Osborne Reynold is a well-known engineer who worked in the feld o uid dynamics. His studies o heat transer and the behavior o uid .improved our understanding o uid mechanics today One o his greatest works was coming up with a dimensionless number that represents the ratio o inertial orces to the viscous orces o a .uid which is known as the reynolds number His breakthrough allowed scientists to determine the behavior o a ow regardless o conditions which gives us the advantage o working with .any system especially i it were a prototype y calculating this number! we could determine the behavior o a uid under certain conditions. "he three main regimes a ow could have are .laminar! turbulent! or transitional ow # "his ratio is simplifed or a uid owing inside a pipe as
ℜ=
v D pipe ሀ
$here v is the velocity o the uid %m&s'! pipe %m'! and
ሀ
D pipe
is the diameter o the 2
is the kinematic viscosity o the uid % m / s ¿ .
"he kinematic viscosity is a measure o the uid(s resistance to shear stress which is e)pressed as# ሀ=
μ ρ where
μ is the dynamic viscosity! and
ρ is the density o
the uid. Reynold e)periment showed that or a uid with reynold(s number o less than *+++ it should be in the laminar regime! i it was above ,+++! it would be turbulent! and in between it would be in the transitional phase. n his e)periment he observed the streamline o water through a pipe by adding ink droplets that would ow with the water. those streamline are parallel and show a parabolic velocity profle! it belongs *
to the laminar regime! while i the lines are random and mi)ing! it would be turbulent. it would oscillate! it would be in the transitional phase. aminar velocity profle is parabolic because it has parralel streamlines. "he outermost lines have /ero velocity because o the pipe wall while the centerline has ma)imum velocity because it has the least resistance. "ransitional oscillates! turbulent is random.
*.
Objectives and Procedure
n this lab! we are going to test his hypothesis by doing his e)periment and calculating the reynolds number o a uid at di0erent velocities .until it shows di0erent regimes $e will frst use the reynold-osborne apparatus to pump water in a hydraulic bench through a glass pipe. nk droplets will be added to the .ow in order to observe its regime $e will determine the uids velocity by measuring how ast it flls a certain volume in the graduated cylinder per unit area. "he stopwatch .will be used or time Q
y using the euation v 2
we will calculate the velocity. 3 is the
A
volume the water will fll % m
3
'! and 4 is the cross sectional area o .% m
2
' pipe measured in seconds
Rocks will be added in the tank as obstacles or the water when it is .pumped to avoid sudden ink dispersion $hen the water flls the tank! overow will let water mi) with ink .droplets and make them ow inside a visuali/ation ow tube
8raph shows that velocity within this range is directly proportional to Reynold(s number
C.
#ample o$ calculations
#aminar ow calculation %9ample 1'
>
@olume 2 1*= ) 1+<-C m<5 "ime 2 1B.>+ s @olume ow rate 2 1*= ) 1+<-C &1B.>+ 2 C.>C,1+5 m<5&s 4rea o cylinder 2 D E %+.++>' <* 2 ;.=> ) 1+<-> m<* @elocity 2 +.+=5C1B1, m&s Re 2 %+.+=5>1B1,E +.+1'&%1.++; ) 1+ <-C' 2 =5+ F*+++ so laminar
;.
%onclusion and Discussion
4ll our values are within the range o Reynold(s e)periment. However! we have to be careul when we are using the stopwatch because it could account or human error. $hen the velocity o the ow increases! Reynolds number increase but only i the temperature o the room is kept constant. ecause viscosity depends on the temperature! and the diameter is f)ed! so the graph will be directly proportional which we saw in our previous graph. aminar ow is the easiest to observe amongst other regimes because o the streamline pattern! and because when the ow is slow! it is easier to calculate its ow rate.
