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EXM5
Experimental methods E181101
Flowrate
Rudolf Žitný, Ústav procesní a
zpracovatelské techniky ČVUT FS 2010
Some pictures and texts were copied
from www.wikipedia.com
EXM5
Flowrate measurement
Rotameter
Turbine
Vortex flowmeters
Nozzles Venturi, orifice
Pitot tube (multihole tube)
Ultrasound
Coriolis
Thermal
Laser Doppler
EXM5
Rotameter, Turbine
Rotameter,
floater and conical glass pipe. Position of floater is
determined by the balance of forces: weight of floater = fluid forces. The higher is
floater, the wider is the gap, therefore the lower are velocities and viscous friction. This
flowmeter can be used not only for liquids, but also for gases (or inviscid fluids). In this
case the fluid forces are not viscous, but inertial and can be derived from Bernoulli’s
equation.
What do you think is the purpose
of these inclined grooves?
Turbine (detector of pulses – flowrate proportional to frequency)
2
fD
Q  fD3 g (
)

f-frequency. g-viscous correction
EXM5
Vortex, orifice
Vortex flowmeters utilize the vortex shedding
principle. The fluid strikes a bluff body, generating vortices (eddies)
that move downstream. The vortices form alternately, from one
side to the other. A piezoelectric sensor housed in a sensor tube
directly downstream of the bluff senses the pressure zones
created by the vortices. The sensor generates a frequency directly
proportional to the vortices (flow).
f 
Sr
u
D
Strouhal’s number Sr=0.21 for cylinder of
diameter D (holds for Re>10000)
Look at more details about von Karman vortex street
Nozzles, Venturi, orifice use the Bernoulli
Equation to calculate the fluid flow rate by measuring the pressure
difference through obstructions in the flow
p
p
1% accuracy, low pressure drop
uk
2 p

p
2%, pressure drop large (vena contracta)
EXM5
Ultrasound flowmeters
Transit time (without particles) expensive, accurate
Measurements are made by sending bursts of signals through a pipe. Sound waves
travelling in the direction of flow of the fluid require less time than when travelling in
the opposite direction. The difference in transit times of the ultrasonic signals is an
indication for the flow rate of the fluid. Since ultrasonic signals can also penetrate
solid materials, the transducers can be mounted onto the outside of the pipe.
t1 
L
L
2 Lu cos 
, t 2 
, t 2  t1  2
c  u cos 
c  u cos 
c  u 2 cos 2 
L-length of beam, u-flow velocity, c-speed of sound (1500 m/s in water)

Doppler effect (reflected wave by particles). Doppler frequency shift
Doppler ultrasonic flowmeters operate on the Doppler shift principle, whereby the
transmitted frequency is altered linearly by being reflected from particles and
bubbles in the fluid. The net result is a frequency shift between transmitter and
receiver frequencies that can be directly related to the flow velocity. Doppler meters
require a minimum amount of solid particles or air in the line to achieve
measurements.
f 2u cos 

f
c

EXM5
UVP monitor (Ultrasound Velocity Profile)
Ultrasound Doppler effect for measurement velocity profiles
1. Piezotransducer is transmitter as well as receiver of US
pressure waves operating at frequency 4 or 8 MHz.
2. Short pulse of few (10) US waves is transmitted
(repetition frequency 244Hz and more) and crystal starts
listening received frequency reflected from particles in fluid.
3. Time delay of sampling (flight time) is directly proportional
to the distance between the transducer and the reflecting
particle moving with the same velocity as liquid.
4. Received frequency differs from the transmitted frequency
by Doppler shift Δf, that is proportional to the component of
http://biomechanika.cz
particle velocity in the direction of transducer axis.
PROBLEMS:
1. What is spatial resolution of velocity, knowing speed of sound in water (1400
m/s) and sampling frequency 8 MHz ?
2. Calculate flowrate in a circular pipe from recorded velocity profile (given angle )
EXM5
Electromagnetic flowmeters
Magnetic flowmeters (electromagnetic or
induction flowmeters), obtain the flow velocity by measuring the
changes of induced voltage of the conductive fluid passing
across a magnetic field. A typical magnetic flowmeter places
electric coils around the pipe of the flow to be measured and
sets up a pair of electrodes across the pipe wall. If the targeted
fluid is electrically conductive, i.e., a conductor, its passing
through the pipe is equivalent to a conductor cutting across the
magnetic field. This induces changes in voltage reading between
the electrodes. The higher the flow speed, the higher the
voltage.

u

F
Lorentz force acting on ion (charge q)
moving with velocity u in magnetic field
(magnetic induction B).

 
F  qu  B
electrode

B
Lorentz force is in balance with
electromotive force


F  qE
EXM5
Coriolis flowmeters


Coriolis force in a rotating pipe

 
F  2mu  

F
Rotation is substituted by vibration in an actual design of flowmeter.
-phase shift

u
Detectors of
position
Elmag.induced
oscillations
m  c

f
[kg/s] f-frequency of
oscillation
  k[(
The flow is guided into the U-shaped tube. When an osillating excitation force is
applied to the tube causing it to vibrate, the fluid flowing through the tube will induce a
rotation or twist to the tube because of the Coriolis acceleration acting in opposite
directions on either side of the applied force. This twist results in a phase difference
(time lag) between the inlet side and the outlet side and this phase difference is
directly affected by the mass passing through the tube. A more recent single straight
tube design is available to measure some dirty and/or abrasive liquids. Vibration of
Coriolis flowmeters has very samll amplitude, usually less than 2.5 mm, and the
frequency is near the natural frequency of the device, usually around 80 Hz. The
vibration is commonly introduced by electric coils and measured by magnetic
sensors. Resonant frequency depends upon density – therefore not only flowrate but
also density is measured.
f empty
f
) 2  1]
[kg/m3] density from
eigenfrequency
EXM5
Thermal flowmeters
Thermal mass-flowmeters heated wire/hot film anemometers electr.current is
controlled so that the temperature of wire (resistance) is constant.

i  ab m
2
D
Power necessary to maintain
constant temperature of heated
wire depends upon flow velocity
i-current is adjusted so that the Rm will be the same
as the fixed resistors in the bridge.
Rm
Um=0 controller
i-source
EXM5
Thermal flowmeters
Hot wire anemometer simplified theory
Rm (Twire )i  DL(Twire  T fluid )
2
Heat generated
in wire
Heat transferred to fluid by
convection
D
D
uD
2/3
2/3
Nu 
 (0.04 Re  0.06 Re ) Pr  0.04


Rmi  c u
2
EXM5
Thermal flowmeters
Differential anemometers – heater + 2
thermocouples symmetrically located
  c(T2  T2 )
m
Heater
T1
T2
EXM5
Correlation flowmeters
Cross-correlation of stimulated or
random signal detected at two locations
(technically it can be a heater and thermocouples)

R12 ( )   T1 (t )T2 (t   )dt
Heater

T1
T2
EXM5
Correlation flowmeters
Example calculated by MATLAB
Heater
Random signal shifted by
100 time steps

R12 ( )   T1 (t )T2 (t   )dt
