Force, Pressure and Flow

Question 1

• Measuring Force

Answer 1

o Force measurements may be made by using a displacement sensor coupled
to an elastic beam.
o Force transfucers are usually constructed from displacement transducers
coupled to elastic elements
§ If a stiffer elastic element is used to minimize the displacement, the
force transducer will have lower sensitivity and lower SNR
§ If a compliant elastic element is used to maximize sensitivity, large
displacements will result and the structure will have a lower resonant
frequency

Question 2

train Gauges on Cantilever Beam

Answer 2

Stiffness of the beam is given by k
§ Beam has a resonant frequency: Almost always want to make the
resonant frequency higher than any signal frequencies that we wish
to measure. Any extra mass added to the force transducer will lower
its resonant frequency.
§ Wheatstone bridge arrangement

Question 3

o Load Cell

Answer 3

§ Usually based on strain gauges and require instrumentation
amplifiers
§ Robust

Question 4

o Piezoelectric force sensor

Answer 4

§ Useful only for dynamic forces
§ The charge movement is
proportional to applied force
§ Very stiff (therefore low sensitivity?)

Question 5

Compensating for compliance

Answer 5

o An alternative approach to measuring force is
to attach a position sensor to a motor and
utilize active feedback to compensate for
compliance
o The position of the force sensor is kept fixed.
o Force is measured by monitoring the input to
the actuator balancing the motion caused by
the applied force. The mechanical characteristics of the device, such as its
stiffness and damping, may be controlled dynamically by the feedback
circuit.

Question 6

o Bourdon Tube

Answer 6

§ Semicircular thin-walled tube usually constructed of brass
§ Gas pressure straightens the Bourdon tube which drives the needle
indicator via a mechanical amplifier

Question 7

Pressure sensors

Answer 7

Bourdon Tube
o Membrane deflection
Sensors manufactured with MEMS techniques:
§ Absolute and differential pressure sensors
oPiezo-resistive Pressure Sensor
§ Gas or fluid

Question 8

• Blood Pressure Sensors/Monitors

Answer 8

o Blood pressure changes from a minimum value (diastole, 11kPa) to a
maximum value (systolic, 16kPa) each heartbeat
o BP often measured by placing an inflatable cuff around the upper arm and
pumping till blood no longer flows
o Cuff is slowly deflated: Pressure at which the sound of blood flowing can be
heard is systole; pressure at which sounds can no longer be heard is diastole

Question 9

o Reynold’s Number

Answer 9

§ Nondimensional measure of the ratio of inertial and viscous forces
§ Flow will be laminar is Re < 2300, transient if 2300 < Re < 4000,
and turbulent if Re > 4000
§ Viscous forces dominate in laminar flow; inertial forces dominate in
turbulent flow

Question 10

o Blood flow in tissue

Answer 10

§ Usually represented as a volume flow per unit mass of tissue
§ If a region is uniformly perfused, the tissue blood flow may be
estimated as the total blood flow into the region divided by the mass
of the tissue in the perfused region

Question 11

Electromagnetic flow meter

Answer 11

§ When a fluid containing electric
charges flows in a magnetic field, an electromotive force is generated on
those charges (Lorentz)
§ In an electrolyte solution, such as blood, positive and negative ions will
move in opposite directions, creating an electric field E so that F balances
the electric force
§ Thus, if two electrodes are placed
along the electric field, a potential
difference will
appear across the electrode pair, where � is the vector connecting
the positions off the two electrodes.

§ Although the blood velocity in a vessel is not uniform, it can be shown
that V = duB still holds where u is axisymmetric and represents the
mean velocity

Question 12

o Ultrasonic flow meter

Answer 12

A sound wave propagating in a moving medium is affected by the
velocity of the medium, and the sound scattered by a moving object
is also affected by the velocity of the scattering object.
§ Both of these phenomena can be used to measure blood flow velocity
or flow rate in a blood vessel

Question 13

o Ultrasonic doppler flow meter

Answer 13

§ When a fluid contains particles by which ultrasound is scattered, the
velocity of the particles can be determined by the Doppler shift of
the scattered ultrasound.
§ The ultrasound Doppler flowmeter measured the Doppler shift in the
scattered wave due to RBCs moving in the blood stream

Question 14

o Indicator dilution flow meter

Answer 14

Flow measurement by indicator dilution is a method in which a known
amount of indicator is injected into the blood stream, and the
average flow rate is estimated from the time course of the
concentration of the indicator downstream

Question 15

o Thermal flow measurement

Answer 15

§ Can detect flow rate by measuring the
temperature gradient across a heat
source
§ (Can also use in reverse to measure
heat)

Question 16

o Particle image velocimetry

Answer 16

§ Introduced particles (or RBCs) are
imaged using high speed cameras.
§ Images are divided into subimages and
cross-correlation techniques are used to
compute velocity

Question 17

o Laser doppler velocimetry

Answer 17

§ Laser light is directed at the skin and
penetrates up to 1mm
§ Light that is scattered from moving RBCs
experiences a Doppler shift
§ The reflected light is measured with a photodetector and the average
blood speed computed
§ Looks at an area of tissue, not the blood flow in a particular vessel

Question 18

o Pneumotachygraph

Answer 18

§ A sensor for measuring respiratory gas flow rate
§ Flow is directed through bundles of parallel capillaries (Fleisch) or a
wire screen (Lilley).
§ Flow rate is proportional to the pressure drop across the device.
§ Water condensation is avoided with a heater

Question 19

o Differential pressure flow meter

Answer 19

rential pressure flow meter
§ If gas flows through a Venturi tube (a tube of varying internal
diameter) the linear speed of the gas increases, and a change in
pressure ΔP results:
§ The change in pressure is in accordance with Bernoulli’s Principle: