Final answer:
To maintain similarity in terms of the Weber number when using a 1:15 scale model with the same density as the prototype, the surface tension scale should be reduced by a factor of 1:225.
Step-by-step explanation:
The student's question involves the Froude number and Weber number, which are dimensionless parameters used to describe fluid dynamics. The Froude number is typically associated with inertial and gravitational forces, while the Weber number relates to inertial forces and surface tension.
When using a scale model for studying fluid flow problems, it is essential to maintain similarity between the model and the prototype. Given that the scale model is 1:15 and the density scale is 1, the surface tension scale can be determined using the Weber number.
The Weber number (We) is defined as We = ρLν²/σ, where ρ represents the fluid density, L is the characteristic length scale, v is the fluid velocity, and σ is the surface tension.
Since the model scale is 1:15 and density scale is 1 (meaning the density remains the same between model and prototype), the characteristic length scale will be reduced by a factor of 15.
Consequently, to maintain similarity in terms of the Weber number, the surface tension in the model should be scaled down by a factor of 1:15² because the Weber number involves L² due to velocity v being squared in the definition. Thus, the required surface tension scale would be 1:225.