Question

A ship is to be operated in a fluid medium with kinematic viscosity \( 0.032 \times 10^{-3} \, {m}^2/{s} \). A one-tenth scale model of the ship is built for testing. Consider, inertia, viscous and gravity forces are dominant for the ship and its model during the operation. The required kinematic viscosity of the liquid for testing the model is \( P \times 10^{-6} \, {m}^2/{s} \). The value of \( P \) (rounded off to 2 decimal places) is ........

Hint:

When performing model testing, ensure that the Reynolds number is consistent between the model and prototype. This requires scaling the kinematic viscosity appropriately.

Answer 1

For model testing, the kinematic viscosity required for the testing liquid should be scaled properly using the Reynolds number. The Reynolds number (\( Re \)) is given by:
\[ Re = \frac{\rho V L}{\mu} \] For geometrically similar objects, the Reynolds number for the model and the prototype should be equal, so we apply the Reynolds number scaling:
\[ \frac{V_m L_m}{\nu_m} = \frac{V_p L_p}{\nu_p} \] Where:
- \( V_m \) and \( V_p \) are the velocities of the model and prototype,
- \( L_m \) and \( L_p \) are the characteristic lengths (scale length),
- \( \nu_m \) and \( \nu_p \) are the kinematic viscosities of the model and prototype.
Since the scale is one-tenth for the model, the kinematic viscosity of the testing liquid (\( \nu_m \)) is calculated using the scaling relationship. After solving, we get \( \nu_m \approx 0.95 \times 10^{-6} \, {m}^2/{s} \), which means \( P \) is 0.95.