Relationship Between Stage And Discharge For Non-Alluvial Rivers Calculator

Formula Used:

\[ Q_s = C_r \times (G - a)^\beta \]

Rating Curve Constant (Cr):

Gauge Height (G):

Constant of Gauge Reading (a):

Rating Curve Constant Beta (β):

Discharge in Stream (Qs):

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1. What is the Stage-Discharge Relationship?

The stage-discharge relationship, also known as a rating curve, describes the mathematical relationship between water level (stage) and discharge in a river or stream. For non-alluvial rivers with stable channels, this relationship remains relatively constant over time.

2. How Does the Calculator Work?

The calculator uses the rating curve formula:

\[ Q_s = C_r \times (G - a)^\beta \]

Where:

\( Q_s \) — Discharge in stream (m³/s)
\( C_r \) — Rating curve constant
\( G \) — Gauge height (m)
\( a \) — Constant of gauge reading corresponding to zero discharge (m)
\( \beta \) — Rating curve constant beta

Explanation: This power-law relationship models how discharge increases with water stage in stable river channels where the cross-sectional geometry remains relatively constant.

3. Importance of Stage-Discharge Relationship

Details: Establishing accurate rating curves is essential for hydrological monitoring, flood forecasting, water resource management, and environmental studies. It allows continuous discharge estimation from easily measured water levels.

4. Using the Calculator

Tips: Enter the rating curve constant (Cr), gauge height (G), constant of gauge reading (a), and rating curve constant beta (β). All values must be positive numbers with appropriate units.

5. Frequently Asked Questions (FAQ)

Q1: What is a non-alluvial river?
A: Non-alluvial rivers have stable beds and banks composed of bedrock or cohesive materials, unlike alluvial rivers with mobile sediment beds.

Q2: How are rating curve constants determined?
A: Constants are derived from field measurements where both stage and discharge are measured simultaneously across a range of flow conditions.

Q3: Why is there a constant (a) for zero discharge?
A: This accounts for the gauge height at which flow theoretically ceases, which may not be at zero due to channel irregularities or measurement reference points.

Q4: How often should rating curves be verified?
A: For stable non-alluvial rivers, annual verification is typically sufficient, but more frequent checks are needed after major flood events.

Q5: Can this formula be used for all river types?
A: This power-law relationship works best for stable channels. Alluvial rivers with mobile beds may require more complex, time-varying rating curves.