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Introduction..... Symbols..... Standards..... Pitot ..... Venturi ..... Nozzle..... Orifice..... Flow condition..... losses.....
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.
The following standards provide detailed information on measuring fluid flow using venturis, orifice plates and nozzles.
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)
Reference ..Stagnation point.
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 Meter Reference ..Fluid Flow
A 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.
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 ).
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 ).
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.
The accuracy of the flow
measuring devices is very much affected by uniformity of the approaching
Therefore ideally there should be a straight length of piping before the
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 devices
The 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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Last Updated 28/01/2013