (lb/ft3 in English units or N/m3 in SI units)
h = distance from the surface in compatible units (ft, in, cm, m, and so on)

Measuring instrument for pressure:

  •  Manometer- (U shaped Manometer/ inclined-tube manometer and  well type manometer).


  •  Diaphragms, capsules, and bellows


  • Bourdon tubes

Bourdon tubes are hollow, cross-sectional beryllium, copper, or steel tubes, shaped into a three quarter circle. They may be rectangular or oval in cross section, but the operating principle is that the outer edge of the cross section has a larger surface than the inner portion. 


  • Other pressure sensors
  • Barometers are used for measuring atmospheric pressure. A simple barometer is the mercury barometer. It is now rarely used due to its fragility and the toxicity of mercury.
  • The an eroid (no fluid) barometer is favored for direct reading (bellows or helical Bourdon tube) and the solid-state absolute pressure sensor for electrical outputs.
  • A piezoelectric pressure gauge, Piezoelectric crystals produce a voltage between their opposite faces when a force or pressure is applied to the crystal. This voltage can be amplified and the device used as a pressure sensor.
  • Capacitive devices use the change in capacitance between the sensing diaphragm and a fixed plate to measure pressure.

All the Best.

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