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, we need to consider the change in height between the two floors.
The pressure exerted by a vertical column of liquid is given by the equation:
P = ρgh
where P is the pressure, ρ is the density of the liquid, g is the acceleration due to gravity, and h is the height of the column of liquid.
In this case, we only need to consider the difference in height between the basement and the top floor. The height difference is given as 40 m.
Assuming that the density of water is approximately 1000 kg/m^3 and the acceleration due to gravity is approximately 9.8 m/s^2, we can plug these values into the equation to calculate the pressure difference.
P_basement = ρgh_basement
P_top = ρgh_top
The difference in pressure, ΔP, is given by:
ΔP = P_basement - P_top
Substituting the values into the equation:
ΔP = ρgh_basement - ρgh_top
ΔP = ρg(h_basement - h_top)
ΔP = (1000 kg/m^3)(9.8 m/s^2)(40 m - 0 m)
Calculating the difference in pressure:
ΔP = 392,000 N/m^2
Expressing the answer to two significant figures:
ΔP ≈ 390,000 N/m^2
Therefore, the difference in water pressure between the basement and the top floor is approximately 390,000 N/m^2.