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Question 80079: please help me out with this i need to turn this in soon possible and also this will help me in the rest homework to. thank u
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.
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:
f = 1250/A
where r is the rate of water in gallons per minute, and A is the cross sectional area of the hose in square inces. Does the function obey the Principal of Continuity in Liquid Flow?
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?
3. During the evening fire, the velocity of the water was 100 gallons per minute. What was the cross sectional area of the hose?
Answer by tutorcecilia(2152)   (Show Source):
You can put this solution on YOUR website! r = 1250/A
r= rate of water in gallons per minute
A=cross sectional area of the hose in square inches
QUESTIONS:
1. Does the function obey the Principal of Continuity in Liquid Flow? Yes, because there is an inverse relationship between the rate of the water and the diameter of the cross section of the hose. As the hose gets bigger (larger diameter cross-section), the flow of the water decreases (less presure). As the hose gets smaller (more pressure), the flow of the water increases.
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?
r=1250/A [start with the original formula]
r=1250/(5) [plug-in the value for the cross-section,
which is A=5 and solve for r]
.
r=250 gallons/minute
.
3. During the evening fire, the velocity of the water was 100 gallons per minute. What was the cross sectional area of the hose?
r=1250/A [start with the original formula]
100gallons/minute=1250/A [plug-in the values of the velocity (r=100) and solve for A]
.
100(A)=1250(A)/A
100A=1250
100A/100=1250/100A
A=12.5 inche diameter of the hose.
.
Compare the answers in #2 and #3. In Question #2, The velocity was 250gal/min when the hose was 5 inches. In Question #3, the velocity was 100gal/min when the hose was 12.5inches. The relationship is inversed, when one goes up, the other comes down; when one goes down, the other goes up.
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