Introduction
The notes on this page related to the methods of measuring flow using devices which are based on bernoulli's equation. There are many other devices which are convenient to use and are very accurate which are based on other principles including vortex shedding, ultrasonics (doppler), turbines, and variable orifice. To obtain information on these devices please consult the linked sites at the bottom of this page.
Pitot tubes, Orifice Plates, Nozzles and Venturi meters are established methods of measuring flows in pipelines . These methods relate the pressure difference across the upstream and downstream sides of the units to the pipeline fluid velocities. In modern piping systems various high technology methods many of which are non-intrusive are replacing these systems. Orifice plates and nozzles are also used as flow balancing and/or limiting devices.
Pitot tubes are specially designed probes inserted into pipes to establish the flow velocity at fixed points in the pipe bore. The flow rate is established using special techniques.
Orifice plates are low cost devices consisting of thin plates trapped between flanges. The orifice plate includes a sized hole with a downstream bevel, through which the fluid flows. The flanges include tapping points to measure the pressure upstream and downstream of the plates. The accuracy of the orifice plate method is about ± 2%
Nozzles are the same as orifice plates except that the thin plate is replaced by a contoured nozzle. The accuracy of the nozzle method is about ± 1%
The venturi is a converging length of pipe followed by a short parallel throat and then a divergence. The accuracy of the venturi method is better than ± 1%
The main differences in the devices are that the orifice plate results in signficant losses, the nozzle has relatively low losses and the venture meter and the pitot tubes are very efficient. The venturi meter is also the most accurate followed by the nozzle and the orifice plate. The orifice plate system is the most widely used because it is the cheapest and most convenient to install and maintain.
SymbolsPitot tubes, Orifice Plates, Nozzles and Venturi meters are established methods of measuring flows in pipelines . These methods relate the pressure difference across the upstream and downstream sides of the units to the pipeline fluid velocities. In modern piping systems various high technology methods many of which are non-intrusive are replacing these systems. Orifice plates and nozzles are also used as flow balancing and/or limiting devices.
Pitot tubes are specially designed probes inserted into pipes to establish the flow velocity at fixed points in the pipe bore. The flow rate is established using special techniques.
Orifice plates are low cost devices consisting of thin plates trapped between flanges. The orifice plate includes a sized hole with a downstream bevel, through which the fluid flows. The flanges include tapping points to measure the pressure upstream and downstream of the plates. The accuracy of the orifice plate method is about ± 2%
Nozzles are the same as orifice plates except that the thin plate is replaced by a contoured nozzle. The accuracy of the nozzle method is about ± 1%
The venturi is a converging length of pipe followed by a short parallel throat and then a divergence. The accuracy of the venturi method is better than ± 1%
The main differences in the devices are that the orifice plate results in signficant losses, the nozzle has relatively low losses and the venture meter and the pitot tubes are very efficient. The venturi meter is also the most accurate followed by the nozzle and the orifice plate. The orifice plate system is the most widely used because it is the cheapest and most convenient to install and maintain.
| A = Area (m2) A 2= Area of Orifice(m2) a = Speed of sound (m/s) C d = Coefficient of Discharge C c = Coefficient of Contraction ρ = density (kg/m3) ρ 1 = density at inlet condtions(kg/m3) g = acceleration due to gravity (m/s2 ) ε = Expansion factor h = fluid head (m) L = Pipe length (m ) m = mass (kg) m = mass flow rate (kg/s) P 1 = Inlet fluid pressure (gauge) (N /m2 ) P 2 = Outlet fluid pressure (gauge) (N /m2 ) P 1 = Inlet fluid pressure (abs) (N /m2 ) P 2 = Outlet fluid pressure (abs) (N /m2 ) P - Absolute pressure (N /m2 ) | p gauge - gauge pressure (N /m2 ) p atm - atmospheric pressure (N /m2 ) p s= surface pressure (N /m2 ) Q = Volume flow rate (m3 /s) Q m = Mass flow rate = Qρ (kg /s) Re = Reynolds Number = u.ρD/μ s = specific volume (m3 /kg) u = fluid velocity (m/s) v = specific volume (m3/kg) v 1 = specific volume at inlet conditions(m3/kg) x = depth of centroid (m) θ =slope (radians) β = Ratio of largest pipe dia to small diameter τ = shear stress (N /m2) μ = dynamic viscosity (Pa.s) ν = kinematic viscosity (m2�s-1) υ = Specific volume (m3 / kg) γ= Ratio of Specific Heats |
Relevant Standards
The following standards provide detailed information on measuring fluid flow using venturis, orifice plates and nozzles.
