   Chapter 12, Problem 22PE

Chapter
Section
Textbook Problem

# (a) Calculate the approximate force on a square meter of sail, given the horizontal velocity of the wind is 6.00 m/s parallel to its front surface and 3.50 m/s along its back surface. Take the density of air to be 1.29 kg/m3. (The calculation, based on Bernoulli's principle, is approximate due to the effects of turbulence.) (b) Discuss whether this force is great enough to be effective for propelling a sailboat.

(a)

To determine

The force per square meter of sail.

Explanation

Given:

Initial pressure =P1

Final pressure =P2

Density of air =ρ=1.29 kgm3

Initial speed =v1=3.5 ms

Final speed =v2=6 ms

Area =A=1 m2

Force =F

Formula Used:

Using Bernoulli's theorem

P+ρgh+(0.5)ρv2=constanthence, we get P1+(0.5)ρv12+ρgh1=P2+(0.5)ρv22+ρgh2 for same levelP1+(0.5)ρv12=P2+(0.5)ρv22P1P2=(0

(b)

To determine

Whether the obtained force is great enough to be effective for propelling a sailboat.

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