document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80080>Question 80080</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Hydrodynamics is the branch of physics that studies the behavior of liquids that are in motion. For example, The Principal of Continuity in Liquid Flow states that the velocity 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. \r<BR>\n" );
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document.write( "On a given day, a fire department uses the same pump to put out two fires. The rate of water is given by the rational function:<BR>\n" );
document.write( "r = 1250/A<BR>\n" );
document.write( "where r is the rate of water in gallons per minute, and A is the cross sectional area of the hose in square inches. Does the function obey the Principle of Continuity in Liquid Flow? <BR>\n" );
document.write( "2. During the morning fire, the fire department used a hose with a cross sectional area of 5 square inches. What was the velocity of the water? <BR>\n" );
document.write( "3. During the evening fire, the velocity of the water was 100 gallons per minute. What was the cross sectional area of the hose?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57442 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=57442\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "r = 1250/A<BR>\n" );
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document.write( "(1) Does this follow the Principle of Continuity which states that the velocity (r) of a liquid <BR>\n" );
document.write( "flowing through a pipe increases as the cross-sectional area of the pipe decreases, <BR>\n" );
document.write( "and decreases as the cross sectional area of the pipe increases. <BR>\n" );
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document.write( "The answer is that it does.  Try it yourself.  Suppose the area is 1 square inch. What is<BR>\n" );
document.write( "the velocity (r)?  Substitute 1 for A and you find that r = 1250/1 = 1250 gal per min.<BR>\n" );
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document.write( "Next increase the Area to 2 square inches.  Substitute 2 for A and you find that r, the<BR>\n" );
document.write( "velocity is now: r = 1250/2 = 625 gal per min.  So as the Area got bigger (increased), <BR>\n" );
document.write( "the velocity got smaller (decreased) ... exactly what the Principle of Continuity <BR>\n" );
document.write( "said it should do.<BR>\n" );
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document.write( "(2) Given that the hose for the morning fire had a cross-sectional area of 5 square<BR>\n" );
document.write( "inches, what was the velocity of the water?  Just substitute 5 for A and you get:<BR>\n" );
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document.write( "r = 1250/5 = 250 gallons per minute<BR>\n" );
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document.write( "(3) During the evening fire, the velocity of the water was 100 gallons per minute.<BR>\n" );
document.write( "Substitute this value for r in the equation and solve for A, the cross-sectional area:<BR>\n" );
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document.write( "100 = 1250/A<BR>\n" );
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document.write( "Multiply both sides of the equation by A to eliminate the denominator of A that appears<BR>\n" );
document.write( "on the right side:<BR>\n" );
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document.write( "100A = 1250<BR>\n" );
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document.write( "Next divide both sides of the equation by 100 to find A:<BR>\n" );
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document.write( "A = 1250/100 = 12.5 square inches<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. </SPAN>\n" );
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