1)The barometric height in a town is 70cm/Hg,given that the standard atmospheric pressure is 76cm/Hg and the density of mercury is 13600kg/m3,determine the altitude of the town (density of air is 125kg/m3

1 answer

To determine the altitude of the town, we need to use the relationship between pressure, density, and height in a fluid.

Using the equation:

P = ρgh

Where:
P = pressure (in Pascal)
ρ = density (in kg/m^3)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height (in meters)

We are given that the standard atmospheric pressure is 76 cm/Hg, which is equivalent to (76 cm/Hg * 1 m/100 cm * 13600 kg/m^3) = 10416.8 Pa.

We are also given that the barometric height in the town is 70 cm/Hg, which is equivalent to (70 cm/Hg * 1 m/100 cm * 13600 kg/m^3) = 9520 Pa.

Using these values, we can calculate the difference in pressure between the standard atmospheric pressure and the town's barometric pressure:

ΔP = P_standard - P_town
ΔP = 10416.8 Pa - 9520 Pa
ΔP = 896.8 Pa

Now, we can use this pressure difference to find the height (altitude) of the town using the equation:

ΔP = ρgh

Rearranging the equation to solve for h:
h = ΔP / (ρg)

Plugging in the known values:

h = 896.8 Pa / (125 kg/m^3 * 9.8 m/s^2)
h ≈ 7.3 meters

Therefore, the altitude of the town is approximately 7.3 meters.