Moff = Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full.
BS EN ISO 5167-1:2003 Moff: General principles and requirements
BS EN ISO 5167-2:2003 Moff: Orifice plates
BS EN ISO 5167-3:2003 Moff: Nozzles and Venturi nozzles
BS EN ISO 5167-4:2003 Moff: Venturi tubes
Note: BS 1042:Part 1(5 sections) and Part 3 :Standards withdrawn and replaced by above standards
MoFFiCC= Measurement of Fluid Flow in closed conduits
BS 1042-1.4:1992 BS 1042-2.1:1983, ISO 3966:1977 MoFFiCC. Velocity area methods. Method using Pitot static tubes
BS 1042-2.2:1983, ISO 7145:1982 MoFFiCC. Velocity area methods. Method of measurement of velocity at one point of a conduit of circular cross section
BS 1042-2.3:1984, ISO 7194:1983 MoFFiCC. Velocity area methods. Methods of flow measurement in swirling or asymmetric flow conditions in circular ducts by means of current-meters or Pitot static tubes
BS 1042-2.4:1989, ISO 3354:1988 MoFFiCC. Velocity area methods. Method of measurement of clean water flow using current meters in full conduits and under regular flow conditions
BS 1042:Part 1:Section 1.5:1997 MoFFiCC. Pressure differential devices. Guide to the effect of departure from the conditions specified in BS EN ISO 5167-1
BS 1042:Part 1:Section 1.5:1987 MoFFiCC. Pressure differential devices. Guide to the effect of departure from the conditions specified in Section 1.1
Moff = Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full.
BS EN ISO 5167-1:2003 Moff: General principles and requirements
BS EN ISO 5167-2:2003 Moff: Orifice plates
BS EN ISO 5167-3:2003 Moff: Nozzles and Venturi nozzles
BS EN ISO 5167-4:2003 Moff: Venturi tubes
Note: BS 1042:Part 1(5 sections) and Part 3 :Standards withdrawn and replaced by above standards
MoFFiCC= Measurement of Fluid Flow in closed conduits
BS 1042-1.4:1992 BS 1042-2.1:1983, ISO 3966:1977 MoFFiCC. Velocity area methods. Method using Pitot static tubes
BS 1042-2.2:1983, ISO 7145:1982 MoFFiCC. Velocity area methods. Method of measurement of velocity at one point of a conduit of circular cross section
BS 1042-2.3:1984, ISO 7194:1983 MoFFiCC. Velocity area methods. Methods of flow measurement in swirling or asymmetric flow conditions in circular ducts by means of current-meters or Pitot static tubes
BS 1042-2.4:1989, ISO 3354:1988 MoFFiCC. Velocity area methods. Method of measurement of clean water flow using current meters in full conduits and under regular flow conditions
BS 1042:Part 1:Section 1.5:1997 MoFFiCC. Pressure differential devices. Guide to the effect of departure from the conditions specified in BS EN ISO 5167-1
BS 1042:Part 1:Section 1.5:1987 MoFFiCC. Pressure differential devices. Guide to the effect of departure from the conditions specified in Section 1.1
Pitot Meter
Consider three glass tubes positioned in a pipe which is carrying flowing fluid
Now the static head of the fluid (p /ρg ), that is the height that the fluid rises in the tube with the fluid velocity at zero, is indicated by the tube at position B. At the interface of a flowing liquid with a solid surface the fluid velocity is zero. The head at position A is a measure of the stagnation head (p /ρg +u 2 /2g)
Now if the flowing fluid was in an open stream that static pressure would be the atmospheric pressure and the stagnation head would be simply the level of fluid in the manometer above the surface level of the flowing fluid. For an enclosed stream the velocity head is the difference in level of the static head as measured by tube B and the stagnation head as indicated by Tube A. The level of fluid in the tube at C is not useful because the fluid is flowing past the end of the tube.
