CE 230-Engineering Fluid Mechanics

Lecture # 28

Laminar flow in circular pipes

Importance of flow in conduits

Water and wastewater

Agriculture

Industry

Transport of water or oil

Medicine

Flow classification

Laminar flow: associated with low velocity and smooth appearance (flow of thick syrup). In pipe flow smooth parabolic velocity distribution.

Turbulent flow: intense mixing with variation of velocity with time.

Reynolds apparatus used to study flow type.

Conclusion:

Important parameter is Re

Laminar flow Re < 2000

Turbulent flow Re > 3000

Laminar flow in circular pipes

Objective is to develop

1 (the shear stress distribution

2 (Velocity distribution

3 (A formula for the head loss

Consider a cylindrical element of length Δsand radius r oriented co-axially with the pipe.Consider equilibrium in s direction (steady flow)

0 sF

0)2(sin)( srWAsds

dpppA

sAW ds

dzsin

0)2( srds

dzsAsA

ds

dp

)]([2

zpds

dr

But

Therefore

And shear stress

2

32

D

LVh f

Determine flow direction and head loss between the two pointsif the fluid is water.

1

2

h1=200/9.81 =20.39 mh2=110/9.81 + 10 =21.21 m

Conclusion flow from 2 to 1Head loss = 0.82 m

Determine flow direction and head loss.

Example 10.1

Example 10.2

Example 10.3 Determine Q if the liquid is keroseneμ = 3.2 x 10-3 Pa.s, γ= 8010 N/m3

2

32

D

LVh f