KNTU CIVIL ENGINEERIG

FACULTY

`

FLOW IN PIPES

With special thanks to Mr.VAKILZADE

Velocity profile:

Friction force of wall on fluid

open channel

pipe

For pipes of constant diameter and incompressible flow

Vavg stays the same down the pipe, even if the velocity profile changes

same

Vavg Vavg

samesame

Conservation of Mass

For pipes with variable diameter, m is still the same (due to conservation of mass),

but V1 ≠ V2

D2

V2

2

1

V1

D1

m m

Laminar and Turbulent Flows

Re < 2300 laminar

2300 ≤ Re ≤ 4000 transitional

Re > 4000 turbulent

Definition of Reynolds number:

Hydraulic diameter:

Ac = cross-section area

P = wetted perimeter

Dh = 4Ac/ P

Consider a round pipe of diameter D. The flow can be

laminar or turbulent. In either case, the profile develops

downstream over several diameters called the entry

length Lh. Lh/D is a function of Re.

Comparison of:

laminar and turbulent flow

Instantaneousprofiles

slope

slope

Laminar Turbulent

ww

w,turb > w,lam w = shear stress at the wall, acting on the fluid

1 2L

w

P1 P2VTake CV inside the pipe wall

Conservation of Mass

Terms cancel since 1 = 2 and V1 = V2

Conservation of x-momentum

or

cancel (horizontal pipe)

V1 = V2, and 1 = 2 (shape not changing)

hL = irreversible head loss & it is felt as a pressuredrop in the pipe

Energy equation (in head form):

w = func( V, , D, )

= average oughness of the inside wall of the pipe

But for laminar flow, roughness does not affect the flow unless it is huge

Laminar flow: f = 64/Re

Turbulent flow: f = Moody Chart

Minor Losses:KL is the loss coefficient.

i pipe sections j components

Energy Line (EL) and Hydraulic Grade Line (HGL)

(Source: Larock, Jeppson and Watters, 2000: Hydraulics of Pipeline Systems)

Pipe Networks :

Pipes in series

Pipes in parallel

1

2

3

A B

1 2 3

1 2 3

f f f ABh h h h

Q Q Q Q

Any question?