The figure below shows a typical design of pitot tube flow meter. The inner tube pressure is the stagnation pressure and the annulus surrounding the inner tube is at the static pressure i.e. it indicates the pressure at the surface of the pitot tube which is static.
Now if the flowing fluid was in an open stream that static pressure would be the atmospheric pressure and the stagnation head would be simply the level of fluid in the manometer above the surface level of the flowing fluid. For an enclosed stream the velocity head is the difference in level of the static head as measured by tube B and the stagnation head as indicated by Tube A. The level of fluid in the tube at C is not useful because the fluid is flowing past the end of the tube.
The figure below shows a typical design of pitot tube flow meter. The inner tube pressure is the stagnation pressure and the annulus surrounding the inner tube is at the static pressure i.e. it indicates the pressure at the surface of the pitot tube which is static.
If ρ m is the density of the manometer fluid and ρ is the density of the flowing fluid then the the fluid velocity results from the equation.
u = C √ (2 Δp /ρ)........ Δp = (ρ m - ρ)gx....... and.... Δh = [(ρ m / ρ ) - 1] x
The pitot tube meter is used to indicate the velocity of the fluid flow in an enclosed pipe or duct. It is very accurate and involves minimum energy losses in the flowing fluid. It requires good alignment with the flow direction to achieve best results. Pitot tube meters are able to achieve accuracy levels of better than 1% in velocity with alignment errors of up to 15o
Venturi MeterA venturi meter includes a cylindrical length, a converging length with an included angle of 20o or more, and short parallel throat, and a diverging section with an included angle of about 6o. The internal finishes and proportions are such to enable the most accurate readings while ensuring minimum head losses.
Assuming an inviscid fluid with no losses due to viscocity. The velocities at section 1 and 2 are u 1 and u 2. The velocities are steady and uniform over areas A 1 and A 2
The contuity exquation applies therefore A 2 u 2 = A 2 u 2 = Q
Applying bernoulli's equation to a streamline passing along the axis between the two sections( 1 & 2 ).
Assuming an inviscid fluid with no losses due to viscocity. The velocities at section 1 and 2 are u 1 and u 2. The velocities are steady and uniform over areas A 1 and A 2
The contuity exquation applies therefore A 2 u 2 = A 2 u 2 = Q
Applying bernoulli's equation to a streamline passing along the axis between the two sections( 1 & 2 ).
Applying bernoulli's equation to the two sections.
Therefore the ideal discharge is given by
Now in practice there is a slight friction loss between 1 and 2 which would result in a high Δh reading and a consequent value of Q which is too high. For real fluids therefore a factor is introduced called the coefficient of discharge factor (C d ).
For low viscosity fluids C d = 0,98. The actual discharge as measured by a venturi is therefore given by.
For low viscosity fluids C d = 0,98. The actual discharge as measured by a venturi is therefore given by.
Design and performance parameters of venturi flow meters are provided in BS EN ISO 5167-4:2003
Nozzle Flow Meter
The nozzle as shown is practically a venturi with the diverging part removed. The basic equations used are the same as for the venturi meter. The friction losses are slightly larger than for the venturi but this is offset by the lower cost of the unit. The fact that the manometer connections cannot be located in the ideal positions for measuring the required piezometric pressures is allowed for in selection of the coefficient of discharge factor C d..
Design and performance parameters of nozzles flow meters are provided in BS EN ISO 5167-3:2003
Orifice Flow Meter
The simplest and cheapest method of measuring the flow using the bernoulli equation is the sharp edged orifice as shown below.
