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Experimental Setup
Before starting the experiment, an apparatus must be constructed to support the head tank through which fluid will flow. The minimum dimensions for the K’NEX structure are 390mm x 390mm x 650mm (l x w x h). The minimum height from the ground to the bottom of the head tank should be 1.65m and the distance between the waterlines of the buck and the pop bottle must be at least 1.6 m. The structure is supported by the lab bench.

There are three PVC piping (½”) in total. One is for inlet pipe, and the rest is used for outlet pipe and an overflow pipe that enters the head tank to allow for water flow. The overflow pipe is attached from the bottom of the 2L soda container and all three pipes must exit into a bucket placed on the ground. It is recommended to arrange the overflow pipe and outlet pipe close enough to each other so that fluid from both can exit into a milk jug opening used as a graduated cylinder. The flow meter will be inserted in the outlet pipe and there must be minimum of 6” of piping on each side of the flowmeter. To ensure there is no leakages and minimum leaks, use Teflon tape or hot glue to seal hose barb

1) Ensure that the pump is fully submerged in the water to avoid any motor burns. As the fluid is pumped up from the bucket of water and flows through inlet tube into the tank, ensure that it accumulates into the head tank.

3)  Ensure that steady flow state is achieved by adjusting the valve and letting the water level pass the top of the overflow tube.
4) Calibrate the flow meter by running the experiment for set amount of test trials and compare it to the calibration curve obtained in Lab 1.
5) If the calibration curve from Lab 1 is similar to the new calibration curve, proceed with the experiment, if the calibration curve doesn't match to the new curve, obtain measurements to find a new calibration curve.

6)  Once steady state is achieved, place the milk jug place under the two outlet tubes to fill it up with the water to some indicate some prescribed volume.

7)  Using stopwatch measure the time it takes to fill up milk jug to prescribed volume.

8)   Also, measure the frequency using USB 6009 during the time the water was exiting into the milk jug.
9) Record all the components and the lengths of the pipes used for making different assemblies

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1)    Lab Manual: ENME 341 Lab Manual, Fundamentals of Fluid Mechanics, Summer 2017, Schulich School of Engineering, University of Calgary.

2)    Fundamentals of Fluid Mechanics Textbook 7th edition, Bruce R.Munson, Theodore H.Okiishi, Wade W.Huebsch, Alric P.Rothmayer, copyright © 2013.

3)    Hydromatic.com. (2017). Head Loss in Piping Systems - TechInfo. [online] Available at: http://www.hydromatic.com/ResidentialPage_techinfopage_headloss.aspx [Accessed 17 Aug. 2017].
4)Engineering Toolbox. Ventilation Ducts Roughess [online]. Available at:
http://www.engineeringtoolbox.com/surface-roughness-ventilation-ducts-d_209.html [Accessed Aug. 2017

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The main purpose of this lab was to quantify the head losses that is the pressure drop in the piping assemblies constructed with a variety of pipe components such as ball valves, elbows, unions, tees, couplers etc. Four different assemblies were constructed and using the pressure tap installed, the differential pressure loss was measured. Friction factors for laminar and turbulent flow and the volumetric flow rate were obtained for all the assemblies. The calibration graphs were plotted for flow rate vs. frequency for each assembly. The R2 value for the flow meter calibration assembly 1 and 2 was 0.8907 and for assembly 3 and 4, it is 0.8901.

The R² value for all assemblies is comparatively close to 1, which demonstrates that the results collected are relatively accurate and develops a relationship with Reynold’s number being varied with the different pipe assemblies. The flow is determined to be turbulent for the assembly 2.  The Reynold number increases with the velocity profile which is evident from Reynold’s formula. Experimental results were collected and compared to theoretical calculations. The inaccuracies of the results could be due to many factors such as leakage in pipes, error in reading the height difference in the Tygon tubing or the error in measuring the volumetric flow rate.Overall, the experiment should be considered successful as the main objectives were met and the basic understanding of head losses in a variety of piping assemblies was covered.

