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Mechanics of the sandglass

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https://www.inf.utfsm.cl/~amoreira/orzelc.pdf


Summary
(i) The traditional sandglass consists of two glass
ampoules joined by narrow tapering necks or, in
early examples, separated by a thin metal diaphragm
pierced with a small central hole.
108 A A Mills et al

(ii) The device constitutes an interval timer, the period
being measured by the time elapsing between the
inversion of the apparatus and the last grains leaving
the upper reservoir. Although commonly called
an hourglass, other periods (such as 1=4, 1=2 and
3=4 hour) were frequently delineated, so the term
sandglass is preferred here.

(iii) Unlike the ancient water-operated clepsydra, the
sandglass is known only from medieval times. This
is especially surprising when it is recalled that it is
not liable to freezing.

(iv) Historical sandglasses were always sealed as tightly
as the technology of the time allowed, for moisture
seeping in could cause caking of the filling and
consequent irregular running. Air displaced by
the descending grains must therefore rise as a
countercurrent and percolate through the particulate
bed in the upper reservoir.

(v) The particles in a sandglass need not be silica sand,
but should always be clean, dry, and sieved to be
of closely similar size.

(vi) Particles of a smooth spherical shape are best,
promoting reproducibility even at low rates of
flow. This requirement is most conveniently met
nowadays by the tiny glass beads available in bulk
as ‘ballotini’.

(vii) To give a smooth and consistent flow without
occasional partial or complete blockage, the aperture
through which the ballotini fall should be at least 4
their maximum diameter. (For particulate material
in general, 5 the maximum grain dimension would
be safer.)

(viii) The rate of flow is independent of height in the
reservoir, except over the last few cm.

(ix) The emptying period is independent of the density
of the particulate filling, provided that its total
volume is the same and the shape, size and surface
characteristics of the grains are identical.

(x) The period P delineated by a sandglass is controlled
by the shape of the vessels from which it is made,
the diameter of the aperture separating them, and
the nature and volume of the particulate material
sealed within it.

(xi) For spherical ballotini passing a sieve of maximum
aperture d mm, it was found that:
P / V
.D − d/2:5
where V represents the volume of ballotini in ml
and D is the diameter of a circular orifice in mm.
(Alternatively, a value of d given by 1:3 the mean
bead diameter may be employed.)

(xii) The shape of the reservoir containing the ballotini
is reflected in the constant of proportionality to
be applied to the above expression to give P in
seconds. For ‘hourglass’, ‘cone’, ‘silo’ and ‘annular
shelf’ designs K is 7–10, 8, 19 and 21 respectively.

(xiii) The above characteristics are the result of internal
flow regimes in the particulate filling that are quite
different from the flow of true liquids. Sandglasses
are normally required to be slow-running and
therefore exhibit ‘plug-flow’—a situation where a
continuously collapsing arch over the exit aperture
generates a channel above it that is continually
replenished by the flow of particles from the
sides. A circular crater is thereby generated in the
upper reservoirwhile a matching cone grows in
the receiver. Their angles are controlled by the
‘angles of repose’ of the particles (25 for ballotini).
Internal flow patterns in reservoirs of various shapes
have been illustrated by sequential photographs of
2-D perspex models containing marker bands of
coloured ballotini.

(xiv) The reproducibility of a 19 m 45 s glass containing
a ‘traditional’ annular orifice 2.8 mm in diameter
was found to be 5 s.0:4%/ if it was allowed to
run without disturbance.

(xv) The period of a sandglass was lengthened by
any disturbance, but was essentially independent of
temperature up to 100 C.

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Mechanics of the sandglass Serg io <invalid@invalid.com> - 2017-09-06 14:28 -0500
  Re: Mechanics of the sandglass benj <benj@nobody.net> - 2017-09-06 18:12 -0400
    Re: Mechanics of the sandglass Serg io <invalid@invalid.com> - 2017-09-06 19:09 -0500
  Re: Mechanics of the sandglass "reber G=emc^2" <herbertglazier0@gmail.com> - 2017-09-07 14:40 -0700

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