The fluid flow pattern in the region of and orifice is shown in the diagram below..
Application of Bernoulli's equation to the fluid flowing through the orifice.
Now u 1 = Q /A 1 and u 2 = Q /A c where A c = The area of the vena-contracta which is the reduced area of the fluid after leaving the orifice hole. (A c = C c A 2 ).
A 2 = the area of the orifice and C c is the Coefficient of contraction.
Finally C d = Coefficient of discharge = C c.C v
Using these factors a relationship for Q can be developed from the above equation
A 2 = the area of the orifice and C c is the Coefficient of contraction.
Finally C d = Coefficient of discharge = C c.C v
Using these factors a relationship for Q can be developed from the above equation
To arrive at a final equation a overall discharge coefficient C is introduced.
Now letting β = d 2 / d 1 that is β 2 = A 2 / A 1. The equation for flow through an orifice becomes
Note: This equation is very similar to the equation provided in BS EN ISO 5167:2 except that an expansion coefficient (ε )is introduced to cater for the measurement of compressible fluids. The equation provided in the standards is .
Values of the discharge coefficient C are provided in BS EN ISO 5167:2 for the different meter tapping arrangements, for different values of β against Reynold number ranges.
Small table showing C values for different Reynold numbers and β values . Detailed tables are provided in BS EN ISO 5167:2
Small table showing C values for different Reynold numbers and β values . Detailed tables are provided in BS EN ISO 5167:2
| β | Re | ||
| 5 x 103 | 1 x 105 | 1 x 108< | |
| 0.25 | 0,6102 | 0,6025 | 0,6013 |
| 0.5 | 0,6284 | 0,6082 | 0,6036 |
| 0.75 | 0,6732 | 0,6171 | 0,6025 |
Flow Conditioning
The accuracy of the flow measuring devices is very much affected by uniformity of the approaching fluid flow. Therefore ideally there should be a straight length of piping before the flow measuring device. It is generally accepted that for accurate flow readings there should be 50 pipe diameters of straight piping before the metering device following any pipe bend, valve, tee, reducer etc. The relevant standard provides a range of recommended minimum straight lengths depending on the nearest upstream fittings varying from 5 to 44 lengths. This length can be reduced if flow straighteners or flow conditioning devices systems are used upstream of the flow measuring device. A flow straightener is designed to remove swirl from the flowing fluid. A flow conditioner is a device which removes swirl and also redistributes the velocity profile to produce near ideal metering conditions.
Losses resulting from flow metering devicesThe orifice plate and, to a lesser extent the nozzle has significant kinetic energy losses downstream of the metering device as the locally generated kinetic energy is dissipated. The figure below illustrates the extent of these losses.
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TYPES OF FLUID FLOW METER
The most common principals for fluid flow metering are:
- Differential Pressure Flowmeters
- Velocity Flowmeters
- Positive Displacement Flowmeters
- Mass Flowmeters
- Open Channel Flowmeters
Among which we are interested in only Differential pressure flowmeter and velocity flowmeters
Differential Pressure Flowmeters
In a differential pressure drop device the flow is calculated by measuring the pressure drop over an obstructions inserted in the flow. The differential pressure flowmeter is based on the Bernoullis Equation, where the pressure drop and the further measured signal is a function of the square flow speed.
The most common types of differential pressure flowmeters are:
- Orifice Plates
- Flow Nozzles
- Venturi Tubes
- Variable Area - Rotameters
Orifice Plate
With an orifice plate, the fluid flow is measured through the difference in pressure from the upstream side to the downstream side of a partially obstructed pipe. The plate obstructing the flow offers a precisely measured obstruction that narrows the pipe and forces the flowing fluid to constrict.
The orifice plates are simple, cheap and can be delivered for almost any application in any material.
The TurnDown Rate for orifice plates are less than 5:1. Their accuracy are poor at low flow rates. A high accuracy depend on an orifice plate in good shape, with a sharp edge to the upstream side. Wear reduces the accuracy.