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A possible source of error in this experiment were the leaks in the pipes. When water was flowing in and out of the system there were spots where minor leakage was occurring. As a result this may have  given inaccurate readings of flowrate and frequency in the flow meter, because the flowrate in was not equal to the flowrate out. A recommendation to resolve this issue would be to properly hot glue the connection between the pipes and the pop bottle, as well as make sure the elbows connecting the pipes are properly secured.

A second source of error was in measuring the flow rate, the calibration curve from either Lab 1 was used or a new one was created for that specific flowmeter. Calibration curve from Lab 1 was used even if the testing flow rates did not match up perfectly with Lab 1 results. Furthermore, if a new calibration curve was created, only 5 data points were taken for it without replicates. Hence, an accurate flow rate reading may have not been used for calculations.

A third source of error was caused by measuring the height difference in the Tygon tubing. It was examined that when measuring the height difference, the Tygon tubing was not completely straight and was slightly curved. This could have resulted in inaccuracies of our measurements when acquiring the height difference of the water levels. A possible recommendation is to cut the Tygon tubing as short as possible and have it held in place. This would assure that the tubing is not curved when measuring the height differences.

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Data regarding this trial. Comparison between the head loss in each section is made as well as the theoretical friction factor for each section for both laminar and turbulent flow. Comparison between total experimental and theoretical head loss is also shown.

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Data regarding this trial. Comparison between the head loss in each section is made as well as the theoretical friction factor for each section for both laminar and turbulent flow. Comparison between total experimental and theoretical head loss is also shown.

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Data regarding this trial. Take note of the comparison between the theoretical and experimental head loss as well as the experimental and theoretical friction factor. Theoretical friction factor calculated for both turbulent and laminar flow but only turbulent friction factor wasvalid since the flow was turbulent.

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Data regarding this trial. Take note of the comparison between the theoretical and experimental head loss as well as the experimental and theoretical friction factor. Theoretical friction factor calculated for both turbulent and laminar flow but only turbulent friction factor was valid since the flow was turbulent.

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Data regarding this test. The friction factor used was the turbulent theoretical since flow was turbulent.

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Data regarding this test. The friction factor used was the turbulent theoretical since flow was turbulent.

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Data regarding this trial. Take note of the comparison between the theoretical and experimental head loss as well as the experimental and theoretical friction factor. Theoretical friction factor calculated for both turbulent and laminar flow but only turbulent friction factor was valid since the flow was turbulent.

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In this test, the flowmeter K value was found. This is done by equating theoretical head loss to experimental head loss as mentioned in Analysis and Theory. This K value is used in all other calculations.

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1.    Attach the designed 2-leg asymmetric assembly piping network to the apparatus.

2.     Design the assembly 4 with different parts such as length of pipe, type and number of connectors in each leg of the assembly.

3.    Assembly 4 requires 2X90° elbows, 2x45° elbows, 2xTee connectors,2 couplers, 1x ball valve and 5 additional connectors

4.    The flowmeter is attached into the final length of each leg before the two legs converge and have a set distance of 6’’ from the opening to either end

5.    Attach a horizontal pressure sensor after the two legs converge

6.    Once the pump is on, adjust the voltage and current to the setting that achieves steady flow.

7.    If there are bubbles in the pipe section, they can be removed by purging the flow

8.    Once calibrated, to quantify the pressure drop across the valves, run LabVIEW while simultaneously measuring the volumetric flow rate and recording frequency by using stopwatch

9.    Measure the height difference of water in the u-tube manometer, make sure the two tubes containing the liquid are arranged as close to one another for easier reading of differential pressure

10. Repeat the steps 9-10 with different current and voltage settings at a variety
11. After switching power off, remove the assembly

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As mentioned in Analysis and Theory, by equating the experimental head loss to theoretical head loss, the friction factor and consequently the relative roughness can be found. The roughness value is used to determine all other friction factors for turbulent flow.

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1.    Attach the designed 2-leg symmetric assembly piping network to the apparatus.

2.     Design the assembly 3 with identical parts such as length of pipe, type, and a number of connectors in each leg of the assembly.

