Final answer:
The water level in a cylindrical tank with a leak drops at a rate determined by the size of the leak and the height of the water above the leak. Bernoulli's principle or Torricelli's theorem is used to calculate the flow rate, which involves the area of the hole and the water's height.
Step-by-step explanation:
The question 'How fast does the water level drop when a cylindrical tank ⚠ ⚠ ⚠?' implies a scenario where the rate of change in water level is being considered. Among the provided options, the correct context that would involve the water level dropping because of the tank's condition is when the tank has a leak.
In the case of a cylindrical tank with a leak, the speed at which the water level drops depends on factors such as the size of the leak, the height of the water above the leak, and the properties of the water. To determine the flow rate of water leaking from the tank, we can use Bernoulli's principle or Torricelli's theorem, which relates the speed of fluid flowing out of an opening to the height of the fluid above the opening.
An example is provided where a large container of water with a hole of area 10 cm² develops 5 m below the water surface. The flow rate of water from this hole can be calculated using the aforementioned principles. The flow rate (in m³/s) can be determined by the formula V = A ∙ (2gh)¹², where A is the cross-sectional area of the hole, g is the acceleration due to gravity, and h is the height of the water column above the hole.