- Orifice, Nozzle and Venturi Meters
Venturi Tube
Due to simplicity and dependability, the Venturi tube flowmeter is often used in applications where it's necessary with higherTurnDown Rates, or lower pressure drops, than the orifice plate can provide.
In the Venturi Tube the fluid flowrate is measured by reducing the cross sectional flow area in the flow path, generating a pressure difference. After the constricted area, the fluid is passes through a pressure recovery exit section, where up to 80% of the differential pressure generated at the constricted area, is recovered.
With proper instrumentation and flow calibrating, the Venturi Tube flowrate can be reduced to about 10% of its full scale range with proper accuracy. This provides a TurnDown Rate 10:1.
- Orifice, Nozzle and Venturi Meters
Flow Nozzles
Flow nozzles are often used as measuring elements for air and gas flow in industrial applications.
The flow nozzle is relative simple and cheap, and available for many applications in many materials.
The TurnDown Rate and accuracy can be compared with the orifice plate.
- Orifice, Nozzle and Venturi Meters
The Sonic Nozzle - Critical (Choked) Flow Nozzle
When a gas accelerate through a nozzle, the velocity increase and the pressure and the gas density decrease. The maximum velocity is achieved at the throat, the minimum area, where it breaks Mach 1 or sonic. At this point it's not possible to increase the flow by lowering the downstream pressure. The flow is choked.
This situation is used in many control systems to maintain fixed, accurate, repeatable gas flow rates unaffected by the downstream pressure.
Recovery of Pressure Drop in Orifices, Nozzles and Venturi Meters
After the pressure difference has been generated in the differential pressure flow meter, the fluid pass through the pressure recovery exit section, where the differential pressure generated at the constricted area is partly recovered.
As we can see, the pressure drop in orifice plates are significant higher than in the venturi tubes.
Variable Area Flowmeter or Rotameter
The rotameter consists of a vertically oriented glass (or plastic) tube with a larger end at the top, and a metering float which is free to move within the tube. Fluid flow causes the float to rise in the tube as the upward pressure differential and buoyancy of the fluid overcome the effect of gravity.
The float rises until the annular area between the float and tube increases sufficiently to allow a state of dynamic equilibrium between the upward differential pressure and buoyancy factors, and downward gravity factors.
The height of the float is an indication of the flow rate. The tube can be calibrated and graduated in appropriate flow units.
The rotameter meter typically have a TurnDown Ratio up to 12:1. The accuracy may be as good as 1% of full scale rating.
Magnetic floats can be used for alarm and signal transmission functions.
Velocity Flowmeters
In a velocity flowmeter the flow is calculated by measuring the speed in one or more points in the flow, and integrating the flow speed over the flow area.
Pitot Tubes
The pitot tube are one the most used (and cheapest) ways to measure fluid flow, especially in air applications as ventilation and HVAC systems, even used in airplanes for the speed measurent.
The pitot tube measures the fluid flow velocity by converting the kinetic energy of the flow into potential energy.
The use of the pitot tube is restricted to point measuring. With the "annubar", or multi-orifice pitot probe, the dynamic pressure can be measured across the velocity profile, and the annubar obtains an averaging effect.
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A comparison table of commonly used flow meters based on the viscosity of fluids that they can handle and for which type of fluid they are suitable, working conditions , accuracy , range are given below
Sr no | Type | Viscous liquid | Slurry | Gas | Output | Pressure loss | Accuracy% full scale | Full range |
1 | Orifice | Limited | Poor | Good | Square root characteristic | High | ±0.5to ±2% | 10-3to 5.5×103m3/hr |
2 | Venturi | Limited | Limited | Good | --do-- | Minimal | ±0.5to ±3% | 1to 5.5×103m3/hr |
3 | Flow nozzle | Limited | Limited | Good | --do-- | Minimal | ±0.5to ±3% | 1to 5.5×103m3/hr |
4 | Pitot tube | Poor | Poor | Good | --do-- | Poor | ±5to ±10% | 10 to 104m3/hr |
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