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An airplane has a mass of $1.7 \times 10^{6} \mathrm{kg},$ and the air flowspast the lower surface of the wings at 95 $\mathrm{m} / \mathrm{s} .$ If the wingshave a surface area of 1200 $\mathrm{m}^{2}$ , how fast must the air flowover the upper surface of the wing if the plane is to stay inthe air?

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$$170 \mathrm{m} / \mathrm{s}$$

Physics 101 Mechanics

Chapter 13

Fluids

Fluid Mechanics

University of Washington

University of Winnipeg

McMaster University

Lectures

03:45

In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids.

09:49

A fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases and plasmas. Fluids display properties such as flow, pressure, and tension, which can be described with a fluid model. For example, liquids form a surface which exerts a force on other objects in contact with it, and is the basis for the forces of capillarity and cohesion. Fluids are a continuum (or "continuous" in some sense) which means that they cannot be strictly separated into separate pieces. However, there are theoretical limits to the divisibility of fluids. Fluids are in contrast to solids, which are able to sustain a shear stress with no tendency to continue deforming.

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So here we're going to, um, first to find, say that the pressure at the top here we know that the upward force, due to the air pressure on the bottom of the wing, must be equal to the weight of the airplane, plus the downward force due to air pressure on the top of the wing. And so then we're going to apply Bernoulli's equation. So the pressure at the top of the wing times the area plus the weight of the airplane itself equals the pressure at the bottom of the wing bot times the area. And so we can say that then the difference in pressures between the bottom of the wing and the top of the wing will be equal to the weight of the airplane divided by the area of the wing. We're going to apply Bernoulli's equation. The atmospheric pressure, plus the, uh, pressure at the bottom plus 1/2 times wrote the velocity at the bottom squared plus road G. Why at the bottom equals the atmospheric pressure, plus the pressure at the top plus 1/2 times row, the density of the the velocity at the top squared plus road G. Why at the top. We can then say that the velocity at the top squared would be equaling two times the pressure at the bottom of the wing minus the pressure at the top of the wing divided by row plus the velocity at the bottom of the wing squared. And so we can then say that the velocity at the top of the wing would be equaling the square root of two. And then we'd substitute this for mg over a so it would be too g over road times, eh? Plus the velocity at the bottom squared. And now we can, uh, substitute and solve. So then the velocity at the top would be equaling the square root of two times the weight. So two times 1.7 times 10 to the sixth kilograms multiplied by 9.80 meters per second squared. This would be divided by the density of air, 1.29 kilograms per cubic meter multiplied by the area of the wing, 1200 meters squared. And then this would be plus the velocity at the bottom. We know to be 95 meters per second quantity squared, and so the velocity of the air on top of the wing would be approximately 175 meters per second. This would be our final answer. That is the end of the solution. Thank you. For what?

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