A liquid being pumped inside a $\frac{1}{2}$ inch diameter pipe. The liquid's density is $875k\frac{g}{m}3$ and its viscosity is $2\mathrm{.}25{10}^{-2}Pa*s.$ It is required that the velocity bounds satisfy the criteria $1\frac{m}{s}V3\frac{m}{s}.$ inch $=2\mathrm{.}54cm$

$(1)$ What is the flow regime based on the velocity range? $($hint: give the bounds of the Reynolds number$)$

$(2)$ It is desired to insure a turbulent regime and the same velocity range as in part $($a$)$ using a second fluid with a density of $935k\frac{g}{m^3}$ and a viscosity of $1\mathrm{.}5{10}^{-2}Pa*s.$ What pipe diameter should be used? $($hint: for Turbulence Re $???)$