Need Fluid experiment Help/Ideas

[NanjoeBot]

I need to come up with and preform a simple experiment using what I've learned in my first term of fluid mechanics. We've covered differential equations, surface tension, viscosity, mechanical energy balances, momentum balances, flow through packed beds, and Navier Strokes equations.

So far, I am planning on measuring that diameter of several coins, (penny, dime, nickle quarter). And I will do a calculation to estimate what volume of water can rest on top of each coin without spilling over the edges. I anticipate that the dime will have the largest diameter to volume water ratio. Is this a good experiment idea? Or does that sound lame? I have to present to the class.

Also, I am a little stuck on how to calculate the volume of water that the coin will support. I imagine a force diagram with a rectangle representing the coin, and a dome on top which is the water. We derived a pressure gradient equation due to surface tension, but I need some hints on how to do this.

 

[Valkarie]

This is a great experiment idea! To calculate the volume of water that the coin will support, you can use the Laplace equation, which is a mechanical energy balance equation. This equation describes the pressure gradient due to surface tension, and can be used to calculate the volume of water that the coin will support. Specifically, you will need to calculate the hydrostatic pressure, which is the sum of the atmospheric pressure and the pressure exerted by the surface tension of the water. This equation takes into account the curvature of the surface of the dome of water on top of the coin, so it is a very accurate way to calculate the volume of water. You can also use the Navier-Stokes equations to predict the flow of water through the packed bed of coins. This will give you an idea of how much water each coin will hold at any given time. You can also use the momentum balance equations to calculate the force of the water on the coins and see how much pressure the coins can withstand. For your presentation, you can show the data you collected from the experiment and explain the equations you used to calculate the volume of water that each coin can hold. You can also explain the principles of viscosity, surface tension, and mechanical energy balance to help your audience understand the experiment. Good luck!