# Shear and Velocity Distribution in Shallow Channels

*by*H. Lundgren,

Ivar G. Jonsson,

**Serial Information**:

*Journal of the Hydraulics Division*, 1964, Vol. 90, Issue 1, Pg. 1-21

**Document Type:**Journal Paper

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**Abstract:**The distribution of the bottom shear stresses in an open channel can be found by various approximate methods. For a shallow channel, a fair approximation is obtained if the shear is assumed to correspond to the vertical depth. If the incline of the bottom is appreciable, however, it is better to calculate the shear by measuring the depth at right angles to the bottom. A more consistent method is to let the shear correspond to the area between two bottom normals. However, these methods do not consider the transfer of shear (in the direction of flow) through the depth lines. The proposed new method overcomes this difficulty by assuming that there is no transfer of shear through the orthogonals to the lines of equal mean velocity. The other basic assumption is that the velocity distribution is logarithmic along the bottom normals, corresponding to the local friction velocity. For a plane bottom with a transverse slope of 30○, the shear stresses will be 40% higher than found by conventional methods. The method cannot be used on polygonal cross sections.

**Subject Headings:**Shear stress | Velocity distribution | Stress distribution | Open channels | Approximation methods | Shear flow | Friction | Slopes |

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