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A culvert is designed for a peak flow of \( Q_P \) based on the rational formula. If a storm of the same intensity as used in the design but with twice the duration occurs, the resulting peak discharge will be:

1. \( Q_P \)
2. \( 2Q_P \)
3. \( \frac{Q_P}{2} \)
4. \( Q_{2P} \)

Answer :

The question you're asking is centered around understanding the concept of peak flow in hydraulic engineering, specifically in relation to culverts and stormwater design.

A culvert is a structure that allows water to flow under a road, railroad, trail, or similar obstruction. It is crucial that these structures are designed to handle peak flows of water to avoid flooding and damage.

The rational formula is commonly used in hydrological design to estimate the peak discharge for a storm event. The formula is given by:

[tex]Q = C \times I \times A[/tex]

Where:


  • [tex]Q[/tex] is the peak discharge (in cubic meters per second, [tex]\text{m}^3/ ext{s}[/tex]).

  • [tex]C[/tex] is the runoff coefficient, which is dimensionless and represents the fraction of rainfall that will runoff.

  • [tex]I[/tex] is the rainfall intensity (in millimeters per hour, [tex]\text{mm/hr}[/tex]).

  • [tex]A[/tex] is the drainage area (in hectares, [tex]ext{ha}[/tex]).


When the formula is used to design a culvert, [tex]Q_P[/tex] represents the peak flow the culvert is designed to handle.

Consideration with Storm Duration:

The rational formula assumes that the storm duration used for [tex]I[/tex] is equal to the time of concentration, or the time it takes for all the runoff to reach the point of interest from the most distant point in the drainage area.

If a storm of the same intensity occurs but has a duration twice as long, the peak discharge, [tex]Q_P[/tex], is unaffected by this change in duration itself. The rational method traditionally considers only peak intensities and not the duration of a storm beyond the time of concentration. Therefore, for a duration twice as long but with the same intensity, the resulting peak discharge is:

1. [tex]Q_P[/tex]

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