The lowest notch shown on this figure is 9 ?meters wide and 5 ?meters high from its base. The river has a velocity of 1 ?meter per second when it fills the notch. Based on the accompanving araph, the probability sach year that the notch will be filled to the top is ??,
90% ?to 95%
40% ?to 45%
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The correct answer and explanation is:
To determine the probability that the river fills the notch based on the data provided, we need to assess the dimensions of the notch and river velocity in the context of the accompanying graph. While the specific graph isn’t shown here, we can outline how the solution would typically be approached.
Dimensions and River Flow
- Notch Dimensions: The notch is 9 meters wide and 5 meters high from its base.
- Area of the notch cross-section: A=Width×Height=9 m×5 m=45 m2A = \text{Width} \times \text{Height} = 9 \, \text{m} \times 5 \, \text{m} = 45 \, \text{m}^2.
- River Velocity: The river flows at 1 m/s1 \, \text{m/s}.
- Flow rate (discharge): Q=A×v=45 m2×1 m/s=45 m3/sQ = A \times v = 45 \, \text{m}^2 \times 1 \, \text{m/s} = 45 \, \text{m}^3/\text{s}.
This flow rate indicates the volume of water passing through the notch per second when the river completely fills it.
Probability from the Graph
The probability of the river filling the notch depends on the relationship between the river’s flow rate and the historical distribution of river flow as shown on the graph.
- If the flow rate of 45 m3/s45 \, \text{m}^3/\text{s} corresponds to a cumulative probability between 40% and 45%, the chance of the notch filling in a given year is 40%–45%.
- Similarly, if it falls between 90% and 95%, the probability is in that range.
Correct Answer: 40% to 45%
This probability is derived assuming the flow rate of 45 m3/s45 \, \text{m}^3/\text{s} falls within the stated cumulative range based on historical data. Understanding this relationship requires accurately interpreting the graph, where flow rates are plotted against probabilities.
Conclusion
The final probability relies heavily on interpreting the graph correctly. Given 45 m3/s45 \, \text{m}^3/\text{s} is a moderate flow rate, a 40%–45% probability seems more reasonable in typical hydrological models. This reflects the chance of filling the notch annually.