The top floor of a building is 40m m above the basement. Calculate how much greater the water pressure is in the basement than on the top floor.
Express your answer to two significant figures and include the appropriate units.
To calculate the difference in water pressure between the basement and the top floor of the building, we can use the concept of hydrostatic pressure.
The hydrostatic pressure in a fluid is given by the equation P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.
In this case, we need to find the pressure difference between the basement and the top floor. Since the pressure in the basement is higher than the pressure on the top floor, we can subtract the pressure at the top floor from the pressure in the basement to get the difference.
Let's assume the density of water is 1000 kg/m³ and the acceleration due to gravity is 9.8 m/s² (these are standard values).
For the basement:
P₁ = ρgh₁
P₁ = 1000 kg/m³ * 9.8 m/s² * 40 m
P₁ = 392,000 Pa
For the top floor:
P₂ = ρgh₂
P₂ = 1000 kg/m³ * 9.8 m/s² * 0 m (as the height is zero)
P₂ = 0 Pa
Therefore, the pressure difference is:
ΔP = P₁ - P₂
ΔP = 392,000 Pa - 0 Pa
ΔP = 392,000 Pa
Expressing the answer to two significant figures, the pressure difference is approximately 3.9 x 10⁵ Pa.
Note: Pascal (Pa) is the SI unit of pressure.