Air is streaming past a horizontal air plane wing such that its speed in 120 m/s over the upper surface and 90 m/s at the lower surface. If the density of air is 1.3 kg per metre3 and the wing is 10 m long and has an average width of 2m, then the difference of the pressure on the two sides of the wing of :
Correct answer: A. 4095.0 Pascal
- A. 4095.0 Pascal
- B. 409.50 Pascal
- C. 40.950 Pascal
- D. 4.0950 Pascal
Explanation
To find the pressure difference between the upper and lower surfaces of the wing, we apply Bernoulli's equation. Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure. For the upper surface of the wing, the speed is 120 m/s, and for the lower surface, it's 90 m/s. Using the equation for pressure difference, ΔP = 0.5 * density * (v2^2 - v1^2), where v2 is the speed over the upper surface and v1 is the speed under the lower surface, we calculate ΔP = 0.5 * 1.3 * (120^2 - 90^2) = 4095.0 Pascal. Option A is correct. The other options are incorrect because they either misapply Bernoulli's equation or do not account for the correct difference in squared speeds.
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Fluid flow is described through speed, pressure and density, including steady flow and the equation of continuity for conserving mass. Bernoulli's equation relates pressure, speed and height, while fluid drag and terminal velocity explain why a falling object eventually moves at constant speed when drag balances its weight.
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