To determine the gauge pressure at the ground floor, we can use the concept of hydrostatic pressure. The hydrostatic pressure in a fluid column is directly proportional to the height of the column.
Assuming the density of water to be constant, we can use the formula:
P = ρgh
where: P = pressure ρ = density of water (approximately 1000 kg/m³) g = acceleration due to gravity (approximately 9.8 m/s²) h = height of the fluid column
Given that the height of the high-rise building is 100 meters and the gauge pressure at the roof deck is 80 psi (pounds per square inch), we first convert the pressure to SI units (Pascal).
1 psi ≈ 6894.76 Pa
Therefore, 80 psi ≈ 80 * 6894.76 Pa ≈ 551,580 Pa
Now, we can calculate the gauge pressure at the ground floor:
P_ground = P_roof - ρgh
where: P_ground = gauge pressure at the ground floor (in Pa) P_roof = gauge pressure at the roof deck (in Pa) ρ = density of water (approximately 1000 kg/m³) g = acceleration due to gravity (approximately 9.8 m/s²) h = height of the building (in meters)
Plugging in the values:
P_ground = 551,580 Pa - (1000 kg/m³ * 9.8 m/s² * 100 m)
P_ground ≈ 551,580 Pa - 980,000 Pa
P_ground ≈ -428,420 Pa
However, it's important to note that a negative gauge pressure does not make physical sense in this context. It indicates that the pressure at the ground floor would be lower than the reference pressure (atmospheric pressure).
In a realistic scenario, we would expect the pressure at the ground floor to be slightly lower than the pressure at the roof deck due to factors such as frictional losses, but it would still be above atmospheric pressure.