Question

If a stream originates at 6000 meters above sea level and travels 2500 kilometers to the ocean, what is its average gradient in meters per kilometer?

Short answer

The stream's average gradient is approximately 2.4 meters per kilometer.

Step-by-step solution

Identify the total elevation change

The stream begins at an elevation of 6000 meters and ends at 0 meters, because the ocean is at sea level. The total elevation change is the difference between the starting elevation and the ending elevation. Therefore, the total elevation change is \[ 6000 - 0 = 6000 \text{ meters}. \]

Measure the total horizontal distance

The total distance traveled by the stream until it reaches the ocean is given as 2500 kilometers. We use this value as the total horizontal distance.

Calculate the average gradient

The average gradient of the stream is found by dividing the total elevation change by the total horizontal distance. Hence, the formula for average gradient is \[ \text{Average Gradient} = \frac{\text{Total Elevation Change}}{\text{Total Horizontal Distance}} = \frac{6000}{2500} \approx 2.4 \text{ meters per kilometer}.\]

Key concepts

Elevation Change

Elevation change refers to the difference in height from the starting point to the end point of a stream's journey. It is an important factor when considering the gradient of the stream.
For this exercise, the stream starts at 6000 meters above sea level and flows down to the ocean, which is at 0 meters.

• This straightforward calculation is: \( 6000 - 0 = 6000 \text{ meters} \).
• The elevation change helps determine how steep the stream is on its path to the ocean.

Understanding how elevation change impacts flow can aid in predicting water speed and erosion potential in streams.

Horizontal Distance

Horizontal distance is the total length of the stream as it flows towards its endpoint, in this case, the ocean.
Unlike elevation change, horizontal distance does not alter based on height. Instead, it measures the "straight-line" ground distance between two points.

• In this example, the entire path of the stream covers 2500 kilometers.
• This distance is a crucial component when calculating the average gradient.

Such measurement helps in understanding the scale and reach of water systems across landscapes.

Average Gradient

Average gradient is a measure of how steep or gentle the slope of a stream is over its course.
It indicates how much elevation is lost for each unit of horizontal distance traveled.

To calculate the average gradient, use the formula: \[ \text{Average Gradient} = \frac{\text{Total Elevation Change}}{\text{Total Horizontal Distance}} \] For this stream, it is \[ \frac{6000}{2500} \approx 2.4 \, \text{meters per kilometer} \].

• This tells us that for every kilometer of horizontal distance, the elevation drops by about 2.4 meters.
• This value assists in understanding the stream's flow characteristics.

Steeper slopes tend to lead to faster flows, potentially increasing erosion speed, while gentler slopes have slower moving water.

Meters per Kilometer

Meters per kilometer is a common unit of measurement used to describe the gradient. It shows the amount of elevation change per unit of distance.
Specifically, this number indicates the stream's average vertical drop for every kilometer it travels horizontally.

• In this problem, we find the stream's gradient to be 2.4 meters per kilometer.
• This means that the terrain "drops" 2.4 meters for every kilometer of horizontal map distance covered.

Such units provide a clear and easy-to-understand way to interpret and compare stream gradients across different regions.