The propeller of a ship is to be studied with a 1:10 scale model.

(a) Assuming that the propeller operates close to the surface, select the propeller speed of the model if the prototype speed is 600 rpm.

(b) What torque would be expected if 1.2 N•m is measured on the model?

Question

The propeller of a ship is to be studied with a 1:10 scale model.

(a) Assuming that the propeller operates close to the surface, select the propeller speed of the model if the prototype speed is 600 rpm.

(b) What torque would be expected if 1.2 N•m is measured on the model?

Accepted Answer

Neglect viscous effects, and account for wave (gravity) effects.

[latex] Fr_m=Fr_p . ∴ \frac{V_m^2}{\ell _mg_m} =\frac{V_p^2}{\ell _pg_p} . ∴ \frac{V_m}{V_p} =\sqrt{\frac{\ell _m}{\ell _p} } . \frac{\omega _m}{\omega _p} = \frac{V_m/\ell _m}{V_p/\ell _p}[/latex]

∴[latex] {\omega _m} ={\omega _p} \frac{V_m}{V_p} \frac{\ell _m}{\ell _p} =600 imes \sqrt{\frac{1}{10} } =1897 rpm[/latex].

[latex]\frac{T_m}{T_p} = \frac{ ho _mV ^2_m\ell _m^3 }{ ho _pV ^2_p\ell ^3_p}. ∴ herefore T_p=T_m \frac{V_p^2}{V_m^2}\frac{\ell _p^3}{\ell _m^3}= 1.2 imes 10 imes 10^3 = \underline{120000 N .m} [/latex].

Question 6.58: The propeller of a ship is to be studied with a 1:10 scale m...

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