A delivery van of width m travels at m s through still air of density kg m and…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity

Fluids and Continuum Physics, Ch Dimensional analysis, dynamical similarity and the dimensionless groups

Problem

A delivery van of width wp=2.4w_p = 2.4 m travels at Up=25U_p = 25 m s−1^{-1} through still air of density ρ=1.2\rho = 1.2 kg m−3^{-3} and dynamic viscosity μ=1.8×10−5\mu = 1.8\times10^{-5} Pa s. The flow is treated as steady and incompressible, and the Reynolds number is built on the width. ((a)) The aerodynamic power PP needed to push the van is taken to depend only on ww, UU, ρ\rho and μ\mu. How many independent dimensionless groups can be formed from these five quantities? ((b)) Compute the Reynolds number of the full-size van. ((c)) A geometrically similar 1/101/10 scale model is tested in a pressurised wind tunnel whose air has density 6.06.0 kg m−3^{-3} and the same dynamic viscosity 1.8×10−51.8\times10^{-5} Pa s. What tunnel speed gives dynamical similarity?

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