Correctly complete this sentence using the words provided.
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%
The correct answer and explanation is:
The correct completion of the sentence is:
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 accompanying graph, the probability each year that the notch will be filled to the top is 40% to 45%.
Explanation
The probability that the river fills the notch to its top annually depends on factors such as the hydrological characteristics of the river, historical flow data, and the notch’s dimensions. In this scenario, the notch is 9 meters wide and 5 meters high, with a river velocity of 1 meter per second when the notch is filled.
The width (9 meters) and height (5 meters) define the cross-sectional area of the notch. When the river fills the notch completely, the discharge QQ (volume of water passing through per second) can be calculated using the formula: Q=A⋅vQ = A \cdot v
where:
- AA is the cross-sectional area (9 m×5 m=45 m29 \, \text{m} \times 5 \, \text{m} = 45 \, \text{m}^2),
- vv is the velocity (1 m/s1 \, \text{m/s}).
Thus, Q=45 m3/sQ = 45 \, \text{m}^3/\text{s}. This discharge represents the threshold flow rate needed to fill the notch.
To determine the probability of this occurring annually, we compare QQ with the river’s flow data, typically derived from historical records. The accompanying graph likely shows flow duration curves or annual peak flow probabilities, which indicate how often specific discharge values are exceeded.
In this case, the graph suggests that the probability of the river reaching the required discharge (Q=45 m3/sQ = 45 \, \text{m}^3/\text{s}) annually falls within the range of 40% to 45%. This means there is a 40–45% chance each year that the river flow will be sufficient to fill the notch completely.
The 90% to 95% range is incorrect as it would indicate much higher flow likelihoods, which are inconsistent with the given dimensions and observed hydrology.