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

11.56521 m/s

Step-by-step explanation:

`A_1` = Area of first section =
`14* 2`

`A_2` = Area of second section =
`5* 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=(A_1V_1)/(A_2)\\\Rightarrow V_2=(14* 2* 1.9)/(5* 0.92)\\\Rightarrow V_2=11.56521\ m/s`

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