Darcy’s law & chezy’s law

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By Group 1 1

Transcript of Darcy’s law & chezy’s law

By Group 1

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Md.Ariful Islam--------10307044

Nur-E-Alam Siddike---10307050

Abu Bakar Siddique---10307076

Mahadi Hasan Rubel---10307059

Arfan Hossain ----------11170119

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Know the formula

Describe the formula

Application of formula

Importants of formula

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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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hf = Loss of head due to friction

L = Length of pipe

D= Diameter of the pipe

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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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Chezy Formula : Can be derived from basic

principles. It states that

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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)

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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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Power generation

Mining

Refrigeration

Vehicles

Water supply drainage system etc.

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