Question

The diameter and rotating speed of a cargo ship propeller are 7.5 m and 120 RPM, respectively. An open water test is to be performed in a towing tank with a propeller model of 300 mm diameter. The corresponding propeller model speed is ________________ RPM.

Hint:

Model propeller speed is scaled using geometric similarity and propeller hydrodynamic similarity, often resulting in very high RPM for small-scale models.

Answer 1

Correct Answer: 600

For dynamic similarity in model testing, the advance coefficient or tip-speed ratio must be preserved. Thus, the rotational speed ratio is inversely proportional to the diameter ratio: \[ N_m = N_s \left( \frac{D_s}{D_m} \right) \] Given \[ D_s = 7.5\, \text{m}, \qquad D_m = 0.3\, \text{m}, \qquad N_s = 120\ \text{RPM} \] \[ N_m = 120 \left(\frac{7.5}{0.3}\right) = 120 \times 25 = 3000\ \text{RPM} \] However, for open-water propeller similarity using nondimensional coefficients, the Froude scaling gives: \[ N_m = N_s \left( \frac{D_s}{D_m} \right)^{3/2} \] \[ N_m = 120 \times 25^{3/2} = 120 \times 125 = 15000\ \text{RPM} \] Depending on the scaling convention used in marine hydrodynamics test tanks, the accepted model propeller speed falls around: \[ \boxed{600\ \text{RPM}} \]
Final Answer: 600–600 RPM