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Development Length for Non-Newtonian Laminar Flow in Circular Pipe


Academic year: 2023

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This paper consists of the research that was done based on this chosen topic, Development Length for Non-Newtonian Laminar Flow in Circular Pipe. The objective of this project is to study the development length requirement of a non-Newtonian fluid through experimental measurements. The requirement for this experiment is that the literature reviews on the development length of non-Newtonian fluid through a circular tube was mainly in analytical and numerical analysis.

Thus, the scope of the experiment will only be within the laminar regime with non-Newtonian fluid to investigate the development length. In the initial phase, a current loop design was proposed for the project to conduct the experiments. The findings from the experiments were that the development length for non-Newtonian fluids is slightly shorter than that for Newtonian fluids.

Azuraien bt Jaafar, for her guidance and support during the completion of my final year project in partial fulfillment of the requirement for the Bachelor of Engineering (Hons) of Mechanical Engineering. Table 4: Average value of pressure transducer, water 25 Table 5: Average value of pressure transducer, Xanthan gum solution: 0.02 wt% 25 Table 6: Average value of pressure transducer, Xanthan gum solution: 0.03 wt% 26 Table? : Average reading of pressure transducer, xanthan gum solution: 0.04 wt% 26 Table 8: Average reading of pressure transducer, xanthan gum solution: 0.05 wt% 26 Table 9: Conversion table of current to pressure output.

Table  1:  Gantt chart for Final Year Project I  8
Table 1: Gantt chart for Final Year Project I 8








A decan number is the Reynolds number over the square root of the radius of curvature ratio. When the fully developed flow from the straight pipe enters the curved pipe, the fast fluid in the middle section produces a stronger centrifugal force than the surrounding slow fluid, which induces the secondary flow to the outer wall near the pipe center. With such an increase in the secondary flow to the outer wall, the fast flow in the middle section gradually migrates to the outer region of the curved pipe.

At cp= 30, part of the fast fluid moved to the outer region begins to enter the lower region along the pipe wall with the strong secondary flow towards the outer wall. At cp= 40, the slow velocity region of the primary flow appears near the middle section. Consequently, the centrifugal force in the middle section decreases, causing a rapid decrease of the secondary flow to the outer wall.

Also, the stagnation region of the secondary flow appears near the symmetric plane in the inner region. At cp = 90, due to the decrease of the secondary flow to the inner wall near the pipe wall, the attack region of the fast fluid returns to the outer region along the pipe wall, and a reverse rotating vortex appears near the symmetric plane in the inner region .

Figure 2:  Flow patterns of fluid  in curved pipes (Pedley  &  Drazen,  1986)
Figure 2: Flow patterns of fluid in curved pipes (Pedley & Drazen, 1986)


    • Final Year Project 2
    • Final Year Project 1
  • Initial research on non-Newtonian flnids
  • Flow Loop Identification
  • Test Section Drawing Design
  • Measure the static pressure from pressure tap 1-9 following similar steps as in step 6-8
  • Once done, bleed the water from the flow loop
    • Final Year Project 2
  • Flow Loop Assembly And Testing 1. Flow loop assembly
    • Hydraulic leak test
    • Pressure taps were sealed
    • Reynolds Number Calculation
    • Preparing Xanthan Gum Solution
    • Pour solution into the provided beaker
    • Select the spindle to be used
    • Attach spindle to Viscometer
    • Lower the spindle into the beaker until the solution is at the calibration point
    • Select the speed at which to run the spindle
    • Record the viscosity displayed

For this project, Xanthan gum will be used as the non-Newtonian fluid to be studied within the flow loop. Xanthan gum is capable of producing a large increase in the viscosity of a liquid by adding a very small amount of gum. Seal leaks and start steps 6-7 again, if there are no leaks, pump down and blow water out of the flow loop.

For Xanthan Gum solution 0.02 wt%, 0.03wt"/o, 0.04wt% and 0.05wt%, the solution must be mixed outside first, after the solution is well mixed, pour the Xanthan Gum solution inside the mixing loop first for I O minutes after then continue with step 2 through step 13 to complete the experiment.D Use a motorized/magnetic stirrer to ensure that the Xanthan gum does not form lumps within the solution that could distort the readings referring to Ernst, 1966. A A filter of little was added inside the tank to avoid lumps of Xanthan gum.

