Final answer:
To find the depth of a well with a bottom pressure 15 times greater than the pressure at 3 meters depth, we first calculate the pressure due to a water column (P0 = 15P) including atmospheric pressure. Since P0 results in 195m of a water column and atmospheric pressure already contributes 10m at the surface, the additional depth needed is 185m. Option D is correct.
Step-by-step explanation:
To calculate the depth of a well with a bottom pressure that is 15 times the pressure at a depth of 3 meters, we first need to understand that the pressure exerted by a column of water is proportional to the depth of the water and the density of the water, according to the equation P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height or depth of the fluid column.
Given that the atmospheric pressure is equivalent to a 10 m column of water and the pressure at a depth of 3 meters is some value P, we can say that at the bottom of the well, the pressure P₀ is 15 times P. Therefore, P₀ = 15P.
Since P includes both the pressure from the water and atmospheric pressure, we must consider that P = 3m + 10m of water column. Thus, P₀ will be equal to 15(3 m + 10 m), which simplifies to P₀ = 15 × 13 m which is 195 m of water column.
However, since the atmospheric pressure is already accounted for once at the well's surface, we subtract 10 m to find the additional depth of water needed to reach the pressure P₀. Therefore, the well depth h = 195 m - 10 m, which equals 185m.