School

Carleton UniversityDepartment

Civil EngineeringCourse Code

CIVE 4307Professor

David Farrell Mc GovernThis

**preview**shows pages 1-2. to view the full**6 pages of the document.**Municipal Hydraulics Notes

General

Bouyancy: Uplift force = weight of displaced fluid

Newtonian Fluids: Fluids having negligible yield stress (no str when static) and a constant

viscosity

Uniform flow: no change in velocity with space (constant cross section)

SS flow: no change in velocity with time (constant discharge)

Continuity

Water considered incompressible, therefore cons. of mass becomes cons. of volume

Bernoulli:

E=z+P

ρg +V2

2g

ρliq=ρwater∗SG

Forces

F=M ∆ v=ρQ ∆ v=PA

e.g.

∑Fx=P1A1x +P2A2x−P3A3x=ρQ ∆ vx

Q¿=−ve , Qout=+ve

Reynolds

Ratio of inertia to viscous force

ℜ= ρvD

μ=vD

γ

Laminar: Re<2000,

f=64

ℜ

Turbulent: Re>4000, use Moody diagram

Friction

1

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Municipal Hydraulics Notes

D-W:

hf=fL

D

V2

2g

Relative Roughness:

r=ε

D

Hydraulic Radius:

R=Area of water

Wetted Perimeter

, for fully flowing circular conduit,

D=4R

H-W:

v=kC R0.63 S0.54

where C: pipe characterstic, S: Hf/L, k: (metric:0.854,

imperial:1.318), R: Hydr. Radius

For pipes between 50-1850 mm, and v<3 m/s

Type I

Know: D, roughness

Calc Re and r

Find f from Moody

Solve D-W

Type II

Know: D, roughness, Hf

Calc relative roughness

Guess f

Find v using D-W

Calculate Re

Adjust estimate of f using

Moody

Iterate

Type III

Need: Pipe size

Assume f

Solve for D using D-W

Calc Re and relative

roughness

Adjust f using Moody

Iterate

Minor Losses

Hm=kv2

2g

Equivalent pipe length:

Le=KD

f

Orifice, based on velocity head:

Q=CdA

√

2gH

Cd is coeff of discharge,

0.6<Cd<0.95, H is headloss across orifice

2

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