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Gravity-Fed 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 gravity-fed 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 build-up and flow rates in a simple water-delivery system. We then incorporate break-pressure tanks, pipes of different diameters, and frictional effects for both laminar and turbulent flow. Finally, we discuss the design and installationof gravity-fedwater deliverysystems in Micronesia and Honduras.

1. INTRODUCTION

2. DERIVATION OF BERNOULLI’S EQUATION

3. APPLICATION TO GRAVITY-FEDWATER SUPPLY SYSTEMS
3.1 Basic Case
3.2 Break-Pressure Tanks
3.3 Water-Flow Rates

4. VISCOUS FLOW IN PIPES
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