TABLE OF CONTENTS Water flows by gravity at a rate of 500 gallons per minute through 5 miles of cast iron pipe from one reservoir to another reservoir located 200 feet below. Calculate the minimum pipe diameter required and the standard size pipe that should be used.
Assume pipe is flowing full and steady uniform flow. Problem will be solved using three different methods to illustrate use of the Manning formula, Hazen-William formula, and Darcy-Weisbach equation. The Manning and Hazen-Williams equations are limited to turbulent flow and common ambient temperatures for water. The Manning equation is commonly used in sewer design and open channel flow, the Hazen-Williams equation for water supply systems. The Darcy-Weisbach equation is often used for fluids other than water.
Method 1 Manning formula may be written as
| where V | = velocity, feet/second |
| n | = Manning coefficient |
| R | = hydraulic radius, feet |
| S | = slope of hydraulic grade line, feet/feet |
Values of n for the Manning equation are shown in Table 1.1. 1 Values indicated are for good to fair construction. For poor quality construction, use larger value of n.
| Type of Channel | Manning's n Range |
|---|---|
| Closed Conduit | |
| Concrete | 0.011 0.013 |
| Corrugated Metal | 0.024 |
| Vitrified Clay | 0.012 0.014 |
| Cast-iron | 0.013 |
| Steel | 0.009 0.011 |
| Brick | 0.014 0.017 |
| Open Channels; Lined | |
| Concrete | |
| Trowel Finish | 0.012 0.014 |
| Float Finish | 0.013 0.015 |
| No Finish | 0.013 0.017 |
| Brick | 0.014 0.017 |
| Asphalt | 0.013 0.016 |
| Gravel Bottom, sides of | |
| Formed Concrete | 0.017 0.020 |
| Random Stone | 0.020 0.023 |
| Riprap | 0.023 0.033 |
| Open Channels; Excavated | |
| Earth,... |
