Hydraulic similitude — acceleration scaling from a 1:30 Froude model of an ogee spillway A 1:30 (model : prototype = 1:30) Froude-scaled model of an ogee spillway measures a local acceleration of 1.3 m/s^2 at a point on the nappe. What is the homologous acceleration at the corresponding point in the prototype (m/s^2)?

Introduction / Context:
In free-surface hydraulic models of spillways and open channels, Froude similarity is the governing similitude because gravity controls the dominant forces. Understanding how kinematics scale (length, time, velocity, acceleration) allows us to translate model measurements to prototype values correctly.

Given Data / Assumptions:

• Geometric scale λ_L = L_p / L_m = 30 (prototype is 30 times larger).
• Froude similarity holds: Fr_p = Fr_m.
• Model acceleration at a point is a_m = 1.3 m/s^2.

Concept / Approach:
Under Froude similarity, time scale λ_T satisfies λ_T = √λ_L. Velocity scale is λ_V = λ_L / λ_T = √λ_L. Acceleration has dimensions L/T^2, so its scale is λ_A = λ_L / λ_T^2. Substituting λ_T = √λ_L gives λ_A = λ_L / (λ_L) = 1. Therefore, accelerations are the same in model and prototype at homologous points when Froude similarity is satisfied.

Step-by-Step Solution:
Compute λ_T = √30.Compute acceleration scale λ_A = λ_L / λ_T^2 = 30 / 30 = 1.Prototype acceleration a_p = λ_A * a_m = 1 * 1.3 = 1.3 m/s^2.

Verification / Alternative check:
Dimensional check confirms L/T^2 scaling cancels under Froude similitude. Many hydraulic laboratories rely on this property when interpreting accelerations and pressure-gradient related measurements.

Why Other Options Are Wrong:
0.043, 0.237: These imply incorrect scaling such as dividing by λ_L or √λ_L.
7.120, 39.000: These imply multiplying by √λ_L or λ_L, which is not valid for acceleration under Froude scaling.

Common Pitfalls:

• Confusing velocity scaling (√λ_L) with acceleration scaling (unity under Froude similarity).
• Mixing Froude and Reynolds similitudes; in practice, Reynolds is not matched in small models.

Final Answer:
1.300