Experimentto Determine the Pressure Loss and Flow Rate

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Abstract

Inmany cases, it is very challenging to most engineers to estimate theflow through pipes accurately. The prediction of the velocity, theflow rate and the drop in pressure through the piping system is anessential step in the design of many engineering systems. As fluidsflow through pipes, local eddy currents may be created within thefluid thus adding some resistance to the fluid flow. The currents areas a result of the internal roughness of the pipe. The resistance inturn causes a pressure loss. With increase in the flow, there is acorresponding rise in pressure loss. This experiment was conducted toinvestigate the viscous flow through a pipe. Special focus was givento the drop in pressure as a result of frictional losses. The resultsof the pressure drop obtained from the experiment are then comparedto the ones predicted by use of pipe flow theories.

Table of Contents

Abstract i

Experiment to Determine the Pressure Loss and Flow Rate 1

Introduction 1

Experimental Setup 4

Procedure 4

Results 5

Discussion 9

Conclusion 10

References 11

Appendix 12

Experimentto Determine the Pressure Loss and Flow RateIntroduction

Inmany cases, it is very challenging to most engineers to estimate theflow through pipes accurately. The prediction of the velocity, theflow rate and the drop in pressure through the piping system is anessential step in the design of many engineering systems. As fluidsflow through pipes, local eddy currents may be created within thefluid, thus adding some resistance to the fluid flow. The currentsare as a result of the internal roughness of the pipe. The resistancein turn causes a pressure loss. To increase in the flow, there is acorresponding rise in pressure loss. This experiment was conducted toinvestigate the viscous flow through a pipe. Special focus was givento the drop in pressure as a result of frictional losses. The resultsof the pressure drop obtained from the experiment are then comparedto the ones predicted by use of pipe flow theories. The followingwere the objectives of the experiment.

Investigate viscous flow through a pipe

Determine the pressure loss as a result of frictional losses

Compare the results obtained from the experiment to those determined by pipe flow theories.

TheEnergy Equation (i) for fluids can be used to summarize the totalenergy as the elevation energy, velocity energy and pressure energy.

_{}= pressure in the fluid (Pa (N/m^{2}),psi (lb./in^{2}))

_{}= pressure loss (Pa (N/m^{2}),psi (lb./in^{2}))

_{}= fluid density (kgm^{-3},slugsft^{-3})

_{}= velocity of flow (ms^{-1},ft.s^{-1})

_{}= gravity acceleration (ms^{-2},ft.s^{-2})

_{}= elevation (m, ft.)

Inthe case of horizontal steady state, the flow, _{}= _{}and _{}=_{}

Theformula can therefore be changed into

Pressureloss can be categorized into major loss resulting from friction andminor loss resulting from alterations in the velocity within valvesand bends. In pipes, the pressure loss is dependent on the length anddiameter of the pipe, the flow velocity and a friction factorrelative to the pipe roughness. It is also important to determinewhether the flow is laminar or turbulent. This is determined by theReynolds Number of flow (Filip, 2013). The pressure loss in a pipe asa result of frictional losses can be calculated using the formula:

_{}= friction coefficient

_{}= length of pipe (m)

_{}= hydraulic diameter (m)

Thisequation is also known as the D’Arcy-Weisbach Equation. It is onlyvalid for fully developed, steady and incompressible flow.

Thefriction coefficient _{}is dependent on whether the flow is laminar, turbulent or transient,and also on the roughness of the pipe. Determining the frictioncoefficient therefore starts with determining whether the flow istransient, laminar or turbulent.

Darcy’sequation can also be used to determine the pressure drop as expressedin equation (IV)

_{}= Pressure drop, psi (Ohira et al., 2012)

The_{}is the density, lbm/ft^{3}

The_{}is the friction factor

Lis the pipe length, ft.

Vis the velocity, ft/sec

The_{}is the pipe inside diameter, in.

Rotlaminar flow, the friction coefficient is determined by:

_{}is the Reynolds number

Aflow is said to be laminar when the _{}is less than 2300, transient when _{}is greater than 2300 but less than 4000 and turbulent when _{}is greater than 4000

Sincethe transient flow ranges between the laminar and turbulent flows, itis not possible to tell the friction coefficient.

