LAMINAR & TURBULENT FLOW IN PIPES

6..1 ObjectivesTo develop a relationship between the friction factor and the Reynolds number for laminar and turbulentflow in horizontal pipes. To measure velocity profiles of turbulent flow in pipes and compare theexperimental results with empirical correlations.

6.2 TheoryLaminar and turbulent flow in pipes (circular tubes) has been treated in 06-152 and in Denn, Chapters 3 and5. Also see Chapter 5 entitled "Flow of Incompressible Fluids in Conduits and Thin Layers," pp 73-86, inMcCabe, Smith and Harriott, Unit Operations of Chemical Engineering.

6.3 ExperimentalFriction factor and Reynolds NumberIn this experiment, the Fanning friction factor, defined as

f = − (∆P )gc D2ρH2OV2 L

is measured as a function of the Reynolds number, NRe = ρDV/µ ,over a range covering both laminar andturbulent flow regimes for water. While collecting data, make an approximate calculation of the Reynoldsnumber for each condition to be certain that a proper range of Reynolds numbers is being used.

The "blue" apparatus (Fig. 1) will be used in this experiment. This apparatus has two flow networkssupplied by two pumps. The small diameter network will be used to yield data for the laminar flow regimeby using the smaller pump and the 0.125 inch ID tube. Turbulent flow can be investigated in the 2.00,1.025, and 0.545 inch ID tubes by use of the main recirculation system (large pump).

The pressure drop over a section of a pipe is measured directly with a manometer. The calculation ofthe Reynolds number requires a knowledge of a volumetric flow rate which is most easily measured withan orifice meter and the second manometer. The values of orifice coefficient for calculating volumetricflow rate from the manometer reading will be given. For the principles of manometers and orifice meters,see 06-152 lecture notes.

For flow through the smallest tube, the flow rate can be determined by the timed amount of fluidvolume drained into the graduated cylinder.

Be careful to allow some bypass for the pumps in most situations. Also application of the excessivepressure drop across the manometer will blow the mercury out of the manometer. A toggle valve has beenplaced between the leads to the manometer (Fig 1). When the toggle valve is open (the handle is straightup) the pressure drop across the manometer legs is reduced due to the flow through the valve. Keep thevalve in the open position when changing the flow rate and when the pump is turned on or off. To make apressure reading, slowly close the toggle valve, wait until an equilibrium pressure is obtained and observethe height of the mercury.

Reservoir

1/8" brass 0.125" I.D.

1/2" brass 0.545" I.D.

1" copper 1.025" I.D.

2" plexiglass 2.00" I.D.

pressure tap

valve

orifice

pitot tube

Figure 1. Laminar/Turbulent Flow System.

to manometer

2.00 " movable impact tube

0.0625 " O.D.

Figure 2. Simple Pitot Tube.

The temperature of the water will change during the course of the experiment. Be sure to measurewater temperature at various times during the experiment.

Velocity profile of turbulent flow

An impact tube (simple pitot tube) (Fig. 2) will be used to measure local velocity of flowing water acrossthe diameter of the largest tube (2.00"ID). A discussion of the principle and operation of an impact tubecan be found in 06-152 lecture notes.

The impact tube measures the difference between the dynamic and static pressures of the flowing fluidand the pressure difference allows the calculation of fluid velocity at the tip of the impact tube.

The tube is positioned with a wheel and gear device attached to a dial indicator which measuresposition in 1/1000 of an inch.

Relevant data for flow measurement is given below.

Dimensions Orifice Coefficients, k1/8” Brass 0.125 none1/2” copper tube 0.545 0.00441” copper tube 1.025 0.01822” plexiglass 2.00 0.0440

Measure velocity profiles for a least two flow rates, one at the high end of the manometer scale and theother at the low end. The pressure drop should be read at 0.100 inch intervals in the turbulent core and 0.05inch or 0.025 inch intervals as the probe nears the wall. When moving the pitot tube allow enough time forthe new ∆P to come to equilibrium; usually 30 to 60 seconds. Since the pump will raise the watertemperature during the course of the experiment, be sure to measure the fluid temperature at intervalsduring the experiment.

