Question

The water in a lake is at 5 °C. A diver measures the pressure of the water at two different depths in the lake. He repeats the measurements on a different day when the water is at 15°C. The density of the water decreases when its temperature increases. Which combination of depth and temperature produces the greatest water pressure?

Answer 1

The pressure of a liquid is given by the formula:

P = ρgh

where P is pressure, ρ is density, g is acceleration due to gravity, and h is depth.

As the temperature of water increases, its density decreases. Therefore, at the same depth, the pressure will be greater when the water is colder.

So, to find the combination of depth and temperature that produces the greatest water pressure, we need to consider the two factors separately.

Assuming the depth is the same in both cases, the greatest water pressure will be produced when the water is at the colder temperature of 5°C.

Conversely, assuming the temperature is the same in both cases, the greatest water pressure will be produced at the greatest depth.

Therefore, without knowing the depth and assuming it's the same in both cases, we can conclude that the combination of greatest water pressure will be at the greatest depth when the water is at 5°C.

Answer 2

The combination of depth and temperature that produces the greatest water pressure is the greatest water density.

As the temperature of the water increases, its density decreases. Therefore, at the colder temperature of 5°C, the water will have a higher density than at the warmer temperature of 15°C.

According to the hydrostatic pressure equation, pressure is directly proportional to the density of the fluid and the depth at which the fluid is located. Therefore, the greatest water pressure will be produced at the greatest water density, which occurs at the colder temperature of 5°C.

Therefore, the combination of the greatest depth and the colder temperature of 5°C will produce the greatest water pressure.