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Transcript

Research

Pipeline Friction

BRAE 312 Term Project

Dr. Stuart Styles

Sarah Alford

by Aidan Fischer and Shane Wyman

What Causes Friction and How its Measured

Background

  • Friction is a force caused by opposing molecules moving at different rates.
  • In pipelines, friction occurs between the moving water and the inner area of the pipeline.
  • This force works against the direction of flow and therefore reduces energy of the water.
  • This energy loss is measured in a loss of pressure in the system in feet of head or PSI.

Hazen-Williams Equation

Hazen-Williams

  • Predominant equation used for modeling energy losses due to friction.

  • Equation is not theoretically based and only made from empirical data collection and curve-fitting
  • More accurate and popular for Civil Engineering/City Water Projects

K-Value

K-Value

  • Empiracal value that includes all necessary conversion factors for the other required inputs in the equation.
  • Varies signifigantly depending on slight changes to the equation
  • For the given equation, the K-value is 10.5 and is theoretiucally unitless, even though it is an amalgamation of unit conversions

Flowrate (Q)

Flowrate (Q)

  • Entered as Gallons per Minute (GPM)
  • This input is taken to the power of 1.852. This is an empiracally-derived number and represents the extent to which flowrate influences friction loss relative to the other inputs

C-Value

C-Value

  • Roughness constant. Dependent on the material and age of the pipeline. This constant slightly varies based on the speed at which the water is moving, but all C-values are assumed constant for each material type and are based on average conditions at about 3 ft/s water velocity.
  • This input is also unitless and

can be found on data tables like

the one at right.

Length

Length

Length is directly proportional to friction losses. Length is always entered in feet of pipe. Some forms of the Hazen Williams Equation omits the length input and measures friction per 100 feet.

Diameter

Diameter

  • The diameter input is the inner diameter of the pipeline. The diameter is the single most important factor in friction losses. This is represented in the equation since the diameter is taken to the -4.87 power. This also means that inner diamter is inversely proportional to friction losses. This is because a smaller ration of water going through the pipes is in contact with the walls of the pipe. In this version

Darcy- Weisbach Equation

  • Secondary energy loss equation that relates head loss to the average velocity of the flowing fluid where Hazen-Williams may not be applicable
  • Hazen-Williams is an empirical equation that is limited to predicting energy loss for conditions with specific temperatures, turbulent flow, and water specifically

Darcy-Weisbach

  • Dary-Weisbach offers a more complex, yet versatile option to calculating energy loss in a pipeline
  • Commonly used in fire protection engineering when designing fire response systems that use fluids other than water

F-Value

F - Value:

  • The Darcy friction factor is comparable to the C value in Hazen-Williams
  • Dynamic value that changes with density, roughness of inner pipe surface, flow rate, diameter, and dynamic viscosity
  • Typically this value will be given as a known constant, if not...
  • Calculate Reynolds Number and Relative Roughness, which is used to determine the friction factor using a Moody Diagram

Velocity

Fluid Velocity:

  • Fluid Velocity is entered in as feet per second (FPS), which is a measurement of the average fluid (typically water) speed as it travels through pipe
  • Entered fluid velocity will be converted to velocity head by squaring the entry and dividing by 64.4 ft/s^2 (2*g)
  • Velocity head is the theoretical amount of potential energy (pressure head) is required to get the fluid up to"speed"
  • Due to conversion characteristics, energy loss is parabolically related to fluid velocity

Length

Pipe Length:

  • Pipe length is a necessary input into the equation
  • Accounts for the amount of pipe being used in the system, the greater the length of pipe, the greater the friction loss experienced
  • Total energy loss in system is proportionally related to the length of pipe used
  • Because of its proportional relationship, total energy loss is much less impacted by an increase in length compared to a diameter reduction

Diameter

Pipe Diameter:

  • Pipe diameter plays a huge role in the Darcy-Weisbach equation as its an input in three different instances and has the most significant impact on total energy loss experienced in a system
  • Much like with Hazen-Williams, energy loss is relative in part to the size of pipe used; larger diameter, the easier water is able to flow with less relative surface area contact with the pipe inner surface
  • In some versions of the equation, it is demonstrated that diameter effects energy loss with an inverse relationship (d^-5)

Research

  • At the Irrigation Practice Field:
  • measured pressure at two points for varying flowrates
  • varied flowrate by closing end valve to varying degrees
  • Plotted data (Flowrate as independent and friction losses as dependent)
  • created polynomial curve of best fit
  • compared with Hazen-Williams and Darcy-Weisbach equations

Hypothesis

Hypothesis

  • We can determine the friction losses between two points and compare these values to their respective flowrates. This will create a data set which can be used to compare the accuracy between Hazen-Williams and Darcy-Weisbach.

Procedure

Procedure

  • Turn on pump at IPF. Entirely open valve at end of pipeline.
  • Record 10 flowrate values off MagMeter and take average of recorded values.
  • Measure pressure at upstream location and downstream location. Find the difference of these values to determine friction losses.
  • Repeat the above process for downstream pressures=0, 5, 10, 15, 20, 25, and 30 PSI

Data

Discussion

Discussion

  • Based on the results of our experiment, the Hazen-Williams friction modeled the experimental data more closely for lower flowrates, but the Darcy-Weisbach model was more accurate at high flowrates.
  • Notably, the experimental data matched with both equations within 5% error. This means that both equations could be viable for use at the range of pressures and flows that were tested.
  • Because only 7 data points were recorded, this may not be a fully accurate description of how these friction models compare to other experimental values in other data ranges.

Conclusion:

Conclusion

  • Based on the data collected, both equations prove to be a viable methods for accurately estimating the friction loss in a pipeline
  • For quick and relatively accurate estimates, Hazen-Williams will be most frequently used
  • Darcy-Weisbach can be just as useful, however takes more time to come to conclusion and requires more information to be sought out
  • Data suggests that Darcy-Weisbach may be more accurate at higher flowrates

The Discussion

Discussion

  • Both equations require entries of some friction factor, diameter, flowrate, and system length
  • Hazen-Williams is desired because friction factor is often an already known value that remains "constant" for all systemic conditions
  • Darcy-Weisbach is desired because friction factor is a dynamic value that does change with systemic changes and extreme conditions
  • Hazen-Williams requires: Q^1.852 and ID^-4.87
  • Darcy-Weisbach requires: Q^2 and ID^-5
  • Very similar conclusions for more applications

So which do I use?

Darcy- or Hazen- ?

  • For our purposes, Hazen-Williams will provide a sufficiently accurate estimate of energy loss in a typical system
  • Data suggest that Darcy-Weisbach provides a better estimate at higher flowrates, but this should be revisited with more testing before we conclude that
  • High pressures and fluid velocities tend to impact physical properties of water to the point that Hazen-Williams breaks down in its empirical assumptions and Darcy should be used instead
  • In friction senistive systems like some fire protection systems, Hazen-Williams may also fail because it does not account for all applicable conditions

Why do we care about any of this?

Why care?

  • As demonstrated by the data, energy loss is pressure loss in a system
  • Irrigation systems are pressure sensitive and require minimum pressures to be met at all outlets in order to be effective
  • Designers need to be able to work around pre-exisitng conditions and design systems with accomodations for pipe diameter, length, and material
  • Friction is especially an important factor in fire-prevention engineering where systems may not necessarily use water, but require minimum pressures in order to be successful

Discussion / Questions

Questions

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