Question

In a rectangular open channel, the flow is critical, and the flow depth is 2 m. Select the correct statement(s)

• A. Specific energy for the flow is 3.0 m
• B. Specific energy for the flow is 2.0 m
• C. Froude number is 1.0
• D. Froude number is 1.5

Answer 1

The Correct Option is A, C

Step 1: Understand critical flow conditions. In an open channel, critical flow occurs when the Froude number (\( F_r \)) is \( 1.0 \). The specific energy (\( E \)) at critical flow is given by: \[ E = y_c + \frac{Q^2}{2gA^2} \] where: \( y_c \): Critical depth (\( 2 \, \text{m} \) in this case). \( Q \): Discharge (not required for determining specific energy in this problem). \( g \): Acceleration due to gravity. \( A \): Cross-sectional area. For critical flow in a rectangular channel, the specific energy simplifies to: \[ E = 1.5 \, y_c \] Step 2: Calculate specific energy. Given \( y_c = 2 \, \text{m} \): \[ E = 1.5 \times 2 = 3.0 \, \text{m} \] Step 3: Determine the Froude number. The Froude number for critical flow is always: \[ F_r = 1.0 \] Step 4: Analyze the options. (1) Specific energy for the flow is \( 3.0 \, \text{m} \): Correct, as calculated. (2) Specific energy for the flow is \( 2.0 \, \text{m} \): Incorrect, as the specific energy is greater than the critical depth. (3) Froude number is \( 1.0 \): Correct, as this is the defining condition for critical flow. (4) Froude number is \( 1.5 \): Incorrect, as this would represent supercritical flow.