Pressure at the bottom of a mountain is 105
Pa and at the top of the mountain shows the
pressure as 1.25 x 105
Pa. What could be the height of this mountain?
To solve this problem, we will use the concept of pressure and the relationship between pressure and height in a fluid column.
The pressure at the bottom of the mountain (P1) is 105 Pa, and the pressure at the top of the mountain (P2) is 1.25 x 105 Pa. Let's assume that the density of the fluid (air) remains constant throughout the mountain.
According to the relationship between pressure and height in a fluid column, we have:
P2 - P1 = ρ * g * h
Where:
P2 = Pressure at the top of the mountain = 1.25 x 105 Pa
P1 = Pressure at the bottom of the mountain = 105 Pa
ρ = Density of the fluid (air)
g = Acceleration due to gravity = 9.8 m/s^2
h = Height of the mountain (unknown)
Substituting the given values into the equation:
1.25 x 105 - 105 = ρ * 9.8 * h
1.25 x 105 - 105 = 0.49 * h
1.24 x 105 = 0.49 * h
h = (1.24 x 105) / 0.49
h ≈ 253,061.22 meters
Therefore, the height of this mountain is approximately 253,061.22 meters.