5/1XRe

x37.0

XRe

x5 7/1

XRe

x16.0

5/1X

fRe

058.0c

X2f

Re06.0ln

455.0c

Xf

Re

664.0c

Key Boundary Layer Equations

Normal transition from Laminar to Turbulent

x

xURe 0

x

Boundary layer thickness (m) at distance x down plate = )x(

5x 10x5Re

Shear stress on plate at distance x down plate

2

Uc

2

f0 U0 free stream vel.

kinematic visco.

Rough tip –induced turbulence

Shear Resistance due to flow of a viscous fluid of density and free stream vel = Uo

Over a plate Length L Breath B

L

0x

20

fs 2

UBLCdxBF

Flow in Conduits --Pipes

+ -

LT

22

22

P

21

11 hh

g2

Vz

ph

g2

Vz

p

Head IN from pumpNote pump power

PP

hQP

Head OUT from TurbineNote power recovered

TT hQP

Q discharge

0< <1 efficiency

Heat Loss

Our concern is to calculate this term

The nature of Flow in Pipes

Development of flow in a pipe

We use energy Eq.—assume = 1

If we select the points [a] and [b] to be at the top of the tanks Eq. 1Simplifies to

(1)

HhL

We can not measure H BUT we can estimate the head loss hL

There are a number of items that contribute to the head loss hL

In current problem Three components for head loss

In Example problem

Minor Losses

Note formDimensionless No X

V2/2g

See Table 10.3 in Crowe, Elger and Robinson

41.0K,6.DD

87.0K,2.DD

1K,0DD

E21

E21

E21

In this case reduces to

Head loss in a pipe

Head loss in a pipe

=0 by continuity

Rearrange

(1)

(2)

Wetted perimeter

(1) And (2)

Introduce a Dimensionless friction factor

Then

In a full circular pipe

So to find head loss hL Need to find friction factor f

Head loss in a pipe

Friction Factor

Friction Factor Turbulent Flow

Friction Factor Turbulent Flow

Friction Factor Turbulent Flow

Friction Factor Turbulent Flow

Friction Factor Turbulent Flow

Friction Factor