ITT we solve obscure and inane problems from anons
No.11111224 ViewReplyOriginalReport
Quoted By: >>11111231 >>11111541 >>11111648
The temperature of water in a container is , and the volume of this water is .
There is a drain in the bottom of the container, you can plug or unplug it. You have control over the rate that new water enters the container (which has a maximum and minimum), and control of the temperature of this water (which again has a maximum and minimum).
You're trying to get the container to temperature , and volume as fast as possible.
For any arbitrary starting and finishing values, can you find the minimum time?
Assume that is between the maximum and minimum temperatures of the faucet.
Also, assume that the water in the container is mixed instantly, no convection currents or any of that nonsense.
You can also start adding in new variables if you want. For example, assume the rate that water exits the container is not constant, but depends on the pressure at the bottom of the container (you'd have to know the shape of the container in this case). Or you can assume the container loses heat to the air based on the surface area of water in the container. Or you can even account for temperature-based evaporation.
There is a drain in the bottom of the container, you can plug or unplug it. You have control over the rate that new water enters the container (which has a maximum and minimum), and control of the temperature of this water (which again has a maximum and minimum).
You're trying to get the container to temperature , and volume as fast as possible.
For any arbitrary starting and finishing values, can you find the minimum time?
Assume that is between the maximum and minimum temperatures of the faucet.
Also, assume that the water in the container is mixed instantly, no convection currents or any of that nonsense.
You can also start adding in new variables if you want. For example, assume the rate that water exits the container is not constant, but depends on the pressure at the bottom of the container (you'd have to know the shape of the container in this case). Or you can assume the container loses heat to the air based on the surface area of water in the container. Or you can even account for temperature-based evaporation.
