Question

In the case of large rivers, a number of equidistant vertical sections of the total width of flow are identified, for the purpose of finding the discharge on any day by numerical integration. On each section, the mean velocity is taken as the arithmetic average of two typical depths on that section. Then the mean velocity is worked out for that section. Usually, the mean velocity of any section, corresponds to which one of the following? (V represents the point velocity at the given section and the depth such as $0.1d,0.2d\cdots etc.$

• A. $\frac{V_{0.1d}+V_{0.9d}}{2}$
• B. $\frac{V_{0.2d}+V_{0.8d}}{2}$
• C. $\frac{V_{0.3d}+V_{0.7d}}{2}$
• D. $\frac{V_{0.4d}+V_{0.6d}}{2}$

Answer 1

The correct option is B $\frac{V_{0.2d}+V_{0.8d}}{2}$

In shallow stream of depth up to 3.0 m, the average velocity
$\overline{V}=V_{0.6d}$
This is called single point observation.
In moderately deep streams the velocity is observed at two points.
$\therefore \overline{V}=\frac{V_{0.2d}+V_{0.8d}}{2}$
In rivers having large flood flows, only surface velocity $\left(V_s\right)$ is measured within a depth of about 0.5 m from the surface. The average velocity
$\overline{V}=k{V}_s$ where $k$ is in the range of 0.85 to 0.95.