Question

A stream is flowing down a slope into a larger river. The elevation of the head of the stream is 2,200 feet above sea level. The elevation of the mouth of the stream is 1,000 feet. The horizontal distance along the stream between those two points is 63,360 feet. What is the gradient of the slope the stream is flowing over in ft/mi

Answer 1

`100\ \text{ft/mi}`

Explanation:

Elevation of the head of the stream is 2,200 feet above sea level

Elevation of the mouth of the stream is 1,000 feet

Rise =
`2200-1000=1200\ \text{ft}`

Distance between the two points =
`63360\ \text{ft}=(63360)/(5280)=12\ \text{mi}` = Run

Gradient is given by

`\frac{\text{Rise}}{\text{Run}}=(1200)/(12)\\ =100\ \text{ft/mi}`

The gradient of the slope the stream is flowing over is
`100\ \text{ft/mi}`.