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Rainwater draining from a neighborhood street initially travels at 4 ft/s through a pipe with a cross-sectional area of 15.7 ft2. This pipe connects down the street to another pipe with a cross-sectional area of 65.4 ft2. What would be the speed of the water as it moves through this larger pipe?

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okpalawalter8

Answer:

The  velocity  is [tex]v_2 = 0.96 \ ft/s[/tex]

Explanation:

From the question we are told that

   The initial speed is  [tex]v_1 = 4 \ ft/s[/tex]

   The  cross -sectional area of the first pipe is  [tex]A_1 = 15.7 \ ft[/tex]

   The  cross -sectional area of the second pipe is [tex]A_2 = 65.4 \ ft[/tex]

Generally from continuity equation we have that

     [tex]A_1 * v_1 = A_2 * v_2[/tex]

So  

     [tex]v_2 = \frac{A_1 * v_1 }{A_2 }[/tex]

=>   [tex]v_2 = \frac{15.7 * 4 }{65.4 }[/tex]

=>   [tex]v_2 = 0.96 \ ft/s[/tex]

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