Exploring the Mathematics of Water Clocks

In summary, the conversation discusses the ancient water clock, specifically its self-regulating ability achieved by a float. The Bernoulli Equation is mentioned as a place to start looking for more information about the mathematics involved. The group also discusses the fluctuation of height without the float, with some members suggesting it would result in overflowing. Finally, the conversation touches on the rate of flow and its relationship to the height of the water in the clock.
  • #1
hanson
319
0
Hi all!
I'm finding information about the ancient time counting machine --- water clock, as shown in the figure.
I know that the water clock invented by Ktesibios has a self-regulating ability. This is achieved by a float.
Anyone got more information about the mathematics involved?
 

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  • #2
Since it is a cone shaped level float, the level changes the effective flow area of the supply line coming into the tank. This is exactly the same principle as a modern day flow regulator.

The Bernoulli Equation would be an appropriate place to start looking.
 
  • #3
can anyone help to derive the fluctuation of height h, if the float is absent? This is a typical control problem I suppose.
 
  • #4
Can't help with the math... sorry. I assume, however, that since the float is there to keep the tank from overflowing, that's exactly what would happen if it wasn't there.
 
  • #5
Looks like just a differential equation problem to me. There is no control system if the float is removed.

Rate of flow IN is constant (if the inlet is always above the surface of the water). Rate of flow OUT is a function of height. So the height is a function of geometry and the two flows.
 

1. How does a water clock work?

A water clock works by using the flow of water to measure time. The clock consists of a container with markings to indicate the passing of time, and a small hole or tube at the bottom for the water to flow out of. As the water flows out, the level of water in the container decreases, indicating the passage of time.

2. What is the relationship between the flow rate of water and the passage of time in a water clock?

The flow rate of water is directly proportional to the passage of time in a water clock. This means that the faster the water flows out of the clock, the quicker the time will pass. Similarly, if the flow rate is slower, the time will pass at a slower rate.

3. How accurate is a water clock in measuring time?

The accuracy of a water clock depends on various factors such as the uniformity of the flow of water, the size and shape of the container, and the precision of the markings. Generally, water clocks are not as accurate as modern timekeeping devices such as digital clocks, but they can still provide a fairly accurate measure of time.

4. Can a water clock be used to measure time for long durations?

Yes, a water clock can be used to measure time for long durations. However, it may require frequent refilling of water and adjustments to ensure accuracy. Additionally, external factors such as changes in temperature and atmospheric pressure can also affect the accuracy of a water clock over long periods of time.

5. What are the advantages of using a water clock over other timekeeping devices?

One advantage of using a water clock is that it does not require any external power source to function, making it a reliable timekeeping device in areas without electricity. Additionally, it can also serve as a decorative piece and a visual representation of the passage of time.

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