```Question 80080
Given:
.
r = 1250/A
.
(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.
.
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.
.
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.
.
(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:
.
r = 1250/5 = 250 gallons per minute
.
(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:
.
100 = 1250/A
.
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
.
Next divide both sides of the equation by 100 to find A:
.
A = 1250/100 = 12.5 square inches
.
Hope this helps you to understand the problem a little better.```