Question 80080
Given:
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r = 1250/A
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(1) Does this follow the Principle of Continuity which states that the velocity (r) of a liquid 
flowing through a pipe increases as the cross-sectional area of the pipe decreases, 
and decreases as the cross sectional area of the pipe increases. 
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The answer is that it does.  Try it yourself.  Suppose the area is 1 square inch. What is
the velocity (r)?  Substitute 1 for A and you find that r = 1250/1 = 1250 gal per min.
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Next increase the Area to 2 square inches.  Substitute 2 for A and you find that r, the
velocity is now: r = 1250/2 = 625 gal per min.  So as the Area got bigger (increased), 
the velocity got smaller (decreased) ... exactly what the Principle of Continuity 
said it should do.
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(2) Given that the hose for the morning fire had a cross-sectional area of 5 square
inches, what was the velocity of the water?  Just substitute 5 for A and you get:
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r = 1250/5 = 250 gallons per minute
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(3) During the evening fire, the velocity of the water was 100 gallons per minute.
Substitute this value for r in the equation and solve for A, the cross-sectional area:
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100 = 1250/A
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Multiply both sides of the equation by A to eliminate the denominator of A that appears
on the right side:
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100A = 1250
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Next divide both sides of the equation by 100 to find A:
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A = 1250/100 = 12.5 square inches
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Hope this helps you to understand the problem a little better.