Assume that 60.0 m/s wind (during a hurricane) is blowing past a 1.50 m by 1.50 m glass windo in a house. Find (a) the pressure difference "delta"P=P(in)-P(out) and (b) the force (Magnus force)tending to blow this window outward. Let the air density p=1.20 kg/m^3.
To find the pressure difference and the force exerted on the window, we can use Bernoulli's principle and the Magnus effect.
(a) Pressure difference (ΔP):
According to Bernoulli's principle, the pressure difference between two points in a fluid can be calculated using the formula:
ΔP = 0.5 * ρ * v^2
Where:
ΔP is the pressure difference,
ρ is the air density, and
v is the velocity of the wind.
Given:
ρ = 1.20 kg/m^3 (air density)
v = 60.0 m/s (wind velocity)
Plugging in the values:
ΔP = 0.5 * 1.20 * (60.0)^2
Calculating:
ΔP = 0.5 * 1.20 * 3600
ΔP = 2160 Pa
Therefore, the pressure difference (ΔP) is 2160 Pa.
(b) Magnus force:
The Magnus force acts perpendicular to the direction of the wind flow. It is given by the formula:
F = ΔP * A
Where:
F is the force,
ΔP is the pressure difference, and
A is the area of the window.
Given:
ΔP = 2160 Pa (pressure difference)
A = 1.50 m * 1.50 m = 2.25 m^2 (area of the window)
Plugging in the values:
F = 2160 * 2.25
Calculating:
F = 4860 N
Therefore, the force (Magnus force) exerted on the window is 4860 N.