Handbook of PVC Pipe Design and Construction

Handbook of PVC Pipe Design and Construction

9 C H A P T E R

Hydraulics

Introduction to Hydraulics ?

Flow in PVC Pressure Pipes ?

Flow in PVC Nonpressure Pipe

Copyright 2012, Industrial Press Inc., New York, NY -

Handbook of PVC Pipe Design and Construction

9.2

Chapter 9

Table of Contents

9.1 Notation ....................................................................................................... 9.3 9.2 Introduction to Hydraulics........................................................................... 9.4

9.2.1 Flow Theories and Equations.................................................................9.4 9.2.2 Hydraulic Radius....................................................................................9.4 9.3 Flow in PVC Pressure Pipe ......................................................................... 9.5 9.3.1 Hazen?Williams Flow Formula .............................................................9.5 9.3.2 Darcy?Weisbach Formula....................................................................9.11 9.4 Flow in PVC Nonpressure Pipe ................................................................ 9.80 9.5 Sources....................................................................................................... 9.95

Copyright 2012, Industrial Press Inc., New York, NY -

Handbook of PVC Pipe Design and Construction

Hydraulics

9.3

9.1 Notation

A 5 cross-sectional area of flow, ft2 Ac 5 cross-sectional area of circle, in.2 As 5 cross-sectional area of ellipse, in.2 a 5 deflected pipe long semi-axis, in. b 5 deflected pipe short semi-axis, in. C 5 Hazen?Williams flow coefficient, dimensionless di 5 pipe inside diameter, in. D 5 pipe inside diameter, ft Di 5 pipe inside diameter, in. f 5 friction loss, ft of H2O/100 ft fD 5 Darcy friction factor, dimensionless g 5 acceleration of gravity, ft/s2 hf 5 head loss, ft of H2O H 5 head loss, ft of H2O/1,000 ft H1 5 upstream pipe elevation, ft H2 5 downstream pipe elevation, ft ID 5 inside pipe diameter, in. L 5 pipe length, ft n 5 coefficient of roughness (Manning's equation and Kutter's formula), dimensionless Pw 5 wetted perimeter, ft P1 5 maximum pressure, psi P2 5 minimum pressure, psi Q or MGD 5 flow rate, gpm or ft3/s or gpd Re 5 Reynolds number, dimensionless RH 5 hydraulic radius, ft ri 5 pipe inside radius, in. S 5 hydraulic slope, ft/ft (pressure pipe) s 5 hydraulic slope, ft/ft (non-pressure pipe) SE 5 slope of energy grade line, ft/ft

Copyright 2012, Industrial Press Inc., New York, NY -

Handbook of PVC Pipe Design and Construction

9.4

Chapter 9

t 5 pipe wall thickness, in. V 5 mean flow velocity, ft/s e 5 equivalent roughness, in. or ft (to match units of pipe inside diameter) n 5 kinematic viscosity of a fluid, ft2/s DX 5 horizontal pipe deflection, in. DY 5 vertical pipe deflection, in.

9.2 Introduction to Hydraulics

9.2.1 Flow Theories and Equations

Many empirical formulas have been developed for solving the variety of problems related to flow in pipes. Equations developed by hydraulic engineers are used daily in the solution of problems encountered by water and sewer engineers. Relatively few specific problems in pipe hydraulics, such as laminar flow, can be solved entirely theoretically by mathematical means; rather, solutions to a majority of flow problems depend to some degree on experimentally determined coefficients. Thus, commonly used flow formulas have been developed through research by (among others) Fanning, Darcy, Chezy, Kutter, Scobey, Manning, Weisbach, Hazen, and Williams.

9.2.2 Hydraulic Radius

The hydraulic radius is used for hydraulic calculations for both pressure and nonpressure pipe. The hydraulic radius is obtained by dividing the cross-sectional area of the flow by the wetted perimeter of the pipe (i.e., the perimeter along which the flow is in contact with the pipe walls). The value of the hydraulic radius varies with the level of flow.

For the pressure pipe portion of this chapter, pipes will be assumed to be flowing full. For the nonpressure portion, pipes will be assumed to be flowing either full or half-full.

Equation 9.1

A RH 5 Pw

where:

RH 5 hydraulic radius, ft A 5 cross-sectional area of flow, ft2

Pw 5 wetted perimeter of flow area, ft

Copyright 2012, Industrial Press Inc., New York, NY -

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