| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
The clepsydra, or ancient water clock, was a bowl from which water was
allowed to escape through a small hole in the bottom. It was often
used in Greek and Roman courts to time the speeches of lawyers,
in order to keep them from talking too much.
Derive the shape equation for a clepsydra in which the water level
falls at a constant rate, i.e., dH/dt = -k ?
Regards,
Mike
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 446.1 | not an answer, just a stupid wisecrack | AVANTI::OSMAN | Mon Mar 03 1986 10:58 | 5 | |
I'd imagine the clepsydra works particularly well at limiting lawyer's
speech time if the lawyer is forced to stand under the dripping
water ! -):
/Eric
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| 446.2 | CLT::GILBERT | Juggler of Noterdom | Tue Apr 08 1986 01:45 | 22 | |
Let V be the volume of water, H be the height of the water, t is time, and a(h) is the surface area of the water, at height h above the hole. Now, the water pressure at the hole is proportional to the height (depth?) of the water (at the water escapes at a rate proportional to the pressure); we want the water level to fall at a constant rate; and we have a simple relation involving a(h). These three equations are: dV dH dV dH -- = c H; -- = k; -- = a(H) --; (for some constants c and k) dt dt dt dt some simple algebra gives: a(H) = c H /k For a cross-section, we want to know the radius (not the area) at height H (I assume radial symmetry of this water clock): r(H) = sqrt(a(H)) = sqrt(cH/k) Thus, the cross-section looks like a parabola! | |||||
| 446.3 | A non-round container? | CIMAMT::HAINSWORTH | Many pages make a thick book. | Wed Dec 09 1987 16:14 | 17 |
Another (non-round ) container which satisfies this constraint is an
inverted triangle of constant thickness:
______________ ______
\ / | |
\ / | |
\ / | |
\ / | |
\ / | |
\ / |__ __|
FRONT VIEW SIDE VIEW
This is much easier to construct.
John
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