2111 2005 water amd wastewater treatemt hydraulics
TRANSCRIPT
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21112005
Water amd wastewater treatemt Hydraulics
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Hydraulics
Objective
- Analysis of pipe flow system
- Head losses in pipes
- Flow measurements
- Small diameter gravity and vaccum sewers
- Introduction to tutorial questions
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Pipe flow analysis
1 2
The Bernoulli’s Equation
E1 = E2 ± ΔE
P1/ ρg + v21 /2g + Z1 = P2/ ρg + v2
2 /2g + Z2 ± ΔE
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Bernoulli’s equation
BE is used in analysis of pipe flow
It states that total energy remains constant along a stream line (That is total head is constant)
It uses certain assumptions
– Flow is steady
– Fluid is incompressible
– Valid at two points along a single streamline
The hydraulic grade and the energy line are graphical presentations of the Bernoulli’s equation (BE)
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Energy and hydrulic grade line
1 2
V
v21 /2g
P1/ ρg
Z1 Z2
P2/ ρg
v22/2g
H1 H2
E2E1
Reference level
Energy grade line
Hydraulic grade line
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Energies, Head
2Z2
P2/ ρg
v22/2g
H2
E2
Reference level
EGL
HGL
Energy Head (total)
Piezometric head
Pressure head
Elevation head (potential)
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Energies, Heads
2Z2
P2/ ρg
H2
Reference level
HGL
Piezometric head
Pressure head
Elevation head (potential)
Velocity head neglected except well above 1 m/s (example: pumping stations)
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Hydraulic gradientSlope of the hydraulic grade line
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Hydraulic gradientSlope of the hydraulic grade line
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Hydraulic lossesFriction, minor
ΔE results from a friction between the water and the pipe wall, and /or a turbulence developed by obstructions of the flow
ΔE = hf + hm = Rf Qn (f) + Rm Qn (m)
hf,m = Friction, Minor loss (respectively)Rf,m = Pipe resistanceQ = Flownf, m = exponents
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Friction Losses
Darcy- Weisbach
– λ = Friction factor (-)
– L = Pipe length (m)
– D = Pipe diameter (m)
– Q = Pipe flow (m3 /s)
– Or propotional to the kinetic energy
25
252 1.12
8Q
D
LQ
gD
LQRh fn
ff
g
V
D
Lh f 2
2
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Friction factor
Friction factor, λ is the most important parameter in the Darcy-weisbach equation
– Is the complex function of the Reynolds number and relative roughness
Reynolds Number
VD
Re
V = Flow velocity (m/s)D = Pipe diameter (m) = Kinematic viscosity (m2/s)
5.1
6
)5.42(
10497
T Temperature, T(0 C)
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Flow regime
Laminar flow – Re falls under 2000
Transitional zone - Re falls between 2000 and 4000
Turbulent flow - Re above 4000
For Laminar flow
λ = 64/ Re
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Choice for rough pipes
There are empirical formula and diagrams to determine friction factor (f) depending on the pipe roughness and Reynolds Number
– Moody diagram
– Colebrook-white equations etc.
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The Moody diagram
Departm
ent o
f Pla
nt a
nd E
nviro
nm
enta
l Scie
nce
s
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Absolute rougness
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Friction losses
Hazen –Williams
852.187.4852.1
68.10Q
DC
LQRh fn
ff
L = Pipe length (m)C = Hazen-Williams factor D = Pipe diameter (m)Q = Pipe flow (m3 /s)R = Hydrualic Radius (flow area/wetted perimeter)S = Slope of energy grade line = hf /L
54.063.085.0 SRCV Or
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Hazen-Williams Factors
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Friction losses
Manning
23/16
229.10Q
D
LnQRh fn
ff
or
2/13/21SR
nV
L = Pipe length (m)n = mannings factor ( m-1/3 s)D = Pipe diameter (m)Q = Pipe flow (m3 /s)R = Hydrualic Radius (flow area/wetted perimeter)S = Slope of energy grade line = hf /L
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Manning factor
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The best formula ?
Darcy-weisbach – the most accurate
Hazen-williams- (straight forward and simpler (friction coefficient not function of diameter or velocity), suitable for smooth pipes not attacked by corrosion)
Mannings- straight forward, suitable for rough pipes, commonly applied for open channel flows
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Difference between pressure flow and open channel flow
HGL
v21 /2g
EGL
Open channel flow (in large gravity sewer)
v21 /2g
EGL
HGL
Pressure flow
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Minor losses
Given byhf = k V2 /2g K determined experimentally for various fittings
Values of K for various fittings:
Valve ( fully open ) 2Tee 0.2 – 2.0Bend 1.2
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Flow measurements in pipes
Orifice plates
Where C = discharge coefficient
5.0
122 2
PP
CAQ
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Flow measurements in open channel flow
Sharp crested weir
L = Length of weir, m
Cd = discharge coefficient
5.15.0)2(3
2HgLCQ d
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Small diameter sewer collection system
• Transport sewage to treatment or disposal point
• Size and length of sewer depends upon the type of sewerage system (centralised or decentralised)
• Need sufficient velocity to transport sewage
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Small diameter sewer network
Septic tank effluent gravity (STEG)
Septic tank effluent pump (STEP) and
pressure sewer with grinder pumps
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Small diameter sewer network
Vacuum sewer
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Friction losses
Hazen –Williams
852.187.4852.1
68.10Q
DC
LQRh fn
ff
L = Pipe length (m)C = Hazen-Williams factor D = Pipe diameter (m)Q = Pipe flow (m3 /s)R = Hydrualic Radius (flow area/wetted perimeter)S = Slope of energy grade line = hf /L
54.063.085.0 SRCV Or
Hazen –Williams formula based on actual flow area- so inside pipe diameter is used.
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Design and layout of collection system
Information required
–Topography of the area
–Depth of soil
–Depth of water table
–Depth of freezing zone
–Amount (daily minimum, average and peak flow rates)
–Population growth rate
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Excersise-Sewer collection system
Prepare a profile
Select a pipe size
Calculate the velocity
Calculate the pipe cross sectional area
and determine the actual capacity
Check for the surcharged condition
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Friction Losses
Hazen –Williams
852.187.4852.1
68.10Q
DC
LQRh fn
ff
L = Pipe length (m)C = Hazen-Williams factor D = Pipe diameter (m)Q = Pipe flow (m3 /s)R = Hydrualic Radius (flow area/wetted perimeter)S = Slope of energy grade line = hf /L
54.063.085.0 SRCV Or
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Pipe selection
Crites and Technobanoglous 1998)
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Crites and Technobanoglous 1998)
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Design of STEP sewer
Design of STEP for a small community as shown in plan view below.
The informations given are:
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54.063.085.0 SRCV
1.31English unit !!!!!!!!
R = D/4
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852.187.4852.1
68.10Q
DC
Lh f
L
Slope should be 0.5 to 1.5 %
If too low -pipe is oversized
Design flow/CA of pipe
EGL/100 *L
Plot EGL –begin from D/S
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References
Water supply and Sewerage – Terence J McGheeChapter 3 (Page 24 – 61) (IHNALibrary catlog No. 628.1 MCG)
Crites, R. and G. Technobanoglous (1998). Small and decentralized wastewater management systems, McGraw-Hill.(Chapter 6)
Advanced Water Distribution Modelling and Management by Haestad and et al. (Chapter 2.3, 2.4, 2.5, 2.6)(IHNALibrary catlog No. 628.1)
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THANK YOU