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A river carries 1500 m³ of water per second. If the river's width is 25 m, what
A river carries 1500 m³ of water per second. If the river's width is 25 m, what is the average depth of the river?
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A river carries 1500 m³ of water per second. If the river's width is 25 m, what is the average depth of the river?
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Discharge = Width × Depth × Velocity. Assuming velocity = 1 m/s, Depth = Discharge / (Width × Velocity) = 1500 m³/s / (25 m × 1 m/s) = 60 m.
Questions & Step-by-step Solutions
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Q: A river carries 1500 m³ of water per second. If the river's width is 25 m, what is the average depth of the river?
Solution:
Discharge = Width × Depth × Velocity. Assuming velocity = 1 m/s, Depth = Discharge / (Width × Velocity) = 1500 m³/s / (25 m × 1 m/s) = 60 m.
Steps: 9
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Step 1: Understand that the river carries 1500 cubic meters of water every second. This is called the discharge.
Step 2: Know that the formula to find the average depth of the river is: Discharge = Width × Depth × Velocity.
Step 3: Identify the width of the river, which is given as 25 meters.
Step 4: Assume the velocity of the water is 1 meter per second (this is a common assumption for this type of problem).
Step 5: Rearrange the formula to find Depth: Depth = Discharge / (Width × Velocity).
Step 6: Plug in the values: Depth = 1500 m³/s / (25 m × 1 m/s).
Step 7: Calculate the denominator: 25 m × 1 m/s = 25 m²/s.
Step 8: Now divide: Depth = 1500 m³/s / 25 m²/s = 60 m.
Step 9: Conclude that the average depth of the river is 60 meters.
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