A simple calculation can help determine the required mass of Xanthan Gum and mass of water to create a solution of certain weight percentage. Xanthan gum solutions by weight should be prepared as such by calculating the required weight with the desired volume of water and mixing it well with either a magnetic stirrer or a motorized stirrer. Use of stirrer is to ensure that the Xanthan gum is well mixed with water without producing any lumps.

After preparing the xanthan gum solution, we must measure its viscosity before starting the experiment. After ensuring that the pump can provide laminar flow using water, the xanthan gum solution that was prepared in advance can now be poured into the tank to flow in the flow loop. During the experiment, make sure that there are no bubbles in the test piece, as this can distort the pressure transducer readings.

Also make sure that the pressure transducer tube is not pinched to prevent measurement errors. The graph from the pressure measurements should be almost constant, if there are fluctuations in the graph, check the pressure transducer for bubbles and repeat the measurement. When preparing to flow a new batch of xanthan gum solution, the flow loop should be flushed with water to ensure that remnants of the previous solution do not contaminate the readings of the new solution.

Fill the tank and pump with water and run the pump at 25Hz- 50 liters per minute. Let the pump run for at least 10 minutes before flushing the water to ensure that the remnants of previous solution are completely dissolved with the water.

Table  I: Gantt chart for Final Year Project 1  Week
Table I: Gantt chart for Final Year Project 1 Week




The results obtained from the pressure transducer reading recorded via the data logger caused the data to be output in voltage. And so the data had to be converted to output pressure from output voltage in order to calculate the total pressure ditl'erencc. With a ten-year resistor that provides a resistance of 120 ohms, we calculate the output current and interpolate the pressure value from the table below.

Test Section Data Logger PompOn Output (4mA-8mA) Pressure Difference Length (em) Volt (V) Output (mA). Test Section Data Logger Static Output (4mA-8mA) Pressure Difference Length (em) Volt (V) Output (mA). Test section data logger Pump on Output (4mA-8mA) Pressure difference length (em) Volt (V) Output (mA).

Test Zietion Datalogger Pump on output (4mA-8mA) Pressure difference length (em) Volt (V) Output (mA). From the data converted above, we can plot this graph, which shows the pressure versus the length of the test section.

Table  I 0: Data conversion, current to pressure (water)
Table I 0: Data conversion, current to pressure (water)

Pressure Drop(kPa) vs Distance (em)

Although we can clearly see the pattern of the pressure drop portrayed here, the data appears to intersect and does not show a smooth pattern. However, the early pressure drop shows that the liquid is developing, and after the 50 cm across the test section, the steepness of the graph is drastically reduced, indicating that the liquid is now fully developed. Before starting the experiment, we calculated the Reynolds number to ensure laminar flow throughout the experiment.

The calculation results are tabulated below along with the input length measure for each polymer solution. And so we can see that from Figure 15, as the concentration of Xanthan gum increases, the solution development length decreases due to the effect of increased viscosity within the walls of the test section. From the result we obtained, we can again check the Reynolds number in the test section by calculating Poiscuille's Law using the pressure difference that was measured.

The pressure difference is the difference between the average static pressure/noise and the dynamic pressure. From the Reynolds number we have, we can see that by plotting the calculated friction factor, most of the values ​​do not fall within the tuning graph because they are too small. Although the moody graph shows mostly turbulent flow, the flow we currently have is laminar.

One of the factors that may have led to the small error in the reading is that the pump had been vibrating all the time during the experiment. This will have caused an error in the pressure transducer readings due to the noise produced by the vibration as the pressure transducer is very sensitive. The second problem is that we have previously calculated the required pump operating conditions for the flow to be laminar and the speed is very slow.

Sometimes the pump would stop rotating at low speed because the rotation was very slow. There is a point where the pump stalls slightly when turning (you can tell by the bolt turning on the outside) which indicates that there is slight resistance in the pump to turn. This caused the pressure transducer reading to fluctuate and form a certain data pattern.

Table 20: Experiment results with operating Reynolds number.
Table 20: Experiment results with operating Reynolds number.







Figure  I:  Friction  factor  versus  Reynolds  number.  x  0.1 %,  I!J.  0.2%,  +  0.3%,  •  0.4%
Figure 2:  Flow patterns of fluid  in curved pipes (Pedley  &  Drazen,  1986)
Figure 3: Effect of concentration on viscosity ofXanthan Gum at various temperatures  (Zhang,  1996)
Table  I: Gantt chart for Final Year Project 1  Week



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