Question

A wide channel is 1 m deep and has a velocity of flow \( V = 2.13 \, \text{m/s} \). If a disturbance is caused, an elementary wave can travel upstream with a velocity of ............

• A. 1.00 m/s
• B. 2.13 m/s
• C. 3.13 m/s
• D. 5.26 m/s

Hint:

In open channel flow, disturbances (elementary waves) travel at the wave celerity relative to the fluid. To compute upstream or downstream speeds, subtract or add the flow velocity, respectively.

Answer 1

The Correct Option is A

The elementary (or dynamic) wave velocity in open channel flow is given by the celerity formula: \[ c = \sqrt{g h} \] where:
- \( g \) is the acceleration due to gravity (\( 9.81 \, \text{m/s}^2 \))
- \( h \) is the flow depth (\( 1 \, \text{m} \))
\[ c = \sqrt{9.81 \times 1} = \sqrt{9.81} \approx 3.13 \, \text{m/s} \] To find the upstream wave velocity, we subtract the flow velocity from the wave celerity: \[ V_{\text{upstream}} = c - V = 3.13 - 2.13 = 1.00 \, \text{m/s} \] Thus, the elementary wave travels upstream with a velocity of \( \boxed{1.00 \, \text{m/s}} \).