21.2 Angle measurement
Measurement of angles is one of the
less common measurement requirements that instrumentation technologists are
likely to meet. However, angle measurement is required in some circumstances,
such as when the angle between adjoining faces on a component must be checked.
The main instruments used are protractors and a form of angle-measuring spirit
level.
In some circumstances, a simple
protractor of the sort used in school for geometry exercises can be used.
However, the more sophisticated form of angle protractor shown in Figure 21.9
provides better measurement accuracy. This consists of two straight edges, one
of which is able to rotate with respect to the other. Referring to Figure 21.9,
the graduated circular scale A attached to the straight edge C rotates inside a
fixed circular housing attached to the other straight edge B. The relative
angle between the two straight edges in contact with the component being
measured is determined by the position of the moving scale with respect to a
reference mark on the fixed housing B. With this type of instrument, measurement
inaccuracy is at least š1%. An alternative form, the bevel protractor, is
similar to this form of angle protractor, but it has a vernier scale on the
fixed housing. This allows the inaccuracy level to be reduced to š10 minutes of
arc.
The spirit level shown in Figure
21.10 is an alternative angle-measuring instrument. It consists of a standard
spirit level attached to a rotatable circular scale that is mounted inside an
accurately machined square frame. When placed on the sloping surfaces of
components, rotation of the scale to centralize the bubble in the spirit level
allows the angle of slope to be measured. Again, measuring inaccuracies down to
±10 minutes of arc are possible if a vernier scale is incorporated in the
instrument.
The electronic spirit level contains
a pendulum whose position is sensed electrically. Measurement resolution as
good as 0.2 seconds of arc is possible.
21.3 Flatness measurement
The only dimensional parameter not so
far discussed where a measurement requirement sometimes exists is the flatness
of the surface of a component. This is measured by a variation gauge. As shown
in Figure 21.11, this has four feet, three of which are fixed and one of which
floats in a vertical direction. Motion of the floating foot is measured by a
dial gauge that is calibrated such that its reading is zero when the floating
foot is exactly level with the fixed feet. Thus, any non-zero reading on the
dial gauge indicates non-flatness at the point of contact of the floating foot.
By moving the variation gauge over the surface of a component and taking
readings at various points, a contour map of the flatness of the surface can be
obtained.
21.4 Volume measurement
Volume measurement is required in its
own right as well as being required as a necessary component in some techniques
for the measurement and calibration of other quantities such as volume flow
rate and viscosity. The volume of vessels of a regular shape, where the
cross-section is circular or oblong in shape, can be readily calculated from
the dimensions of the vessel. Otherwise, for vessels of irregular shape, it is
necessary to use either gravimetric techniques or a set of calibrated
volumetric measures.
In the gravimetric technique, the dry
vessel is weighed and then is completely filled with water and weighed again.
The volume is then simply calculated from this weight difference and the
density of water.
The alternative technique involves
transferring the liquid from the vessel into an appropriate number of
volumetric measures taken from a standard-capacity, calibrated set. Each vessel
in the set has a mark that shows the volume of liquid contained when the vessel
is filled up to the mark. Special care is needed to ensure that the meniscus of
the water is in the correct position with respect to the reference mark on the
vessel when it is deemed to be full. Normal practice is to set the water level
such that the reference mark forms a smooth tangent with the convex side of the
meniscus. This is made easier to achieve if the meniscus is viewed against a
white background and the vessel is shaded from stray illumination.
The measurement uncertainty using
calibrated volumetric measures depends on the number of measures used for any
particular measurement. The total error is a multiple of the individual error
of each measure, typical values of which are shown in Table 21.1.
21.5 Viscosity measurement
Viscosity measurement is important in
many process industries. In the food industry, the viscosity of raw materials
such as dough, batter and ice cream has a direct effect on the quality of the
product. Similarly, in other industries such as the ceramic one, the quality of
raw materials affects the final product quality. Viscosity control is also very
important in assembly operations that involve the application of mastics and
glue flowing through tubes. Clearly, successful assembly requires such
materials to flow through tubes at the correct rate and therefore it is
essential that their viscosity is correct.
Viscosity describes the way in which
a fluid flows when it is subject to an applied force. Consider an elemental
cubic volume of fluid and a shear force F applied to one of its faces of area
A. If this face moves a distance L and at a velocity V relative to the opposite
face of the cube under the action of F, the shear stress (s) and shear rate (r)
are given by:
s
= F/A; r = V/L
The coefficient of viscosity (CV)
is the ratio of shear stress to shear rate, i.e.
CV = s/r.
CV is often described
simply as the ‘viscosity’. A further term, kinematic viscosity, is also
sometimes used, given by KV = CV/p, where KV
is the kinematic viscosity and p
is the fluid density. To avoid confusion, CV is often known as the
dynamic viscosity, to distinguish it from KV. CV is
measured in units of poise or Ns/m2 and KV is measured in
units of stokes or m2/s.
Viscosity was originally defined by
Newton, who assumed that it was constant with respect to shear rate. However,
it has since been shown that the viscosity of many fluids varies significantly
at high shear rates and the viscosity of some varies even at low shear rates.
The worst non-Newtonian characteristics tend to occur with emulsions, pastes
and slurries. For non-Newtonian fluids, subdivision into further classes can
also be made according to the manner in which the viscosity varies with shear
rate, as shown in Figure 21.12.
The relationship between the input
variables and output measurement for instruments that measure viscosity
normally assumes that the measured fluid has Newtonian characteristics. For
non-Newtonian fluids, a correction must be made for shear rate variations (see
Miller, 1975a). If such a correction is not made, the measurement obtained is
known as the apparent viscosity, and this can differ from the true viscosity by
a large factor. The true viscosity is often called the absolute viscosity to
avoid ambiguity. Viscosity also varies with fluid temperature and density.
Instruments for measuring viscosity
work on one of three physical principles:
• Rate of flow of the liquid through
a tube
• Rate of fall of a body through the
liquid
• Viscous friction force exerted on a
rotating body.
21.5.1 Capillary and tube viscometers
These are the most accurate types of
viscometer, with typical measurement inaccuracy levels down to ±0.3%. Liquid is
allowed to flow, under gravity from a reservoir, through a tube of known
cross-section. In different instruments, the tube can vary from capillary-sized
to a large diameter. The pressure difference across the ends of the tube and
the time for a given quantity of liquid to flow are measured, and then the
liquid viscosity for Newtonian fluids
can be calculated as (in units of poise):
CV
= 1.25πR4 PT/LV
where R is the radius (m) of the
tube, L is its length (m), P is the pressure difference (N/m2)
across the ends and V is the volume of liquid flowing in time T (m3/s).
For non-Newtonian fluids, corrections
must be made for shear rate variations (Miller, 1975a). For any given
viscometer, R, L and V are constant and equation (21.1) can be written as:
CV = KPT
where K is known as the viscometer constant.
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