Question

At a dairy farm milk flows through a 22mm diameter pipe at an average velocity of 0.25m/s

p=1028kg/m^3 , u=3.0*10^-3 Pa.s

1) what is the volumetric flow rate in L/s

2) Determine whether the flow in the pipe is laminar or turbulent.support your answer.

3)Futhure along the pipe , the pipe dismeter reduces to 15mm. For the reduced section,determine whether the flow regime has remained the same as in (2) or has changed . Support your answers

Answer 1

1)The volumetric flow rate in L/s

$V= \frac{AD^2}{32 \mu} \frac{\triangle P}{L}=\frac{ \pi r^2 D^2}{32} \frac{\triangle P}{1}$

$V=\frac{ \pi*(\frac{22}{2000})^2(\frac{22}{1000})^2}{32} \frac{3.0*10^{-3}}{1}=17.25*10^{-12}L/s$

2) Determine whether the flow in the pipe is laminar or turbulent.support your answer.

The Reynolds number determines whether the flow in a pipe is laminar or turbulent.

$Re=\frac{\rho u L}{\mu}=\frac{1028* 0.25 *1}{1}=257 < 4000$ . laminar

3) $V=\frac{ \pi*(\frac{15}{2000})^2(\frac{15}{1000})^2}{32} \frac{3.0*10^{-3}}{1}=3.73*10^{-12}L/s$

The flow changed