In case of incompressible flow, for flow around immersed bodies

Explanation:

In the case of incompressible flow around immersed bodies, Reynolds number is the primary dimensionless number that determines the similarity between the model and the prototype. The Reynolds number is defined as: 

R_e=ρ⋅V⋅L/μ​

Where:

• $\rho$ is the density of the fluid,
• $V$ is the velocity of the flow,
• $L$ is a characteristic length (e.g., diameter of the body),
• $\mu$ is the dynamic viscosity of the fluid.

Importance of Reynolds Number:

1. Flow Similarity: For modeling the flow around immersed bodies, maintaining equal Reynolds numbers between the model and the prototype ensures that the flow patterns, including boundary layer behavior, separation points, and wake formation, will be similar. This allows accurate predictions and analyses of the flow characteristics of the prototype based on model experiments.

2. Incompressible Flow: In incompressible flow, the effects of compressibility (density changes) are negligible. The Reynolds number becomes the primary parameter because it encapsulates the relative effects of inertial forces to viscous forces in the flow, which dictate the flow behavior around immersed bodies.