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Water Pressure and Flow Analysis. Engineers Without Borders South Central Regional Workshop November 12 th , 2011. Brad Appel, Texas A&M University. Purpose. Survey the concepts and equations to calculate the flow properties of a pipeline

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water pressure and flow analysis

Water Pressure and Flow Analysis

Engineers Without Borders South Central Regional Workshop

November 12th, 2011

Brad Appel, Texas A&M University

  • Survey the concepts and equations to calculate the flow properties of a pipeline
  • Practice these equations by comparing to a test flow rig
  • As a reminder: The EWB-USA website has a great list of resources

Log-in Project Resources  Technical Resources

  • Flow rate and pressure units
  • Gravity head
  • Pump curves
  • Friction pressure drop (Darcy-Weisbach)
  • Friction pressure drop (Hazen-Williams)
  • Minor Losses
  • Energy Grade Lines
  • Experiment Competition
flow rate units
Flow Rate Units
  • In general:

where = mass flow rate, = fluid density, and

= fluid velocity

  • For room-temperature water:

where = volume flow rate

pressure units
Pressure Units
  • Metric: 1 Pascal (Pa) = 1 Newton / m2 = 10-5 bar
  • English: 1 psi = 144 psf
  • Head is a way to represent the height that a column of fluid will reach under a particular static pressure.
  • Head is widely used because it will not change with fluid density.
bernoulli s equation
Bernoulli’s Equation
  • Conservation of energy for an inviscid fluid along a streamline.
  • If we neglect energy changes due to friction or heat transfer, the total head of a fluid will remain constant, and can only be traded between dynamic, static, and potential energy.
  • Bernoulli’s is particularly useful for predicting the static pressure after a flow area change.
gravity head
Gravity Head
  • When working with head, gravity is the simplest quantity to calculate.
  • The head difference is independent of the path between the two measurement points.
  • This is the most common driver for rural water distribution systems.
  • To convert back to pressure:



gravity driven system example
Gravity-Driven System Example
  • EWB-TAMU project in Costa Rica: 2000 people supplied with water without any pumps.
pump curves
Pump Curves
  • A given pump will have a characteristic curve showing the flow rate it can produce when operating over a particular head rise.
  • The operation point on the curve will shift to match the pressure drop of the system.
friction pressure drop
Friction Pressure Drop
  • Method 1: Darcy-Weisbach
  • Friction factor f can come from a Moody Chart, where the Reynolds number is needed:
  • Values for surface roughness are tabulated and widely available.
friction pressure drop1
Friction Pressure Drop
  • Method 2: Hazen-Williams (this is the metric version)
  • C factors are typically between 70 and 150, and are widely available for different materials.
minor losses
Minor Losses
  • We already know how to calculate the pressure drop due to wall friction (Darcy-Weisbach and Hazen-Williams).
  • For everything else (including bends, valves, orifices, expansions & contractions, etc…), we use minor losses.

Typical k values can vary from 0.2 to 20

All this…wrapped into “k”

energy grade lines
Energy Grade Lines
  • The available head in a pipeline is commonly graphed on a energy/hydraulic grade line chart.
  • Bernoulli’s equation (velocity head), friction losses, minor losses, gravity head changes, and pumps can all be visualized.
flow networks
Flow Networks
  • While hand calculations for flow through a single pipeline can be easy, a pipe network quickly turns into a large system of equations.
  • Parallel flow circuits require iterative solving.
  • For student EWB chapters, EPANET is a great tool for simulating large networks.
  • EPANET model of San Juan de PenasBlancas includes 500 nodes and pipes, 7 tanks, and stretches over a 10 km2 area.
  • Solves for a 24 hour demand pattern in a matter of seconds.
experiment competition
Experiment Competition!
  • Break into 4-person groups
  • Use either Darcy-Weisbach or Hazen-Williams
  • Collect flow rate data
  • Predict the head on the second piezometric tube
experiment setup
Experiment Setup

Piezometer tubes


Vinyl tubing


Tubing length = 84 cm

Tubing inner diameter = 0.4318 cm