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Re: Mechanics of the sandglass

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On 9/6/2017 5:12 PM, benj wrote:
> On 9/6/2017 3:28 PM, Serg io wrote:
>>
>> 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.
> 
> If a sandglass is traveling near the speed of light does it take longer 
> to empty? Is that because the sand grains get longer and hence tend to 
> be more likely to to get stuck in the hole/

if so just turn it 90 degrees from direction of travel, then they are 
skinny like needles and fall through the hole.

[what if instead of sand, mini-black holes?]

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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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