Question

Many adventures like to go rafting on the Colorado River through Grand Canyon National Park. There are many locations where the river becomes more narrow, both the distance between the canyon walls as well as the depth changes due to debris like boulders on the bottom of the river; this leads to changes in the water speed. In the park, the Colorado River has an average width of 100m and an average depth of 8m, and an average speed of 3 m/s. At the Lava Falls Rapids, the river has an average width of about 25m and an average depth of about 15m. What is the approximate speed of the water in this location

Answer 1

6.4 m/s

Step-by-step explanation:

Given that :

The average width of the Colorado river = 100 m

Average depth of the river is = 8 m

Therefore, area =
`$A_1= 100 \ m * 8 \ m$`

Speed of the river,
`$v_1 = 3 \ m/s$`

After the lava falls on the river,

Width of the river becomes = 25 m

Depth of the river became = 15 m

Therefore, area =
`$A_2= 25 \ m * 15 \ m$`

Now, since the volume flow rate of the Colorado river is same, then from the Continuity equation,

`$Q_1=Q_2$`

`$A_1v_1=A_2v_2$`

∴
`$100 * 8 *3 = 25 * 15 * v_2$`

`$v_2=(100 * 8 * 3)/(25 * 15)$`

= 6.4 m/s

Therefore, the speed of the river in this location is 6.4 m/s