Startup procedure

1. Turn the main pump switch on and attach the leads from a mercury manometer to the orifice fittingson the pipe. The orifice meter will be used to measure the bulk flow rate in the pipe.

2. Slowly close the toggle valve on the manometer and adjust the flow rate through the pipe to a Dh ofthe manometer of about 20 to 25 inches of mercury. Make sure one of the other pipes in the circuitis open to act as a bypass for the pump at lower flow rates.

3. Position the impact tube in the center of the pipe and slowly close the toggle valve on the manometerattached to the tube. Observe the pressure drop. If the manometer is in danger of blowing(indicating fluid within 1.5 inches of the top) reduce the flow rate. If the pressure drop is too low,increase the flow rate to a safe higher level. Note: when the toggle is first closed or the flow rate ischanged, the time required for the pressure drop to come to equilibrium is longer, about 3 or 4minutes, then when moving the tube to measure the profile.

4. Always make sure all manometer toggle valves are open before shut down, start up or largechanges in the flow rate!!! This will prevent blowing of the manometer and extra time in the lab.

6.4 Treatment of DataFriction factor and Reynolds Number

•Calculate the Fanning friction factor and Reynolds number from the data collected.

•Correlate the friction factor as a function of the Reynolds number in a power form for bothlaminar and turbulent flow.

•Compare your results with the theoretical relationship for laminar flow and some of the existingcorrelations for turbulent flow.

Velocity Profile of Turbulent Flow

•Calculate local fluid velocities from the impact tube measurements.

•Represent the measured velocity profile by the "power rule" and evaluate the constant n. (See 06-152 lecture notes)•Compare your value of n with the generally accepted n = 1/7.

•Calculate u+ and y+ from friction factor and local velocity.

•Represent the measured velocity profile in the form of the universal velocity distribution law andevaluate constants A and B. (See 06-152 lecture notes).

•Compare your values of A and B with those found in the literature.

•Perform an integration using local velocity to find the volumetric flow rate and compare it withthe value obtained by orifice meter measurement.

6.5 Discussion questions and pointsFriction factor and Reynolds Number

•If the experimental relationship between the friction factor and Reynolds number for laminar flowdisagrees with theory, suggest reasons for the disagreement.

•For the turbulent flow regime, discuss how closely the experimental friction factor agrees withsome of the existing correlations of the friction factor chart (e.g. McCabe, Smith and Harriott;"Unit Operations of Chemical Engineering," Fig 5-9, p. 88). Explain if disagreements are found.

Velocity Profile of Turbulent Flow

•Which of the forms, the power rule or the universal velocity distribution, better represents theexperimental profile?

•Explain disagreements if any between your results and the literature.

•Is the local velocity data consistent with the volumetric flow measured by the orifice meter?

•Can your data reveal the thickness of the laminar sublayer and the buffer layer?

6.6 Prelab for Laminar & Turbulent Flow in Pipes

Questions1. How does the value of f measured depend on flow rate and the specific gravity of the manometer fluidused?

Calculations1. Plot f vs. NRe for the following correlations.

f = 16/NRe 0 < NRe < 2100

f = 0.079/NRe.25 4000 < NRe < 105

2. The following sample data was collected for the 1/8 in. dia. tube.

? p(in. Hg) 12.2 11.4 8.95 6.3 3.3V (m/s) 1.5 1.4 1.14 0.9 0.6

Calculate and plot f vs. NRe. Does the data obtained agree with your expectation based on prior work?

3. Calculate u/umax for y/R = 0.05, 0.1, 0.2, 0.4, 0.6, 0.8, 0.9, and 1.0 based on the 1/7 power rule correlation for the velocity profile in turbulent flow.

4. The following velocity profile data was taken in the 2 in. Plexiglas tube.

∆Porifice = 17.4 in. Hg Q(ft3/s) = 0.044 h1/2 (ft H2O)

y/R 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1∆P 3.9 3.9 3.9 3.8 3.8 3.7 3.6 3.4 3.0 2.8

Calculate u/umax and compare the actual profile to the 1/7 power correlation.

Lab Planning1. What is the maximum flowrate that should be studied for laminar flow in the apparatus?

2. Submit a workplan and schedule.