Wind blows around a skyscraper with a speed of 18 m/s outside a large pane of plate glass. What is the difference in air pressure between the inside and outside of the skyscraper? Take the density of air to be 1.3 kg/m3 and assume the air inside the skyscraper is still.
According to the Bernoulli equation,
delta P = (1/2)*(air density)*V^2
V is the outside velocity, 18 m/s
The pressure difference will be in Pascals
To calculate the difference in air pressure between the inside and outside of the skyscraper, we can use Bernoulli's equation, which states that the sum of the pressure, kinetic energy, and potential energy per unit volume in a fluid is constant.
Let's break down the steps to find the solution:
Step 1: Calculate the kinetic energy of the wind outside the skyscraper:
The kinetic energy per unit volume of a fluid is given by the formula:
KE = 0.5 * ρ * v^2
where KE is the kinetic energy per unit volume, ρ is the density of the fluid, and v is the velocity of the fluid.
Substituting the given values, we have:
KE = 0.5 * 1.3 kg/m^3 * (18 m/s)^2
KE = 0.5 * 1.3 * 324
KE = 210.6 J/m^3
Step 2: Calculate the pressure difference between the inside and outside of the skyscraper using Bernoulli's equation:
Bernoulli's equation can be expressed as:
P + 0.5 * ρ * v^2 + ρ * g * h = constant
where P is the pressure, ρ is the density of the fluid, v is the velocity of the fluid, g is the acceleration due to gravity, and h is the height difference.
Since the wind inside the skyscraper is assumed to be still, its velocity is zero. Therefore, the second term in the equation becomes zero.
We can now rewrite Bernoulli's equation as:
P + 0 + ρ * g * h = constant
Assuming the height difference h is the height of the skyscraper (or the difference in altitude between the inside and outside of the skyscraper), we can solve for the pressure difference:
P = -ρ * g * h
Substituting the given values, we have:
P = -(1.3 kg/m^3) * (9.8 m/s^2) * h
P = -12.74 * h
Therefore, the pressure difference between the inside and outside of the skyscraper is -12.74 times the height difference between them.
Note: The negative sign indicates that the pressure inside the skyscraper is lower than the pressure outside.