Question

A sphere is moving in water with a velocity of 1.6 m/s. Another sphere of twice the diameter is placed in a wind tunnel and tested with air which is 750 time less dense and 60 times less viscous (dynamically) than water. The velocity of air that will model dynamically similar conditions is

• A. 5 m/s
• B. 20 m/s
• C. 10 m/s
• D. 40 m/s

Answer 1

The correct option is C 10 m/s

According to Reynold's Model law
$(Re{)}_m=(Re{)}_p\frac{{\rho }_r{V}_r{L}_r}{{\mu }_r}=Constant\frac{{\rho }_w\times 1.6\times D}{{\mu }_w}=\frac{\frac{{\rho }_w}{750}\times V\times 2D}{{\mu }_w/60}V=\frac{750\times 1.6}{60\times 2}=10m/s$