Example $6\mathrm{.}4$ Determine the effect of a change in the cross$-$sectional area on the pressure drop of a square pipe. The original square pipe has a cross section side length of $70\mathrm{.}7$ mm $.$

To reduce the pressure drop, an engineer decided to double the pipe cross section with a side length of $141\mathrm{.}4$ mm over the pipe length of $1$ m $.$ Consider air flowing at $0\mathrm{.}05k\frac{g}{s}$ at $27C.$ The air density and dynamic viscosity are $1\mathrm{.}1614k\frac{g}{m^3}$ and $184\mathrm{.}6{10}^{-7}Pa*s,$ respectively. For fully developed turbulent flow for rectangular $($and square$)$ ducts, consider

$f=0\mathrm{.}0791R{e}^{-0\mathrm{.}25}(1\mathrm{.}0875-0\mathrm{.}1125{}^{**})$

where ${}^{**}$ is the aspect ratio of the rectangular flow passage.

Ins: What if the pipe length was $10$ m instead of $1$ m $?$ Would an increase in the diameter have any benefit?

Example $6\mathrm{.}4$ Determine the effect of a change in the cross$-$sectional area on the pressure drop of a square pipe. The original square pipe has a cross section side length of $70\mathrm{.}7$ mm $.$

To reduce the pressure drop, an engineer decided to double the pipe cross section with a side length of $141\mathrm{.}4$ mm over the pipe length of $1$ m $.$ Consider air flowing at $0\mathrm{.}05k\frac{g}{s}$ at $27C.$ The air density and dynamic viscosity are $1\mathrm{.}1614k\frac{g}{m^3}$ and $184\mathrm{.}6{10}^{-7}Pa*s,$ respectively. For fully developed turbulent flow for rectangular $($and square$)$ ducts, consider

$f=0\mathrm{.}0791R{e}^{-0\mathrm{.}25}(1\mathrm{.}0875-0\mathrm{.}1125{}^{**})$

where ${}^{**}$ is the aspect ratio of the rectangular flow passage.