Derivation of the shape of a clepsydra

In summary, the Clepsydra is a water clock that was used in ancient times. It works by allowing water to escape through a small hole at the bottom, causing the water level to fall at a constant rate. This can be explained using Torricelli's law and the concept of calculus of variations. By finding the shape of the walls of the Clepsydra, one can determine the rate of water flow and ultimately find a simple shape that accurately represents the Clepsydra.
  • #1
jakncoke
16
0

Homework Statement


Clepsydra was a water clock used in old times in which water was allowed to espace through a small hole at the bottom. Find the shape of the clepsydra, if the water level is to fall at a constant rate.


Homework Equations


Torricelli Law


The Attempt at a Solution


No clue.
 
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  • #2
The point is that water falls at a constant rate- that is, the volume of water is reducing at a constant rate dV/dt. If you know the shape of the curve forming the walls (I would assume a volume of rotation), you can find V as a function of h, then you can find dV/dt as a function of dh/dt and find the function so that dh/dt is also constant. In its full generality, this is a "Calculus of Variations" problem but you are probably expected to guess a simple shape and then show it is correct.
 

Related to Derivation of the shape of a clepsydra

What is a clepsydra?

A clepsydra, also known as a water clock, is an ancient device used for measuring time by the regulated flow of water from one container to another.

Who invented the clepsydra?

The earliest recorded inventor of the clepsydra is the Greek mathematician and inventor, Ctesibius, in the 3rd century BC.

How does a clepsydra work?

A clepsydra works by using the principle of the constant flow of water from a higher container to a lower container. As the water level decreases in the lower container, time is measured by markings or graduations on the container.

What is the shape of a clepsydra?

The shape of a clepsydra is typically cylindrical, with a wider base and a narrower top. This shape allows for a constant flow of water and more accurate time measurements.

Why was a clepsydra important in ancient times?

In ancient times, the clepsydra was an important tool for measuring time, which was crucial for various activities such as agriculture, trade, and religious ceremonies. It was also a significant advancement in timekeeping technology compared to other primitive methods.

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