Darcy’s law & chezy’s law
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Transcript of Darcy’s law & chezy’s law
Md.Ariful Islam--------10307044
Nur-E-Alam Siddike---10307050
Abu Bakar Siddique---10307076
Mahadi Hasan Rubel---10307059
Arfan Hossain ----------11170119
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Major Losses
losses due to friction
Minor Losses
entrance and exit
sudden change of cross sections
valves and gates
bends and elbows ect
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When the water is flowing in a pipe, it
experiences some resistance to its motion,
whose effect is the velocity and ultimately
the head of water available. An empirical
formula for the loss of head due to friction
was derived by Henry Darcy
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Let,
l= length of the pipe
D= diameter of the pipe
v= Velocity of water in the pipe
f'= Frictional resistance per unit area at unit
velocity
Consider sections (1-1) and (2-2) of the pipe
Let,
p1= Intensity of pressure at section (1-1)
p2= Intensity of pressure at section (2-2)
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Chézy was born at Chalon-sur-Marne, France, on September 1, 1718, and died on October 4, 1798. He retired in 1790 under conditions of extreme poverty. It was not until 1797, a year before his death, that the efforts of one of his former students, Baron Riche de Prony, finally resulted in Chézy's belated appointment as director of the Ecole des Ponts et Chaussées.
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V is velocity
R is hydraulic radius
S is slope of the channel
C is Chezy coefficient and is a function of
hydraulic radius and channel roughness
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Let,
l= length of the pipe
D= diameter of the pipe
v= Velocity of water in the pipe
f'= Frictional resistance per unit area at unit
velocity
Consider sections (1-1) and (2-2) of the pipe
Let,
p1= Intensity of pressure at section (1-1)
p2= Intensity of pressure at section (2-2)
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Figure from Hornberger et al. (1998)
Generalization of Darcy’s column
h/L = hydraulic
gradient
q = Q/A
Q is proportional
to h/L
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Figure from Hornberger et al. (1998)
Linear flow paths
assumed in Darcy’s
law
True flow paths
Average linear velocity
v = Q/An= q/n
n = effective porosity
Specific discharge
q = Q/A
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Inflow = OutflowRecharge
Discharge
Steady State Water Balance Equation
Transient Water Balance Equation
Inflow = Outflow +/- Change in Storage
Outflow - Inflow = Change in Storage
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