/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 92 How does an airplane wing develo... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 92

How does an airplane wing develop lift?

Short Answer

Expert verified
An airplane wing develops lift due to its special shape known as an 'airfoil' and its movement. When air hits the wing, it splits, causing air to flow faster over the curved top and slower beneath the flat bottom, creating a pressure difference. According to Bernoulli's principle, the slower-moving air beneath the wing exerts more pressure, resulting in an upward force, or lift, which counteracts the airplane's weight, allowing it to fly.

Step by step solution

01

Understanding the Shape of the Wing - Airfoil

An airplane wing, or airfoil, has a special shape where it is curved on the top and flatter on the bottom. When air hits the front of the wing, it gets split into two - with some air going above and some going below the wing.
02

Understanding Movement and Air Pressure

When the airplane moves, air flows faster over the curved top surface and slower beneath the flatter bottom surface. According to Bernoulli's principle, slower-moving air exerts more pressure than faster-moving air, so the pressure beneath the wing is greater than the pressure above it.
03

Creating Lift

This difference in pressure creates an upward force on the wing which is known as lift. This lift force counteracts the weight of the airplane, allowing it to stay airborne or climb to a higher altitude.

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Most popular questions from this chapter

Some experimental data for the viscosity of helium at 1 atm are $$\begin{array}{cccccc}\boldsymbol{T},^{\circ} \mathbf{C} & 0 & 100 & 200 & 300 & 400 \\ \boldsymbol{\mu}, \mathbf{N} \cdot \mathbf{s} / \mathbf{m}^{2}\left(\times \mathbf{1 0}^{5}\right) & 1.86 & 2.31 & 2.72 & 3.11 & 3.46 \end{array}$$ Using the approach described in Appendix A.3, correlate these data to the empirical Sutherland equation \\[\mu=\frac{b T^{1 / 2}}{1+S / T}\\] (where \(T\) is in kelvin) and obtain values for constants \(b\) and \(S\).

The flow field for an atmospheric flow is given by \\[\vec{V}=-\frac{M y}{2 \pi} \hat{i}+\frac{M x}{2 \pi}\\] where \(M=1 \mathrm{s}^{-1}\), and the \(x\) and \(y\) coordinates are the parallel to the local latitude and longitude. Plot the velocity magnitude along the \(x\) axis, along the \(y\) axis, and along the line \(y=x,\) and discuss the velocity direction with respect to these three axes. For each plot use a range \(x\) or \(y=0 \mathrm{km}\) to \(1 \mathrm{km}\). Find the equation for the streamlines and sketch several of them. What does this flow field model?

A viscous clutch is to be made from a pair of closely spaced parallel disks enclosing a thin layer of viscous liquid. Develop algebraic expressions for the torque and the power transmitted by the disk pair, in terms of liquid viscosity, \(\mu\) disk radius, \(R,\) disk spacing, \(a,\) and the angular speeds: \(\omega_{i}\) of the input disk and \(\omega_{o}\) of the output disk. Also develop expressions for the slip ratio, \(s=\Delta \omega / \omega_{i},\) in terms of \(\omega_{i}\) and the torque transmitted. Determine the efficiency, \(\eta,\) in terms of the slip ratio.

Streaklines are traced out by neutrally buoyant marker fluid injected into a flow ficld from a fixed point in space. A particle of the marker fluid that is at point \((x, y)\) at time \(t\) must have passed through the injection point \(\left(x_{0}, y_{0}\right)\) at some earlier instant \(t=\tau .\) The time history of a marker particle may be found by solving the pathline equations for the initial conditions that \(x=x_{0}, y=y_{0}\) when \(t=\tau .\) The present locations of particles on the streakline are obtained by setting \(\tau\) equal to values in the range \(0 \leq \tau \leq t\). Consider the flow ficld \(\vec{V}=a x(1+b t) \hat{i}+c y \hat{j},\) where \(a=c=1 \mathrm{s}^{-1}\) and \(b=0.2 \mathrm{s}^{-1}\). Coordinates are measured in meters. Plot the streakline that passes through the initial point \(\left(x_{0}, y_{0}\right)=(1,1),\) during the interval from \(t=0\) to \(t=3\) s. Compare with the streamline plotted through the same point at the instants \(t=0,1,\) and \(2 \mathrm{s}\).

A flow is described by velocity field \(\vec{V}=a x \hat{i}+b \hat{j},\) where \(a=1 / 5 \mathrm{s}^{-1}\) and \(b=1 \mathrm{m} / \mathrm{s}\). Coordinates are measured in meters. Obtain the equation for the streamline passing through point \((1,1) .\) At \(t=5 \mathrm{s}\), what are the coordinates of the particle that initially (at \(t=0\) ) passed through point (1,1)\(?\) What are its coordinates at \(t=10\) s? Plot the streamline and the initial, \(5 \mathrm{s}\), and 10 s positions of the particle. What conclusions can you draw about the pathline, streamline, and streakline for this flow?
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