
Product No.
99803 
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GravityFed Water Delivery Systems
Andrew Dornbush, Paul Isihara with Timothy Dennison, Kristianna Russo, and David Schultz

Mathematics Topic: Calculus 2, Difference Equations 
Application Areas: Fluid mechanics, engineering 
Prerequisites: Courses in calculus and physics (mechanics) 

 ©2010 by COMAP, Inc.  The UMAP Journal 31.4  42 pages 

This Module introduces calculus students to elementary
fluid mechanics applied to the modeling of simple
gravityfed water delivery systems, which are of
great importance in the developing world. We first derive
Bernoulli’s equation so as to understand the relations
among pressure, velocity, and elevation as a
fluid particle travels along a streamline. Next, we apply
Bernoulli’s equation to analyze pressure buildup
and flow rates in a simple waterdelivery system. We
then incorporate breakpressure tanks, pipes of different
diameters, and frictional effects for both laminar
and turbulent flow. Finally, we discuss the design and
installationof gravityfedwater deliverysystems in Micronesia
and Honduras.
Table of Contents
1. INTRODUCTION
2. DERIVATION OF BERNOULLI’S EQUATION
3. APPLICATION TO GRAVITYFEDWATER SUPPLY SYSTEMS 3.1 Basic Case 3.2 BreakPressure Tanks 3.3 WaterFlow Rates
4. VISCOUS FLOW IN PIPES 4.1 Head Loss 4.2 Reynolds Number
4.3 Laminar Flow
4.4 Turbulent Flow
4.5 Pipe Selection
5. DESIGNING A SYSTEM
6. CASE STUDY: HONDURAS
7. FURTHER DIRECTIONS
8. SOLUTIONS TO THE EXERCISES
REFERENCES
ABOUT THE AUTHORS



