Answer :
Air Pressure
The pressure on the upper surface of the airplane wing can be calculated by finding the weight of the airplane, then determining the pressure difference between the upper and lower surface. The weight is due to the pressure difference over the wing's area, with the upper pressure being the lower pressure minus this difference. The upper pressure thus calculated is 59020 Pascal.
The question is about calculating the pressure on the upper surface of an airplane wing which is in level flight at an elevation of 4000 meters. In order to find this out, we need to know the pressure difference between the upper and lower surfaces of the wing, which is related to the airplane's weight and wing's area. The weight can be found by multiplying the airplane's mass (8000 kg) by the gravity (9.8 m/s^2), which gives us 78400 N. This force is the result of the pressure difference over the wing's area (80 m^2).
So, the pressure difference (ΔP) is weight/area = 78400 N / 80 m^2 = 980 Pa (Pascal). Therefore, if the lower pressure is 6.0 x 10^4 Pa (Pascal), the upper pressure will be that value minus the pressure difference, which results in: upper pressure = 6.0 x 10^4 Pa - 980 Pa = 59020 Pa.
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The pressure at the upper surface of the wing is approximately [tex]\( 4.0 \times 10^4 \)[/tex] Pascals. This calculation is based on the principle of lift in aerodynamics, where the difference in pressure between the lower and upper surfaces of the wing generates the necessary lift force to keep the airplane in level flight.
Calculation Details:
1. Identifying Required Lift Force:
- The lift force must equal the weight of the airplane for level flight.
- Weight [tex]\( W = \text{mass} \times \text{gravity} = 8000 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 78480 \, \text{N} \)[/tex].
2. Calculating Pressure Difference:
- Lift force is also the product of pressure difference across the wings and wing area.
- [tex]\( \text{Lift Force} = \text{Pressure Difference} \times \text{Wing Area} \)[/tex].
- Rearranging, [tex]\( \text{Pressure Difference} = \frac{\text{Lift Force}}{\text{Wing Area}} \)[/tex].
3. Computing Pressure at Upper Surface:
- Given: Pressure at lower surface is [tex]\( 6.0 \times 10^4 \) Pascals and Wing Area is \( 80 \, \text{m}^2 \)[/tex].
- [tex]\( \text{Pressure Difference} = \frac{78480 \, \text{N}}{80 \, \text{m}^2} = 981 \, \text{Pascals} \)[/tex].
- Pressure at upper surface = Pressure at lower surface - Pressure Difference.
- [tex]\( \text{Pressure at Upper Surface} = 6.0 \times 10^4 \, \text{Pascals} - 981 \, \text{Pascals} \approx 4.0 \times 10^4 \, \text{Pascals} \)[/tex].
Thus, the pressure at the upper surface of the wing during level flight at an elevation of 4000 meters is approximately [tex]\( 4.0 \times 10^4 \)[/tex] Pascals.
