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FAQ / It diverges when overflowing in a river given the HQ formula

Near the confluence of the main river with the tributary, the calculation diverges when overflowing from the tributary (the inundation depth becomes abnormally deep).

response

cause

If you give an HQ formula to a backwater section and overflow from that section, the calculation may diverge. This is thought to be because the assumption that the water level is uniquely determined for a certain flow rate, which is the premise of the HQ equation, is difficult to hold in the backwater section. It is desirable not to use the HQ formula in the backwater section.

In the River Sabo Technical Standards Survey (June 24), the following requests are made.

River Sabo Technical Standards Survey (June 24) Chapter 2, Section 4 p. 29

In a slow-flowing river, the influence of changes in water surface gradient due to the influence of backwaters due to tides, confluences, weir operations, etc. on the downstream side cannot be ignored, so the water level flow curve cannot be expressed as a univalent function of the water level only. Therefore, it is desirable not to use the water level flow curve method at such a point. Even if it is not a slow-flowing river, as described above, when sudden changes in the longitudinal direction of river accumulation and roughness (especially the overgrowth of tree groups) are observed, it is desirable to reconsider the adoption of the water level flow curve method.

In tidal sections and backwater sections with a gentle riverbed gradient, backflow may occur. On the other hand, when calculating the water level by the HQ equation, the square root of the flow rate is obtained as shown in the following equation.

\[ H = \sqrt{Q / a} - b \]

Since there is no real solution for the square root of a negative value, the HQ equation cannot be applied when the flow rate \(Q\) becomes negative (when reverse flow occurs). For numerical purposes, the HQ formula applies only to positive flow rates and not to negative flow rates.

If the HQ equation is applied near the stenosis, the result may be unreasonable. In the upper reaches of the constricture, water accumulates, and as the water level rises, the water surface slope becomes slower and the flow velocity decreases. In addition, just below the stenosis, the water level is low, the water surface slope becomes tight, and a fast flow occurs. Applying the HQ formula in such cases will have the following absurd results:

  • In the upper reaches of the narrowed part of the river, the higher the water level obtained by the irregular flow, the smaller the flow rate, and the lower the water level obtained by the HQ formula **** .
  • Directly below the narrowed part of the river, the lower the water level obtained by the irregular flow, the larger the flow rate, and the higher the water level obtained by the HQ formula **** .

countermeasure

If you must use HQ expressions, changing the settings of the following three properties may improve the situation.

  • Set the [HQ formula applies to positive flow rate only]Project Properties [False] to .
  • Set the [Applying the HQ formula to confluences]Project Properties [False] to .
  • Set the [Application of HQ formula to drainage destination river]Project Properties [False] to .

In addition, the following measures may be effective:

  • [HQ type applied upper flow limit] to full flow rate (HQ is not applied when overflowing)
  • Reduce the spacing between river channel cross-sections (reduce the flow rate per section)
  • [Overflow coefficient alpha] (reduce the flow flow per section)
  • Add or remove cross-sections before and after places where the cross-section of the river channel changes significantly, such as head work (reduce the overflow flow per section)

Technical Reference/ River Model/ Correcting the water level with the HQ formula

Last update: 2023-03-20