The truck in that example is traveling at 19 m/s. The density of air is 1.29 kg/m3. By how much does the pressure inside the cargo area beneath the tarpaulin exceed the outside pressure?
Try, .5*1.29kg/m^3*(19)^2
Should equal 232.845Pa
To determine the pressure difference between the inside and outside of the cargo area beneath the tarpaulin, we can use the Bernoulli's equation, which relates the velocity and pressure of a fluid.
The formula for Bernoulli's equation is:
P₁ + 0.5 × ρ × v₁² = P₂ + 0.5 × ρ × v₂²
where:
P₁ and P₂ are the initial and final pressures (inside and outside the cargo area).
ρ is the density of air.
v₁ and v₂ are the initial and final velocities (inside and outside the cargo area).
Given:
v₁ = 0 m/s (since the cargo area is stationary).
v₂ = 19 m/s (the truck's velocity).
ρ = 1.29 kg/m³ (density of air).
Substituting these values into Bernoulli's equation, we get:
P₁ + 0.5 × 1.29 × 0² = P₂ + 0.5 × 1.29 × 19²
Simplifying the equation, we have:
P₁ = P₂ + 0.5 × 1.29 × 19²
Since the truck is moving, the outside pressure (P₂) is atmospheric pressure (typically around 101,325 Pa).
Let's calculate the pressure difference:
P₁ = P₂ + 0.5 × 1.29 × 19²
P₁ = 101,325 Pa + 0.5 × 1.29 × 19²
Using a calculator, we can determine P₁:
P₁ ≈ 133,351.06 Pa
Therefore, the pressure inside the cargo area beneath the tarpaulin exceeds the outside pressure by approximately 133,351.06 Pa.
To determine how much the pressure inside the cargo area beneath the tarpaulin exceeds the outside pressure, you would need additional information such as the speed of the truck relative to the air and the area of the tarpaulin. However, I can explain the concept behind this scenario and guide you on how to calculate it once you have all the necessary information.
When a truck is moving, the air around it experiences a change in velocity. This change in velocity creates a pressure difference known as the Bernoulli effect. The Bernoulli principle states that as the speed of a fluid (in this case, air) increases, its pressure decreases, and vice versa.
To calculate the pressure difference, you would need the speed of the truck relative to the air. Let's assume the truck's speed relative to the air is 19 m/s (as mentioned in the question). You would also need the area of the tarpaulin that is creating the pressure difference.
Once you have the speed and the area, you can now calculate the pressure difference using the Bernoulli equation:
ΔP = 0.5 * ρ * v^2
Where:
ΔP is the pressure difference
ρ is the density of air (given as 1.29 kg/m^3)
v is the speed of the truck relative to the air (given as 19 m/s)
Substituting the given values:
ΔP = 0.5 * 1.29 kg/m^3 * (19 m/s)^2
Simplifying the equation:
ΔP = 0.5 * 1.29 * 361
ΔP = 233.295 Pa
Therefore, the pressure inside the cargo area beneath the tarpaulin exceeds the outside pressure by approximately 233.295 Pascal (Pa).