$\backslash$#$4.(15)$ In fluid mechanics, it can be useful to consider physical phenomenon with nondimensional parameters. The Reynolds number, named after Osborne Reynolds$(1842-1912),$ is one of the most general and frequently used parameter as you already have been encountered. Answer the following questions.

a$)$ Write down the definition of the Reynolds number and explain its physical meaning.

b$)$ Considering the previous answer, simplify the Navier$-$Stokes equation in high Re $\backslash$#$.$ Why can you physically simplify the equation with high Re $\backslash$# condition?

c$)$ Derive the previous answered equation with non$-$dimensional variables.