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Chapter 14: Problem 10

The elevation of the Fraser River at Hope is \(41 \mathrm{~m}\). From there it flows approximately \(147 \mathrm{~km}\) to the sea. What is the average gradient of the river \((\mathrm{m} / \mathrm{km})\) over this distance?

Short Answer

Expert verified
The average gradient of the river is approximately 0.279 m/km.

Step by step solution

01

Define the elevation drop

The elevation of the Fraser River at Hope is given as 41 meters. When it reaches the sea, its elevation is 0 meters. Thus, the elevation drop is 41 meters.
02

Measure the distance to the sea

The distance from Hope to the sea is given as 147 kilometers.
03

Calculate the gradient formula

The gradient is calculated by dividing the elevation drop by the distance. Use the formula: gradient = \( \frac{\text{elevation drop}}{\text{distance}} \)
04

Perform the calculation

Substitute the values into the formula: gradient = \( \frac{41 \text{ m}}{147 \text{ km}} \) Perform the division: gradient \approx 0.279 \text{ m/km}

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

elevation drop
To understand the concept of elevation drop, imagine a river flowing from a high point to a lower point. The elevation drop is the difference in height between these two points. In this example, the Fraser River starts at Hope with an elevation of 41 meters and flows down to sea level, which is 0 meters. So, the elevation drop is simply the difference:
  • Starting elevation: 41 meters
  • Ending elevation: 0 meters
  • Elevation drop: 41 meters (41 m - 0 m = 41 m)
Understanding elevation drop is crucial because it tells us how much the river descends over its course.
distance measurement
Distance measurement is all about knowing how far the river travels from one point to another. For the Fraser River, we are looking at the distance from Hope to the sea. This distance is given as approximately 147 kilometers.
  • Distance from Hope to the sea: 147 km
Accurately measuring this distance is important for calculating the gradient, which we will discuss next. It鈥檚 like measuring the length of a path the river takes as it flows downstream.
gradient formula
The gradient formula helps us understand how steep or gentle the slope of the river is over a given distance. The formula to calculate the gradient is:
\[ \text{gradient} = \frac{\text{elevation drop}}{\text{distance}} \]
  • Elevation drop: 41 meters
  • Distance: 147 kilometers
So, applying these values in the formula, we get:
\[ \text{gradient} = \frac{41 \text{ m}}{147 \text{ km}} \approx 0.279 \text{ m/km} \] This result means that for every kilometer the Fraser River travels, it drops an average of 0.279 meters in elevation.
Fraser River
The Fraser River is a significant waterway in British Columbia, Canada. It originates in the Rocky Mountains and flows through various landscapes before reaching the Pacific Ocean. Let's break down some interesting details:
  • The Fraser River is approximately 1,375 kilometers long.
  • It brings life to a diverse range of ecosystems along its path.
  • Hope is one of the key locations where the river鈥檚 elevation is notably measured.
Understanding the characteristics of the Fraser River helps contextualize why and how we calculate its gradient, as we did in the example. Knowing the gradient helps with planning and managing resources, as well as with environmental studies.

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Most popular questions from this chapter

How do BC's coastal streams differ from most of the rest of the streams in Canada in terms of their annual flow patterns? Why?
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