Physics formula for determining accuracy of clepsydra?

[silverlament]

Hey, new to the site. Sorry if this has already been addressed and I missed it.


For my science fair project I'm thinking of building either a clepsydra or an hour glass and testing it's accuracy. I was just wondering if there were any formulas out there that could help me determine exactly how much water was passing through at any given time or, how to time exact intervals of water (which I'm guessing would be harder)?


Also, if anyone's had experience with either clepsydras (?) or hourglasses and would know which was easier to construct/measure, that would be greatly appreciated .


Thanks so much! <3

[deleted-71572]

New to the site myself, but not new to water...

Your question is about the amount of time it takes for something to happen, in this case, for a certain volume of water (or sand) to flow from one place to another. So your variables are time, volume, and flow rate. Can you think of a simple equation that relates these three things? (Hint: Flow rate is often measured as gallons per minute.)

As for whether it is easier to measure the volume associated with a given time, or time for a given volume, the answer is: It depends on your experimental set-up. In the first case, you are watching your timer, and after a certain amount of time passes, you shut off the flow of water, and measure the volume of water you collected. In the second case, you watch the volume of water, and when it reaches a certain point, you stop your timer, and record the time it took. Which is easier to do, with the set-up you have in mind? Based on the equation you developed, does it make a difference which way you do it?

One thing to keep in mind is that the flow rate might not be constant. You can do a search on Bernoulli's equation and pressure head for discussion on this.

Hope this helps, let me know if you have more questions.

[deleted-71555]

If you look at the clepsydra machine (http://www.britannica.com/clockworks/clepsydra.html) you'll notice the water flow is controlled by a reservoir with a maintained water level (overflow outlet). Roughly, the amount of water accumulated in lower cup moves the clock level, and follows the function:

Volume = S*time
and the
Height = V / S' (S' is the area of the bottom of the lower cup)

where S is speed of the water flow in the tube; it is the function of pressure / force at the tube (depend on the water level of the reservoir, etv ... ) and area of the cross-section of the tube. You should check these things in the text books.

To construct an accurate mechanic clock, only the theory is not enough. You may need a knob to 'fine-tune' the water flow in the tube and calibrate to the accurate atomic clock.