Fora turbulent flow, the roughness of the wall of the pipe and theReynolds Number are responsible for the friction coefficient as shownin equation (vi)

_{}is the absolute roughness of the pipe wall measured in (mm, ft)

_{}represents the relative roughness, which is also referred to as theroughness ratio.

Theabsolute roughness for copper is about 0.001-0.002×10^{-3}mor 3.3-6.7×10^{-6}ft.

Fornew cast iron, k is about 0.25-0.8×10^{-3}mor 8- 27 10^{-4}ft.

Forworn cast iron, the value is 0.8-1.5×10^{-3}mor 2.7- 5×10^{-3}ft.

Forrusty cast iron, the value is 1.5-2.5×10^{-3}mor 5- 8.3×10^{-3}ft.

UsingReynolds number and the Moody friction factor, Re can be determinedby

Where_{}is the density in lbm/ft^{3},D is the internal diameter of the pipe in ft., V is the flow velocityin ft/sec and _{}is the viscosity in lbm/ft-sec.

ExperimentalSetup

Theexperiment was set up as shown in Fig. 7. Fig. 8 is a photograph ofthe setup of the experiment. In the setup, a pump is used tocirculate water through a piping loop. The water is made to flow in aclockwise direction through the piping loop. Within the loop are apump or circulator, a flow meter and three sections for testing. Thethree test sections are given their names with regard to the type ofpipe used. In this experiment the test sections were copper, wroughtiron and cross-linked polyethylene (PEX). For wrought iron and thePEX test sections, there were only the straight length of the pipes.In the copper section, however, included a combination of pipesections, valves and fittings. The valves were used in directing theflow through the test sections. A differential pressure transducerwas used in measuring the pressure difference between the differentpoints in the system. An impeller style flow meter was also used inthe setup. Connected to the system is a Data Acquisition system(DAQ). Its function is to log the results of the experiment. Thepipes that were used were as shown in Table 1.

Procedure

Thefollowing procedure was used in obtaining the experimental data.

First, we opened the copper switch, turned to low pressure, and recorded the pressure and flow rate data. We then turned to high pressure, and read the pressure and flow rate data.

Next, the copper switch was turned off and the iron pipe switch was opened, we turned to low pressure and recorded the pressure and flow rate data

Then we turned to high pressure, and recorded pressure and flow rate data.

Third, we turned off the iron switch and opened the PEX pipe switch, we turned to low pressure and noted the pressure and flow rate data.

Finally, we turned to high pressure, and recorded the pressure and flow rate data.

Copper switch turned on | High pressure | Low pressure |

Iron pipe switch on | High Pressure | Low Pressure |

PEX pipe switch on | High Pressure | Low Pressure |

Table1: List of experiments conducted

Results

Thedata that was obtained from the experiment are recorded in Tables 2,3 and 4.

The length of the copper pipe was 109 cm.

Copper Pipe switch | High Pressure | Low Pressure |

Pressure reading | 0.417 | 0.200 |

Flow rate | 4.119-4.396 | 2.441-2.721 |

Table2: Copper pipe switch on

The iron pipe had a length of 117 cm

Iron Pipe switch | High Pressure | Low Pressure |

Pressure reading | 0.315 | 0.150 |

Flow rate | 4.5-4.958 | 2.831-3.054 |

Table3: Iron pipe switch on

The PEX pipe was 119 cm long and had the following readings

PEX Pipe switch | High Pressure | Low Pressure |

Pressure reading | 0.396 | 0.194 |

Flow rate | 4.227-4.598 | 2.612-2.906 |

Table4: PEX pipe switch on

Thepressure of water at 25 degrees Celsius is 1 kg/l while its kinematicviscosity is 0.001 Pa-s.

