Chapter 13: Problem 9

How would the gradient of a stream be affected if a meander is cut off?

Short Answer

Expert verified

When a meander is cut off, the gradient of the stream increases due to the shortening of the stream length while the elevation change remains constant. This results in a steeper slope, which leads to water flowing more rapidly downstream through the straightened section after the meander is cut off.

Step by step solution

Understand the meander and its effect on the stream length

A meander is a winding curve or bend in a river that naturally occurs due to the erosion of the river banks, particularly on the outside of bends and deposition on the inside. This causes the river to take a more tortuous path downstream, increasing the total stream length. When a meander is cut off, the stream effectively shortens, as water takes the more direct course that bypasses the loop that was formed.

Calculate the original gradient

Before cutting off the meander, the stream has a certain gradient. The gradient is given by the change in elevation (ΔElevation) divided by the stream length (L): \(G_{original} = \frac{\Delta Elevation}{L_{original}}\), where \(L_{original}\) represents the original stream length before the cut-off.

Calculate the new gradient

After cutting off the meander, the stream length shortens, leading to a new stream length, \(L_{new}\). The gradient after the cut-off is given by \(G_{new} = \frac{\Delta Elevation}{L_{new}}\), where \(L_{new}\) is the reduced stream length after the meander is cut off.

Compare the original and new gradient

We can analyze how the gradient is affected by cutting off the meander by comparing the two gradients: \(G_{original}\) and \(G_{new}\). Since the elevation change of the stream remains the same, but the stream length decreases after cutting off the meander, the new gradient will be greater than the original gradient (\(G_{new} > G_{original}\)).

Conclude the effect of cutting off the meander on the gradient of the stream

In conclusion, when a meander is cut off, the gradient of the stream increases due to the shortening of the stream length while the elevation change remains constant. This results in a steeper slope, which leads to water flowing more rapidly downstream through the straightened section after the meander is cut off.

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How would the gradient of a stream be affected if a meander is cut off?

Short Answer

Step by step solution

Understand the meander and its effect on the stream length

Calculate the original gradient

Calculate the new gradient

Compare the original and new gradient

Conclude the effect of cutting off the meander on the gradient of the stream

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