Question

The hydraulic jump in a stilling basin was found to be 10 cm in a model with \( \frac{I_p}{I_m} = 36 \). The prototype jump height would be

• A. \( 0.6 \) m
• B. \( 3.6 \) m
• C. \( 21.6 \) m
• D. Indeterminable with this data

Hint:

- Froude’s model law governs free-surface flows like hydraulic jumps. - Use length ratio \( \frac{I_p}{I_m} \) for linear dimensions like height and length. - Velocity and time scale differently as per the Froude number relationship.

Answer 1

The Correct Option is B

Step 1: Understanding Hydraulic Jump Scaling According to hydraulic similitude (Froude model law), the length and height scale as: \[ \frac{H_p}{H_m} = \frac{I_p}{I_m} \] where: - \( H_p \) = Prototype jump height - \( H_m \) = Model jump height = 10 cm = 0.1 m - \( \frac{I_p}{I_m} \) = 36 Step 2: Calculate Prototype Jump Height \[ H_p = H_m \times \frac{I_p}{I_m} = 0.1 \times 36 = 3.6 { m} \] Thus, the correct answer is Option (B) 3.6 m.