Chapter 22: Problem 69
What three variables influence the speed of stream flow?
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Chapter 22: Problem 69
What three variables influence the speed of stream flow?
These are the key concepts you need to understand to accurately answer the question.
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Name three erosional features caused by groundwater in carbonate rocks.
Darcy's law gives us the volume flow rate-volume per time (for example, cubic meters per day, \(\mathrm{m}^{3} /\) day). Another way to express volume is on a per-unit-area basis. For example, if we have a \(1-\mathrm{m}^{3}\) cube, we know its base is \(1 \mathrm{~m}^{2}\)-the cross-sectional area of the cubeand its height is \(1 \mathrm{~m}\). If we fill the cube with water, we can say we have \(1 \mathrm{~m}\) of water per unit area. Darcy's law can be rearranged to calculate the volume flow rate per unit area. This is called the specific discbarge, which has units of length per time (for example, meters per day, \(\mathrm{m} /\) day). Completing parts (a) through (c) will illustrate how specific discharge is related to the volume flow rate. (Hint: Assume that the units for hydraulic conductivity are \(\mathrm{m} /\) day and the units for cross-sectional area are \(\mathrm{m}^{2}\).) (a) Suppose \(1 \mathrm{~m}^{3}\) of water is pumped from a well into an empty cylindrical tank. If the water level is \(2 \mathrm{~m}\) above the base, what is the cross-sectional area of the tank? (Hint: Volume of a cylinder \(=\pi r^{2} b=\) area of base \(\times\) height.) (b) If it takes half a day to pump the \(1 \mathrm{~m}^{3}\) of water into the tank, what is the flow rate in terms of both volume per unit time and specific discharge? (c) Write Darcy's law so that it calculates the specific discharge.
A particular stream widens as it progresses downstream. Using your answers for parts (a) and (b), briefly describe the changes in discharge. (a) If the cross-sectional area of the stream is \(1 \mathrm{~m}^{2}\) and the stream speed is \(0.5 \mathrm{~m} / \mathrm{s}\), what is the stream's discharge? (b) If the cross-sectional area of the stream increases to \(2 \mathrm{~m}^{2}\) and the stream speed remains \(0.5 \mathrm{~m} / \mathrm{s}\), what is the stream's discharge?
In descending order, rank the rocks in terms of their susceptibility to chemical erosion: (a) marble, (b) limestone, (c) sandstone, (d) quartzite.
How do deposits from glacial ice differ from rocks deposited by rivers?
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