3.    Assembly 3 requires 2X90° elbows, 2x45° elbows, 2xTee connectors,2 couplers and 1x ball valve

4.    The flowmeter is attached to the final length of each leg before the two legs converge and have a set distance of 6’’ from the opening to either end

5.    Attach a horizontal pressure sensor after the two legs converge

6.    Once the pump is on, adjust the voltage and current to the setting that achieves steady flow.

7.    If there are bubbles in the pipe section, they can be removed by purging the flow

8.    Calibrate both flow meters by opening one valve and running LabVIEW and then opening the closed valve and closing the current valve and running LabVIEW

9.    Once calibrated, to quantify the pressure drop across the valves, run LabVIEW while simultaneously measuring the volumetric flow rate and recording frequency by using stopwatch

10.Measure the height difference of water in the u-tube manometer, make sure the two tubes containing the liquid are arranged as close to one another for easier reading of differential pressure

11.Repeat the steps 9-10 with different current and voltage settings at a variety

12.After switching power off, remove the assembly

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Results Flowmeter 1 Calibration (Assembly 3 and 4)

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Results Flowmeter 1 Calibration (Assembly 3 and 4)

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Assembly 3 and 4 each had two sections each with their own flowmeters. The sections are labelled as section 0 and section 1. The calibration for section 0 matched calibration curve from Lab 1. Hence Lab 1 calibration curve will be used for that. For section 1, the flow meter was re calibrated as shown below. Flowmeter 1 of assembly 3 and 4 is different from Flowmeter 1 of assembly 1 and 2.

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1.    Attach the designed ball valve(s) assembly piping network to the apparatus.
2.     For assembly 2, design it with ball valves placed in series or parallel. For our design, 2 ball valves were attached in parallel view.

3.    The flowmeter is attached into the outflow line below the ball valves besides the pressure probe.

4.    Once the pump is on, adjust the voltage and current to the setting that achieves steady flow

5.    If there are bubbles in the pipe section, they can be removed by purging the flow

6.    To quantify the pressure drop across the valves, run LabVIEW while simultaneously measuring the volumetric flow rate and recording frequency by using stopwatch

7.    Measure the height difference of water in the u-tube manometer, make sure the two tubes containing the liquid are arranged as close to one another for easier reading of differential pressure

8.    Repeat the steps 6-7 with different current, voltage, back pressure settings at a variety of valve opening such as 1/3 closed valve, 2/3 closed valves and fully closed.

9.    After switching power off, remove the assembly

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1.    Attach the designed assembly 1 piping network onto apparatus.

2.     For assembly 1 attach the flow meter and additional pressure sensor at the level of current outlet pressure probe.

3.    Once the pump is on, adjust the voltage and current to the setting that achieves steady flow

4.    To quantify the pressure drop across the flow meter and in the vertical pipes, run LabVIEW while simultaneously measuring the volumetric flow rate and recording frequency by using stopwatch

5.    Measure the height difference of water in the u-tube manometer

6.    Repeat the steps 4-5 twice with different current, voltage and back pressure settings

7.    After switching power off, remove the assembly

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Results Flowmeter 1 Calibration (Assembly 1 and 2)

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Results Flowmeter 1 Calibration (Assembly 1 and 2)

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After conducting a few tests using the milkjug method, it was found that the calibration curve from Lab 1 relating frequency of flowmeter to flow rate could not be used. A new calibration curve was created for the flowmeter used for Assembly 1 and 2.

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The following parameters were used for calculations:

Diameter of pipe(D) =0.5inch=0.0127m
Water density=1000kg/m^3
Water viscosity=1.12*10^-3 Ns/m^2

Image below has all the K values used for calculations.

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Lab 2 consisted of measuring pressure of a balloon using a manometer. A similar concept is applied in this lab. The pressure difference between two points is measured using pressure taps. In Lab 2, it was observed that the pressure difference is the difference in height of the fluid multiplied by density and gravity. Hence, it was efficient to have the tubes of the manometer close together for easy height difference readings. In lab 5, the tygon tubes were placed close together as well for easy measurements. In this lab, the energy equation simplifies so that the head loss is simply the height difference in pressure taps. This is proven in the link provided in above slide. Hence, the pressure difference is not actually needed. Essentially, if there were no head losses at all, there would be no difference in height of the pressure taps if measured with reference to datum placed on upper pressure tap. The difference in height is due to losses.

