Adjustment Factor For Velocity

The average flow velocity used in contraction scour analysis applies only to a long contraction where the flow velocity is considered uniform. For flow constricted by an abutment, the velocity across the section is not uniform because the velocity at the face of the abutment is higher. The average velocity used for contraction scour, accordingly, needs to be modified to account for the higher velocity and resulting deeper scour at the abutment.

The two dimensional potential flow pattern around a rectangular abutment was used for evaluating the velocity distribution across the contracted section. A study of the velocity distribution in this constricted section (3, 4) applying the principles of potential flow revealed that the ratio of the velocity at the toe of the abutment to the mean velocity of the flow in the contracted section can be approximated by the following equation:

kv = 0.8(q1/q2)1.5 + 1
Where:
kv = ratio of velocity at the abutment toe to the mean velocity in the contracted section.
q1 = unit discharge at the left or right of the approach channel
q2 = unit discharge at the left or right of the channel at contracted section

This equation was developed considering flow through a simple contraction, where the unit discharge of the approach section is less than that in the contraction, q1 < q2.

The values of kv should be limited to the range of values between 1.0 and 1.8. If the computed value is less than 1.0, use a value of 1.0; if the computed value is greater than 1.8, use a value of 1.8.