CHEN2610 Laboratory Exercises, June 26, 2009
In this lab session you will complete three different exercises. Three groups of six
students each will rotate between the three exercises described below:
1. Reynolds Experiment- The Reynolds Number is a dimensionlessi quantity that for
pipe flow may be expressed in several forms, one of which is:
Re 
DV

Where D is the diameter of the pipe, V is the linear velocity in the pipe, µ is the viscosity
of the liquid and  is the density of the liquidii. The Reynolds number determines the
characteristics of the flow: laminar or turbulent. In laminar flow (Re < approx. 2100)
“viscous forces” dominate. Note that if viscosity is high the Reynolds number will go
down. In the laminar regime the relatively high viscosity holds the fluid together in what
can be thought of as layers. Frictional resistance in the laminar regime is due to the
layers tendency to “stick” together due to the high viscosity. Energy, from a pump for
instance, is needed to shear the layers (move them over one another) and this frictional
loss of energy dissipates as heat, taking away from the energy devoted to forcing the
liquid through the pipe. (You experience this when you drink a milkshake through a
straw as opposed to soda. The higher viscosity forces require you to use more energy to
suck up the milkshake!).
When the viscosity is small or when the numerator is large (high Re), “inertial forces”
dominate over the viscous forces. Recall from Newton’s First Law of motion that inertia
= mass x velocity and is the tendency of a body (packets of fluid in this case) once in
motion in a given direction to stay in motion and in that direction unless acted upon by an
outside force. The numerator of the Re can be thought of as density of inertia across the
cross sectional area of the pipe (cancel units in the numerator). Unless acted upon by an
outside force (viscosity!) the fluid will tend to tumble down the pipe in turbulent flow.
The Re can thus be thought of as the ratio of inertial forces to viscous forcesiii.
i
Plug units into the Re equation and convince yourself that they cancel to give the dimensionless term.
The Reynolds Number and other dimensionless quantities may seem mysterious at first, but they can
actually be derived very easily using dimensional analysis and the Buckingham-Pi theorem. You may end
up deriving these in one of your courses. The folding of the four terms of the Reynolds number into one
dimensionless quantity is very powerful. Imagine if we had to do experiments varying density, diameter,
viscosity, etc. independently as opposed to just varying the Reynolds number- that would be a LOT of
experiments! The Reynolds number contains all the information we need in one tight package.
iii
All dimensionless numbers have some similar qualitative interpretations of the ratio of terms.
ii
In the Reynolds experiment you are duplicating the original experiments done by
Osborne Reynolds in his famous pipe flow research. The apparatus consists of a constant
head tank in which the liquid level in the overhead tank is maintained by overflowing a
surplus of water (think: why is it necessary to provide constant pressure?) The tank is
full of marbles which serve as baffles to settle and still the water in the tank. A bellshaped inlet feeds an observation tube (glass pipe) that runs vertically down from the
tank. At the inlet is a small nozzle into which a colored dye is introduced to allow us to
observe the character of the flow with varying Re. The flow rate, and hence Re is
controlled by a valve at the outlet of the tube.
The TA will assist you in operating the apparatus- keep a few concise notes of what you
observe. You will start the dye flowing and starting at very low flow rate gradually
increase the flow. This part is very cool: at low Re you will observe a parabolic velocity
profile defined by the shape of the dye- you should also be able to visualize as “layers”
sliding over one another and held together by viscous attractive forces. The parabola will
stretch as it proceeds down the pipe since the velocity in the center of the tube is the
greatest (velocity at the pipe wall is zero- the “no-slip” condition and the profile is
symmetric around the center. (You may derive the velocity profile equation later in class
using this information). As you increase the flow rate, you will observe the flow
transition to the turbulent regime. This will be evident from the loss of the parabolic
shape and thorough mixing of the dye into the liquid as the water tumbles this way and
that on its course through the pipe. Also try seeing what happens when you suddenly
shut of the flow control valve while in the laminar regime!
Hopefully this experience will give you some insight that will help you later in the course
to relate the mathematical equations describing aspects of fluid flow to what is physically
going on in the pipe.
2. Flow Meters and Frictional Losses In Pipes
In this experiment you calibrate two different types of flow meters. One is called a
rotameter and is an example of a variable area type flow meter. In this meter a float
moves up and down in a glass tube according to flow rate. The cross sectional area of the
tube expands towards the top of the tube. The float will move to a position based on a
force balance- gravity acting downward and drag force acting upwards. Since the area of
the tube increases as the float moves up, the velocity of the fluid decelerates spatially and
the float will find a balance point higher in the tube for higher flow rates. The tube is
designed such that there will be a linear relationship between position and flow.
The other flow meter is an orifice plate. This is the simplest form of a very important
class of flow sensors known as “pressure drop” flowmeters. These work by intentionally
restricting flow with a sharp-edged orifice of precise diameter. The relationship of
pressure drop across the orifice to flowrate can be derived via energy balance (look up
“orifice meter” in the index of your text book if you are curious about this and want a
preview of coming course material!). You will find that the relationship of flow to
pressure drop is a square root function. This is an inexpensive flow meter but note that it
adds friction to the system so there is a tradeoff in terms of energy usage versus cost
when designing a piping system.
