Question

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.

Answer 1

Answer:

11.56521 m/s

Explanation:

$A_1$ = Area of first section = $14\times 2$

$A_2$ = Area of second section = $5\times 0.92$

$V_1$ = Velocity in first section = 1.9 m/s

$V_2$ = Velocity in second section

From the continuity equation we get

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

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