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Assembly 4 consists of two sections, one identical to that of Assembly 3 and one new section with more components. Both sections have flow meters attached to them. This means that theoretical head loss can be individually calculated as well as theoretical friction factors for both. This time, the theoretical friction factor for the sections should differ since they are no longer identical. The theoretical head loss for both sections combined should be compared to experimental since that is what experimentally is being measured. The theoretical friction factor to experimental one can be compared if theoretical is found using parameters accounting for both sections.

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Assembly 3 consists of two identical sections each with their own flow meters. The head loss measured experimentally however is the total sum of the two sections. The total theoretical head loss can be calculated for each section independently since there is a flow meter at each section. The theoretical friction factor can also be calculated for each section theoretically for both laminar and turbulent flow. However, the experimental head loss can only be compared to the theoretical sum of both section's head loss. If comparing the experimental friction factor to theoretical friction factor, the theoretical will be found by using parameters accounting for both sections.

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Effectively, the relative roughness and the K value for the flow meter has been determined. Now, Assembly 2 can compare experimental head loss to the theoretical head loss.

Experimental head loss is simply the height difference of the water in pressure taps. Theoretical can be calculated by summing minor and major head losses. The theoretical friction factor for this calculation is determined using Colebrook, Moody or Halaand equation if the flow is turbulent. If it is laminar, simply use relationship between friction factor and Reynolds number.

The experimental friction factor can be found by stating that experimental head  loss is the sum of major and minor losses. Minor losses K value can be found through reference source, hence minor losses can be computed. The friction factor can then be isolated for.

Now, there is a comparison between experimental and theoretical head loss as well as a comparison between experimental friction factor and theoretical friction factor (for both laminar and turbulent).

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Assembly 1 Vertical Pipe

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Assembly 1 Flowmeter

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Assembly 1 can also be used to measure the experimental head loss between the flow meter. This is since there is a pressure tap on either side of the flow meter. The K value for the flow meter is not indicated in the reference sources. However, this is an important value since all other tests contain the flow meter in between the pressure taps. Hence, its minor loss needs to be accounted for.

The K value for the flow meter can be found using assembly 1 by again equating the total experimental head loss across the flow meter to the theoretical head loss. Now, the friction factor can be directly found using Colebrook, Moody or Halaand since the relative roughness is known as well as the Reynolds number for this test. This is if the flow is turbulent. If not, use simple relationship between friction factor and Reynolds number. The theoretical head loss is the sum of the major and minor head losses, hence, friction factor is needed for major losses. Using equation below, only unknown will be the K value. This is K value for flowmeter since it is only component between pressure taps.

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As stated, the friction factor for turbulent flow depends on pipe roughness. Most flows in real life and in this lab are going to be turbulent, hence the roughness will be needed.

To find relative roughness of the pipe, the friction factor and Reynolds number is needed. Since
roughness is not known, the first part of the assembly 1 will be used to determine this. The head loss in the vertical component of the pipe will be measured using the pressure tap after the flow meter and at the exiting section. In this section there are 2 90 degree elbows as seen in photos of Assembly 1.

By measuring total experimental head loss for this section, it will be assumed that this experimental value is 100% accurate to the theoretical value. From this, the friction factor can be obtained by equating theoretical head loss (consisting of minor and major losses) to the total measured experimental head loss. In equation below, all is known except for friction factor. The value of K can be found in reference sources. For this first test, K value is the sum of 2 90 degree elbows.

Once friction factor is known, relative pipe roughness can be found if flow is turbulent. This is done through Colebrook's, Moody Diagram or Halaand equation which all relate friction factor and Reynolds number (easily calculated) to the relative roughness. Colebrook equation was used in results section (second equation shown). Once pipe roughness is found, it will be used for all other tests. If flow is not turbulent, increase power in pump to increase the flow rate and consequently the velocity and Reynolds number.

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In the theoretical major head loss term, there is the friction factor term. The friction factor essentially is a representation of the friction effects and varies depending on pipe parameters and flow characteristics.

One way to characterise flow is through the dimensionless number called Reynolds number. If the Reynolds number is less than 2300 it is considered laminar flow and if is above 4000 it is turbulent flow. Values in between constitute the transitional region.