You will also measure the pressure drop across several lengths of pipe and correlate the
pressure drop to frictional losses in the pipe. You will measure pressure drops using a
differential pressure cell (DP cell). The DP cell we are using has a full scale calibration
of 415 inches of water (1 psi = 27.68 inches of water); if the meter reads 100%, the
pressure = 415 inches, 50% = 207.5 inches, etc. A centrifugal pump moves fluid first
through the rotameter and then to a manifold that feeds several pipes. Feed to a given
pipe is selected using ball valves on the manifold.
Rotameter Calibration
i)
Open the ball valves to allow flow through all pipes simultaneously
and turn the pump on. Make sure the flow control valve at the
rotameter is open enough to allow some flow- the pump can be
damaged if the flow is totally blocked for more that 15 seconds or so.
ii)
Open the flow control valve to give the maximum reading on the
rotameter. Use the 4L graduated cylinder to measure a volume of
liquid pumped for a length of time- it is easiest to just fill the cylinder
to about ¾ full while accurately measuring time and then read the
volume precisely after the tube is removed. Repeat for 4 more
flowrates approximately evenly spaced between zero flow and the max
flow on the rotameter. Note that rotameters are always read from the
widest part of the float.
Analysis: Plot in Excel the volumetric flow rate on the Y-axis and % reading
from the rotameter on the X-axis. A line fit through the points will give a
calibration curve for the rotameter.
Oriface Meter
i)
ii)
iii)
iv)
v)
vi)
Turn on the DP cell.
Close valves to all pipes except the one with the orifice meter installed.
Turn on the pump.
Pug the high pressure side of the DP cell into the side labeled high on the
orifice meter. Likewise connect the low pressure sides.
Open the bleed valves located on the DP cell housing. Purge and then close
the valves. This will flood each compartment so as to give accurate readings.
Collect DP % readings at least 8 flowrates across the range possible (record
both the rotameter reading and the DP reading).
Analysis: Plot in Excel the log of volumetric flowrate (using your data from [vi]
above as well as your rotameter calibration) on the Y-axis, and the log of DP on the
X-axis. What is the slope of the line? Since flowrate goes as the square root of DP
you should have a straight line log-log plot with a slope equal to ½. Save your data.
Later on in the course you might want to use the equation for an orifice plate along
with your data and the size of the pipe and orifice to calculate the orifice coefficient.
Pressure Drop in Pipes
For now, in this exercise you will take data for the pressure drop through 2 different
pipes and at several flow rates. The goal here is to see how the pressure drop is
affected by the Re of the flow, as well as to see how the pressure drop at a given Re
varies with pipe diameter.
i)
ii)
iii)
iv)
v)
Close the appropriate valves so as to isolate the 3/8” PVC pipe.
Connect the DP cell across the pipe and open the control valve at the
rotameter all the way.
Pump as much fluid through the pipe as possible (note that there is a limit to
how much head the pump can generate; the friction in the small pipe restricts
the flow!) Record the DP and rotameter reading.
Repeat readings for several flow rates.
Repeat steps iii-iv using the ¾” PVC pipe.
Current Analysis: Report what happened when you increased the flow rates. Why
does the DP go up? Calculate Re for the pipe flows. At the same Re (you may have
to interpolate your data to find the same Re) which pipe has the greater pressure
drop? Why, do you think? Save your data. You may need it for a homework
problem later in the semester.
Sneak Preview!: Later in the course you will learn that frictional losses for flow in
pipes (pressure drop) for a given pipe size and Re can be predicted using a quantity
called the “friction factor” (or “resistance coefficient”) f along with a tabulated value
of pipe roughness. Pipe roughness is a measure of how much small “bumps” or
imperfections on the pipe surface protrude from the wall of the pipe (picture a piece
of course sandpaper- the grains on the paper are raised a certain height (ks)in relation
to the paper surface- same thing in the pipe although the imperfections are usually
much smaller in size).
Later in the course you will apply the plot below to make further use of your data and
to tie these concepts together. For now, you might observe on the chart that for
laminar flow, pipe roughness does not seem to matter (note pipe roughness is given
here as relative pipe roughness, ks /D, another dimensionless number!), while for
turbulent flow it does. Why? Remember for laminar flow we saw that the friction
was caused by “layers” sliding over one another, opposed by the “stickiness” of the
viscosity. For turbulent flow, there is less of a stagnant layer at the wall of the pipe
than in laminar flow, and the flow protrudes into the areas of roughness and
experiences drag due to the bumps and grains the pipe wall. You can see in the chart
that roughness does affect the friction factor in the turbulent regime.
3. In the third exercise you will be given a handout with descriptions of a number of
different pipe fittings, valves, flow and pressure meters, as well as other devices
associated with fluid flow. All items are laid out on the lab bench and have a numbered
label. Go through with your group members and see how many of the items you can
identify from the description. I will help you with those you can’t identify and tell you
about each one. Return your completed sheet to the instructor or TA as directed.