5/1XRe
x37.0
XRex5
7/1XRe
x16.0
5/1X
f Re 058.0c
X2f Re06.0ln
455.0c X
f Re664.0c
Key Boundary Layer Equations
Normal transition from Laminar to Turbulent
x
xURe 0x
Boundary layer thickness (m) at distance x down plate = )x(
5x 10x5Re
Shear stress on plate at distance x down plate 2
Uc2
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 2UBLCdxBF
Flow in Conduits --Pipes
+ -
LT
22
22
P
21
11 hh
g2Vzph
g2Vzp
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.DD87.0K,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