Darcy公式

Darcy

–

Weisbach equation

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In

fluid dynamics

, the

Darcy

–

Weisbach equation

is a

phenomenological

equation, which relates the

head loss

—

or

pressure

loss

—

due to

friction

along

a

given

length

of

pipe

to

the

average

velocity

of

the

fluid

flow. The equation is named after

Henry Darcy

and

Julius Weisbach

.

The Darcy

–

Weisbach equation contains a

dimensionless

friction factor,

known as the

Darcy friction factor

. This is also called the

Darcy

–

Weisbach friction factor

or

Moody friction factor

. The Darcy

friction

factor

is

four

times

the

Fanning

friction

factor

,

with

which

it

should not be confused.

[1]

Contents

[

hide

]

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1 Head loss form

2 Pressure loss form

3 Darcy friction factor

o

3.1 Confusion with the Fanning friction factor

4 History

5 Derivation

6 Practical applications

7 See also

8 References

9 Further reading

10 External links

[

edit

] Head loss form

Head loss

can be calculated with

where

?

?

?

?

?

?

h

f

is the head loss due to friction;

L is the length of the pipe;

D is the

hydraulic diameter

of the pipe (for a pipe of circular

section, this equals the internal diameter of the pipe);

V

is

the

average

velocity

of

the

fluid

flow,

equal

to

the

volumetric

flow rate

per unit cross- sectional

wetted area

;

g

is the local acceleration due to

gravity

;

f

is

a

dimensionless

coefficient

called

the

Darcy

friction

factor

.

It can be found from a

Moody diagram

or more precisely by solving

Colebrook equation

.

[

edit

] Pressure loss form

Given

that

the

head

loss

h

f

expresses

the

pressure

loss

Δ

p

as

the

height

of a column of fluid,

where

ρ

is the density of the fluid, the Darcy

–

Weisbach equation can

also be written in terms of pressure loss:

where the pressure loss due to friction

Δ

p

is a function of:

the ratio of the length to diameter of the pipe,

L/D

;

?

the density of the fluid,

ρ

;

?

the mean velocity of the flow,

V

, as defined above;

?

a (dimensionless) coefficient of

laminar

, or

turbulent flow

,

f

.

?

Since

the

pressure

loss

equation

can

be

derived

from

the

head

loss

equation

by multiplying each side by

ρ

and

g

.

[

edit

] Darcy friction factor

See also

Darcy friction factor formulae

The

friction

factor

f

or

flow

coefficient

λ

is

not

a

constant

and

depends

on

the

parameters

of

the

pipe

and

the

velocity

of

the

fluid

flow,

but

it

is

known

to

high

accuracy

within

certain

flow

regimes.

It

may

be

evaluated

for given conditions by the use of various empirical or theoretical

relations,

or

it

may

be

obtained

from

published

charts.

These

charts

are

often referred to as

Moody diagrams

, after L. F. Moody, and hence the

factor itself is sometimes called the

Moody friction factor

. It is also

sometimes called the

Blasius

friction factor, after the approximate

formula he proposed.

For laminar (slow) flows, it is a consequence of

Poiseuille's law

that

λ

=64/

Re,

where

Re

is

the

Reynolds

number

calculated

substituting

for

the

characteristic length the hydraulic diameter of the pipe, which equals

the inside diameter for circular pipe geometries.

For turbulent flow, methods for finding the friction factor

f

include

using

a

diagram

such

as

the

Moody

chart

;

or

solving

equations

such

as

the

Colebrook-White

equation

,

or

the

Swamee-Jain

equation

.

While

the

diagram

and Colebrook-White equation are iterative methods, the Swamee-Jain

equation

allows

f

to

be

found

directly

for

full

flow

in

a

circular

pipe.

[

edit

] Confusion with the Fanning friction factor

The Darcy

–

Weisbach friction factor is 4 times larger than the

Fanning

friction

factor

,

so

attention

must

be

paid

to

note

which

one

of

these

is

meant

in

any

factor

chart

or

equation

being

used.

Of

the

two,

the

Darcy

–

Weisbach

factor

is

more

commonly

used

by

civil

and

mechanical

engineers,

and

the

Fanning

factor

by

chemical

engineers,

but

care

should

be taken to identify the correct factor regardless of the source of the

chart or formula.

Most charts or tables indicate the type of friction factor, or at least

provide the formula for the friction factor with laminar flow. If the

formula for laminar flow is f = 16/

Re

, it's the Fanning factor, and if

the formula for laminar flow is f = 64/

Re

, it's the Darcy

–

Weisbach

factor.

Which

friction

factor

is

plotted

in

a

Moody

diagram

may

be

determined

by

inspection

if

the

publisher

did

not

include

the

formula

described

above:

1.

Observe the value of the friction factor for laminar flow at a

Reynolds number of 1000.

2.

If

the

value

of

the

friction

factor

is

0.064,

then

the

Darcy

friction

factor

is

plotted

in

the

Moody

diagram.

Note

that

the

nonzero

digits

in 0.064 are the numerator in the formula for the laminar Darcy

friction factor: f = 64/

Re

.