To determine the height of a water column producing the same pressure as a 60 cm mercury column, you can use the formula relating pressure, height, density, and gravity:
P = h * ρ * g
For mercury:
P = h_mercury * ρ_mercury * g
Given:
h_mercury = 60 cm = 0.6 m (as 100 cm = 1 m)
ρ_mercury = 13.6 * 10^3 kg/m³
g (acceleration due to gravity) is approximately 9.81 m/s² (but it cancels out in this calculation, so we won't use its value)
We can calculate the pressure:
P = 0.6 m * 13.6 * 10^3 kg/m³ * g
For water, let's call the height of the water column h_water, and the density of water (ρ_water) is 1 * 10^3 kg/m³. The pressure from the water column will be the same as the pressure from the mercury column, so we have:
h_water * 1 * 10^3 kg/m³ * g = 0.6 m * 13.6 * 10^3 kg/m³ * g
Now we cancel g from both sides and solve for h_water:
h_water = (0.6 m * 13.6 * 10^3) / (1 * 10^3)
h_water = 0.6 m * 13.6
h_water = 8.16 m
So the height of the water column would be 8.16 meters.
