Water Pressure and Flow Analysis

1. Water Pressure and Flow Analysis Engineers Without Borders South Central Regional Workshop November 12th, 2011 Brad Appel, Texas A&M University

2. Purpose • 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

3. Overview • 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

4. Flow Rate Units • In general: where = mass flow rate, = fluid density, and = fluid velocity • For room-temperature water: where = volume flow rate

5. 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.

6. 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.

7. 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: 1 2

8. Gravity-Driven System Example • EWB-TAMU project in Costa Rica: 2000 people supplied with water without any pumps.

9. 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.

10. 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.

11. Moody Chart

12. 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.

13. 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”

14. 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.

15. 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.

16. 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

17. Experiment Setup Piezometer tubes Pump Vinyl tubing Tee Tubing length = 84 cm Tubing inner diameter = 0.4318 cm