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Chapter 3: Problem 15

Air flows smoothly over the hood of your car and up past the windshield. However, a bug in the air does not follow the same path; it becomes splattered against the windshield. Explain why this is so.

Short Answer

Expert verified
The bug gets splattered on the car's windshield because, unlike the air, the bug has mass and therefore inertia. So, while the air follows the curved path over the car due to pressure difference (Bernoulli's principle), the bug continues its straight-line path due to inertia and hits the windshield.

Step by step solution

01

Understand Bernoulli's principle

According to Bernoulli's principle, faster-moving fluid (air, in this case) exerts less pressure than slower-moving fluid. When a car moves, the air above the car (over the hood and the windshield) moves faster than the air coming directly against the car. This causes a pressure difference.
02

Discuss the bug's inertia

The bug that's carried by the air also experiences this pressure difference. However, the bug has mass and hence, inertia. Once the airspeeds up over the car's hood, the bug does not have time to adjust to that speed because of its inertia; it continues to travel in a straight line as per Newton's first law.
03

Explain the splattering of bug

Because of its inertia, the bug doesn't follow the fast-moving air curve over the car's hood. Instead, it follows its initial straight-line path which leads directly into the windscreen, hence getting splattered.

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Most popular questions from this chapter

The Bemoulli equation is valid for steady, inviscid, incompressible flows with constant acceleration of gravity. Consider flow on a planet where the acceleration of gravity varies with height so that \(g=g_{0}-c z,\) where \(g_{0}\) and \(c\) are constants. Integrate \(" \mathbf{F}=m \mathbf{a}^{\prime \prime}\) along a streamline to obtain the equivalent of the Bernoulli equation for this flow.

A small card is placed on top of a spool as shown in Fig. \(P 3.121 .\) It is not possible to blow the card off the spool by blowing air through the hole in the center of the spool. The harder one blows, the harder the card "sticks" to the spool. In fact by blowing hard enough it is possible to keep the card against the spool with the spool turned upside down. Give this experiment a try. (Note: It may be necessary to use a thumb tack to prevent the card from sliding from the spool.) Explain this phenomenon.

Figure \(P 3.119\) shows two tall towers. Air at \(10^{\circ} \mathrm{C}\) is blowing toward the two towers at \(V_{0}=30 \mathrm{km} / \mathrm{hr}\). If the two towers are \(10 \mathrm{m}\) apart and half the air flow approaching the two towers passes between them, find the minimum air pressure between the two towers. Assume constant air density, inviscid flow, and steady-state conditions. The atmospheric pressure is \(101 \mathrm{kPa}\).

Consider a compressible liquid that has a constant bulk modulus. Integrate \(^{*} \mathbf{F}=m \mathbf{a}^{\prime \prime}\) along a streamline to obtain the equivalent of the Bernoulli equation for this flow. Assume steady, invicid flow.

Water flows in a vertical pipe of 0.15 -m diameter at a rate of \(0.2 \mathrm{m}^{3} / \mathrm{s}\) and a pressure of \(200 \mathrm{kPa}\) at an elevation of \(25 \mathrm{m}\). Determine the velocity head and pressure head at elevations of 20 end 55 m.
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