Usingthe formula_{},the pressure loss can be calculated for the three pipes

ForPEX pipe, the Reynolds Number = 5000

Frictionalfactor = 0.0376

PressureDrop = 0.526 psi

Thevolume flowrate is 1.96 m/s

Forcopper pipe

ReynoldsNumber, R: 1.27 × 10^{4}

FrictionFactor, f: 0.0315

PressureDrop: 0.196 psi

VolumeFlowrate: 1.27 m/s

Forwrought iron pipe,

Pressuredrop = 0.900 psi

Flowrate = 3.51 m/s

The values can be compared as shown

Iron Pipe switch | High Pressure | Low Pressure | Theoretical value |

Pressure reading | 0.315 | 0.150 | 0.900 |

Flow rate | 4.5-4.958 | 2.831-3.054 | 3.51 |

Copper Pipe switch | High Pressure | Low Pressure | Theoretical value |

Pressure reading | 0.417 | 0.200 | 0.196 |

Flow rate | 4.119-4.396 | 2.441-2.721 | 1.27 |

PEX Pipe switch | High Pressure | Low Pressure | Theoretical value |

Pressure reading | 0.396 | 0.194 | 0.526 |

Flow rate | 4.227-4.598 | 2.612-2.906 | 1.96 |

*Fig.1. Pressure loss for iron pipe*

*Fig.2. Flow rate for iron pipe*

*Fig.3. Pressure drop for copper pipe*

*Fig.4. Flow rate for copper pipe.*

*Fig.5. Pressure reading for PEX switch*

*Fig.6. Flow rate for PEX pipe*

Discussion

Fromthe comparison figure for iron pipe (Fig. 1), it can be seen that thehigh pressure reading for the pressure drop from the experiment wasmuch higher than the theoretical values while the low pressurereading is close to the theoretical value on the lower side. Thetrend is similar in Fig. 2, 3, 4, and 5. In Fig. 6, the theoreticalvalue is lower than even the low pressure flow rate reading (Geropp,& Odenthal, 2001). These differences are as a result ofexperimental errors including failure to consider the friction causedby bubbles in the water, failure to recognize the elevation of thepipe and error in reading the measuring instruments. The bubbles moveat their own velocity within the water causing internal friction. Ifthis is unaccounted for, it can lead to a lower reading than thetheoretical values. Errors in the calculations of the theoreticalvalues can also lead to unusually lower values like in Fig. 6 andunusually high values like in Fig. 5.

Conclusion

Thisexperiment was carried out to determine the rate of flow in differentpipes and the pressure loss due to friction within the pipe. Waterwas used as the fluid. From the experiment, it was found out that,due to various limitations and errors, the experimentally obtainedvalues are either lower or higher than the values obtained throughflow theories. There were as a result of experimental and calculationerrors. Better software for the calculation of pressure losses andvolume flow rates are necessary.

References

Filip,A. (2013). Determination of Pressure Drop in Horizontal Pipes for Air– Water Two Phase Flow. *MathematicalModelling In Civil Engineering*,*9*(2),1-8. http://dx.doi.org/10.2478/mmce-2013-0005

Geropp,D. & Odenthal, H. (2001). Flow rate measurements in turbulentpipe flows with minimal loss of pressure using a defect-law. *FlowMeasurement And Instrumentation*,*12*(1),1-7. http://dx.doi.org/10.1016/s0955-5986(00)00033-9

Ohira,K., Okuyama, J., Nakagomi, K., & Takahashi, K. (2012). Pressuredrop of slush nitrogen flow in converging–diverging pipes andcorrugated pipes. *Cryogenics*,*52*(12),771-783. http://dx.doi.org/10.1016/j.cryogenics.2012.09.001

Appendix

Pipe | Length (in.) | Diameter (in.) | Roughness (mm) | Type |

PEX | 38 | 0.5 | 0.00015 | SDR-9 PEX |

Wrought Iron | 38 | ¾ | 0.0015 | ASTM A53 SCH-40ST |

Copper | (Measured) | ½ | 0.0015 | M |

Table5: Specifications of the used pipes in the experimental setup

Fig.7: Schematic drawing of pipe flow experimental setup

Fig.8: Picture of the experimental setup