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.
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