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As a summer intern assigned to the Olympics Kayaking committee, you need to determine the speed of water flowing through a rapids section of the river in order to classify the rapids. For the purposes of your calculation, you assume the river has a rectangular cross section. You determine that for the region of interest, the river narrows from a width of 14 m to a width of 5.0 m and the depth of the river decreases from 2.0 m to 0.92 m. You also know that the speed of the river before the rapids is 1.9 m/s. Determine the speed of the river through the section of rapids.

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Answer:

11.56521 m/s

Explanation:

[tex]A_1[/tex] = Area of first section = [tex]14\times 2[/tex]

[tex]A_2[/tex] = Area of second section = [tex]5\times 0.92[/tex]

[tex]V_1[/tex] = Velocity in first section = 1.9 m/s

[tex]V_2[/tex] = Velocity in second section

From the continuity equation we get

[tex]A_1V_1=A_2V_2\\\Rightarrow V_2=\dfrac{A_1V_1}{A_2}\\\Rightarrow V_2=\dfrac{14\times 2\times 1.9}{5\times 0.92}\\\Rightarrow V_2=11.56521\ m/s[/tex]

The speed of the river through the section of rapids is 11.56521 m/s

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