The friction factor depends on type of flow. If flow is laminar it is a simple function of Reynolds number as stated below. If it is turbulent flow, then friction factor depends on both Reynolds number as well as relative roughness. If turbulent, the friction factor has to be found through Moody Diagram, Colebrook equation or Haaland equation which all relate friction factor to the Reynolds number and relative roughness.

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In Lab 1, the calibration curve was created for a flow meter. This was done by placing the flow meter into the inlet pipe and measuring the flow rate through the time it took to fill a prescribed volume in milk jug. From there, the premeasured volume of milk jug could be divided by time it took to fill milk jug to find find flow rate. When filling milk jug in Lab 1, both overflow and outlet pipe had to empty into milk jug. This is only since flow meter was situated in the inlet pipe, hence total outflow has to be measured. If calibration is needed for this lab, the flow meter is situated at the outlet pipe already, hence milk jug only needs to capture water from the outlet pipe and not overflow. Calibration will be needed if the calibration curve does not fit for the flow meters used in Lab 5. Hence, conduct a few trials for each flow meter and measure the flow rate using the milk jug technique and corresponding frequency. If the flow rate does not match calibration curve from Lab 1 for that same frequency, re calibration needs to be done. This applies to all flow meters used in lab.

Graph below is calibration curve from Lab 1.

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Theory and Analysis Measuring Experimental Head Loss and Flowrate

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Theory and Analysis Measuring Experimental Head Loss and Flowrate

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In experiment, the total head loss is being measured for different assemblies. Effectively this is done by measuring the difference in height of the water for the different tygon tubing pressure taps. Be sure to set the bottom of the upper pressure tap as the datum or reference point. For more more in depth explanation as to why the total head loss is equal to the difference in height of the pressure tap, click link below:

Hence, experiment has a simple method to determine the experimental total head loss. This can then be compared to the theoretical head loss. Theoretical head loss is a combination of minor and major head loss as stated in previous slide.

In theoretical head loss terms, average velocity is needed. Velocity is also needed to calculate Reynolds number as explained later. This can be found through equation below using the flow rate. The flow meters that are used to measure flow rate measure the frequency of the blades of the flow meter and not the flow rate directly. Similar to what was done in Lab 1, they need to be calibrated. Since the model of the flow meter is the same as that of Lab 1, it is possible that the calibration curve is the same as Lab 1. If not, a new calibration curve needs to be created with similar procedure to Lab 1.

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Assembly 4

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Assembly 3

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Assembly 2

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Theory and Analysis Major and Minor Head Loss

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Theory and Analysis Major and Minor Head Loss

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In the energy equation there is the term head loss. This represents the total energy lost in the fluid. Energy in pipe flow can be lost when simply moving through a straight section of pipe due the interaction it has with the walls (no slip condition causes shear stress in fluid). This is called major head loss. When fluid moves through different components of a pipe such as an elbow, connector (union), valve, etc energy is also lost. As an analogy to these losses, imagine a river that flows past rocks, debris and trees. As the river flows past these things, its flow is disturbed and energy is lost. This is called minor head loss.

total head loss= major head loss + minor head loss

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Assembly 4 Video

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Assembly 3 Video

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Assembly 2 Video

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The flow meters that had to be re calibrated are flow meter 1 used in Assembly 1 and 2 as well as flow meter 1 used in Assembly 3 and 4. Although both labelled flowmeter 1 they are different flowmeters used for difference assemblies. Lab 1 flow meter calibration curve had an equation of flowrate=(0.0051)(frequency). The re calibration curves have equations of flowrate=(0.0058)(frequency) and flowrate=(0.0026)(frequency) respectively for Assembly 1 and 2 and Assembly 3 and 4. Hence, one flow meter has a slope 0.007 more than Lab 1 and other has slope about half of that of Lab 1. It was important that the flow meter calibration curve was recreated since accurate measurement of flowrate and consequently the velocity is needed for calculations.

