Question $1$

Engine oil at $25C$ flows through a $1\mathrm{.}5cm$ diameter pipe with a pressure drop of $10$kPa along

a $1m$ length pipe, as shown in Figure $1.$ Determine the flow rate, $V^{},$ in $\frac{m^3}{s},$ velocity, in $\frac{m}{s}$

and Reynolds number of water through the pipe if it is

$($a$)$ horizontal,

$($b$)$ vertical,

$($c$)$ inclined $10$ upward from the horizontal, and

$($d$)$ declined $10$ downward from the horizontal.

Engine Oil

Figure $1$

Answer: $($a$)V^{}=0\mathrm{.}182\frac{m^3}{s},V=10\mathrm{.}3\frac{m}{s},Re=2004,($b$)V^{}=0\mathrm{.}024\frac{m^3}{s},V=1\mathrm{.}358\frac{m}{s},Re=264,$

$($c$)V^{}=0\mathrm{.}155\frac{m^3}{s},V=8\mathrm{.}752\frac{m}{s},Re=1548,($d$)$ hat$(V)=0\mathrm{.}21\frac{m^3}{s},V=11\mathrm{.}858\frac{m}{s},Re=2306.$