- #1
ramb
- 13
- 0
Hi,
My differential equations professor wanted us to think about this problem:
How would you go about modeling the rate at which water raises on a paper towel dipped into a puddle with fixed water level.
I figure this would be a differential equation, but I'm not sure as to the form of this. He hinted that the solution could be, say a number raised to the variable, or the variable raised to a power.
I'm having trouble with the physics. Initially, in the in class experiment, the paper towel soaked up the water very, very fast at first (within the first couple of seconds), then slowed down dramatically, Further, we found that the soaking level does not go past a certain point in the paper towel after a long time - and that when this experiment was repeated, it stopped at the same place. We figured that it had to do with the rate at which the water was evaporating was making up for the flow rate that the water was going upwards the towel.
So the differential equation should involve both evaporation, something to do with the towel's absorbtion, and gravity, right? The independent variable should be time, and the dependent variable should be the height on the towel the water has gotten to.
Thanks
My differential equations professor wanted us to think about this problem:
How would you go about modeling the rate at which water raises on a paper towel dipped into a puddle with fixed water level.
I figure this would be a differential equation, but I'm not sure as to the form of this. He hinted that the solution could be, say a number raised to the variable, or the variable raised to a power.
I'm having trouble with the physics. Initially, in the in class experiment, the paper towel soaked up the water very, very fast at first (within the first couple of seconds), then slowed down dramatically, Further, we found that the soaking level does not go past a certain point in the paper towel after a long time - and that when this experiment was repeated, it stopped at the same place. We figured that it had to do with the rate at which the water was evaporating was making up for the flow rate that the water was going upwards the towel.
So the differential equation should involve both evaporation, something to do with the towel's absorbtion, and gravity, right? The independent variable should be time, and the dependent variable should be the height on the towel the water has gotten to.
Thanks