From the test of Assembly 1 part 1, the friction factor was found by equating experimental to theoretical head loss. From there the roughness was found to be 0.0051m using Colebook equation. In online literature [4], the value for roughness for PVC piping is 0.0015m. Hence, there is a 240% percent error. Due to this inaccuracy, other results will be affected since roughness value obtained from this test are used for all other calculations. It was appropriate to use this trial since the flow was turbulent. Turbulent flow had to be ensured since the friction factor depends on roughness only when flow is turbulent. Friction factor obtained by equating experimental to theoretical head loss is 0.2726.

From the test of Assembly 1 part 2, the K value for the flow meter was obtained by again equating experimental to theoretical head loss. The theoretical friction factor for turbulent flow (0.2709) was used since flow was turbulent and it differs significantly from laminar friction factor of 0.01242. The K value was found to be 0.0286 which is comparing to a valve fully open which has K value of 0.05. It is expected for K value for flow meter to be low since its purpose is not to disrupt the flow.

Assembly 2 tested for flow affected by 2 ball valves opened to different amounts. First test had valves fully open which resulted in turbulent flow. The theoretical head loss (1.6507m) is greater than experimental (0.51m) with a percent error of 61%. This is likely due to inaccurate readings of the flowmeter, air in the pipe or since roughness obtained had high percent error itself. Notice that the theoretical turbulent friction factor is closer to experimental friction than theoretical laminar since flow was turbulent. For test with valve closed 1/3 the flow was laminar and similar trends arise.The experimental head loss is greater which is expected since minor losses are now more with valve closed more. In this trial, the experimental head loss is greater than theoretical but there is not as much discrepancy as with valve fully open. Again, theoretical turbulent friction factor closer to experiment since flow was turbulent. In last test with valve 2/3 closed, flow is laminar.The theoretical value for head loss is much greater than experimental likely since K value is very high for 2/3 valve closed. The experimental friction factor is closer to the theoretical turbulent friction factor than it is for laminar. This breaks trend since flow is supposed to be laminar. Hence, flow rate readings may have been lower than what they were.

Assembly 3 had two section each with laminar flow and similar flowrates. This is expected since the sections are identical. Similarly, the theoretical friction factors for both turbulent and laminar flow are similar for the two sections. The total head loss has to be compared to the collective head loss of the two sections since measurements were taken above and below the separation and conjunction of the sections collectively. Total head loss is closer to the turbulent head loss when turbulent friction factor is used even though flow is laminar. Exerpimental head loss is much more than theoretical. Hence, there could have been other losses that were not account for such as dust on pipes, sound disturbances, etc.

Assembly 4 had two sections, one identical to assembly 3 and other section with many more components. The flow for identical section was laminar and it was in transition region for new section. Due to similarity in Reynolds number, the theoretical friction factors are similar for both sections for both laminar and tubulent friction factors. This follows theory since adding components does not change the friction factor but simply increases the K value for minor losses. Comparing total head loss with experimental, it is closer to the collective turbulent theoretical head loss. This may mean that the transitional region is closer to turbulent than it is to laminar since head loss is more aligned to experimental results.

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The objective of this experiment is to design and build a piping system that has different pipe components such as elbows, valves and return bends and examine Reynolds number for each system. From here, the friction factor can be found for experiment. To do this, the roughness of pipe and K value of flow meter needs to be determined which is also done in the lab.

The pressure drop and head losses that occur due to major and minor head losses needs to be quantified and measured. The head losses are measured in the system experimentally and to know what variables affect them, as well as to compute them using empirical data. Hence, both a experimental and theoretical analysis will be done.

Lastly, calculate the energy losses in the system due to the different pipe components and to determine the friction factor for ½’ PVC pipe in both laminar and turbulent flow.

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Under ideal situations there would be no friction between two moving particles. However, in reality there is always friction and losses when movement occurs between two particles. This equally applies to fluid dynamics. When fluid such as water flows in a pipe, some of its energy is lost due to the shear stress from the wall and dissipated into the surroundings. The Bernouilli's equation which governs ideal flow with no losses is modified to account for losses by adding a head loss term(units of length). The first equation is the full energy equation. Yet, it will be assumed that the velocity and velocity profile at two points of measurement in the experiment is the same since there is constant flow rate and area and fully developed flow. Hence, it can be reduced to second equation show.