Not sure if I'm posting this in the correct forum but it is algebra help I need please.
Design a simple water clock, using a tank, to accurately measure time for a minimum period of 8 hours after which it may be reset.
Principle of operation: water drips from a tank which has markings on the inside. As water drips out, the water level drops, revealing successive hour markings.
Ideally, the hour markings should be equidistant but this can only be achieved with uniform flow, which is dependent on the shape of the tank.
I must use excell to work out calculations on the shape of the tank of the water clock.
Above is a link to my simple shaped tank (square) water clock and you can see in the graph how it takes longer for the tank to empty as the water level decreases.
The second link is to my cone shaped tank water clock. The diameter of the cone decreases towards the bottom of the tank, this means that the volume of water expelling from the hole per 1mm height drop is less. You can see from the graph that this shaped tank is an improvement in that the height of the water decreases at a more steady rate.
My problem is where I go from here? I think an exponential function or natural log function is needed to calculate the rate at which the diameter decreases. This would make a curved shaped tank. I'm thinking the function which will calculate the diameter each mm will need to use the velocity?
Any ideas would be great, thank you.