CHEE 3363Spring 2013Handout 22

Reading: Fox 9.4--9.5

1

Learning objectives for lecture

1. Calculate the different boundary layer thicknesses.

2.

2

Recall from last class: boundary-layer

3

u

U= f

(

y

√

U

νx

)

δ ∝

√

νx

U

x):

τw

ρ=

d

dx(U2θ) + δ∗U

dU

dx

δ∗ =

∫

∞

0

(

1 −

u

U

)

dy ≈

∫ δ

0

(

1 −

u

U

)

dy

θ =

∫

∞

0

u

U

(

1 −

u

U

)

dy ≈

∫ δ

0

u

U

(

1 −

u

U

)

dy

displacement thickness

momentum thickness

δ

x=

√

30µ

ρUx

and

4

or

pipe of radius R V:

5

∂p

∂x= 0

Comments on pressure gradients 1

Laminar:

Turbulent:

τw = µ∂u

∂y

∣

∣

∣

∣

y=0

Favorable

Adverse

6

H =

δ∗

θ

Comments on pressure gradients 2

U xU x

under same conditions

7

8

Given ρh

uniform velocity U0. At a distance D

δ2*. Find Δ

Assumptions:1. Steady2. Incompressible3. No friction outside boundary layer

5. Horizontal

Equations:

9

Given ρh

uniform velocity U0. At a distance D

δ2*. Find Δ

Apply Bernoulli:

Solution check: Δp = -8.05 × 10-3 psi

10

GivenH

L δ2.Determine:

δ*

τ

Assumptions:1. steady2. incompressible

11and solve for τ.