Two streams merge to form a river. One stream has a width of 8.3 m, depth of 3.2 m, and current speed of 2.2 m/s. The other stream is 6.8 m wide and 3.2 m deep, and flows at 2.4 m/s. If the river has width 10.4 m and speed 2.8 m/s, what is its depth?

The depth of the resulting stream is 3.8 meters.

Explanation:

Under the assumption that streams are formed by incompressible fluids, so that volume flow can observed conservation:

(1)

All volume flows are measured in cubic meters per second.

Dimensionally speaking, we can determine the depth of the resulting stream (), in meters, by expanding (1) in this manner:

(2)

- Speed of the merging streams, in meters per second.

- Depth of the merging streams, in meters.

- Width of the merging streams, in meters.

- Width of the resulting stream, in meters.

- Speed of the resulting stream, in meters per second.

If we know that , , , , , , and , then the depth of the resulting stream is:

The depth of the resulting stream is 3.8 meters.

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2