TK3201

Transport Phenomena

I Dewa Gede Arsa Putrawan

Chemical Engineering ITB

Shell Momentum & Velocity Distribution

in Laminar Flow

8-Jan-13 TK3201 DGA/1

Outcomes

Students are able to derive microscopic balances for simple

problems on momentum transfer.

Students are able to estimate flux and velocity profiles from

microscopic balances.

Students are understand the application of transport

phenomena in viscosity measurement.

8-Jan-13 TK3201

DGA/2

Momentum Flux: diffusive

(x-component)

xx

yx zx

y

xx yx zxy z x z x y

x

y z

8-Jan-13 TK3201

DGA/3

z

Momentum Flux: convective

(x-component)

x

y

z

v

volumetric flow rate v

v

x

y z

v x z

x y

x

y

z

( v )( )

( v )( )

( v )( )

x

x

x

y z v

x z v

x y v

Qx

Qy Qz

xy

8-Jan-13 TK3201

DGA/4

Momentum Balance

= +

+

+

8-Jan-13 TK3201

DGA/5

Forces

Forces acting on fluid

Generation (same direction to fluid flow)

Consumption (opposite direction to fluid flow)

Gravity

F = m g

Pressure

F = P A

8-Jan-13 TK3201

DGA/6

Methodology

Problem analysis

Microscopic balances

Newtons law

Boundary conditions

Profiles of transfer flux, transfer rate, and other variables

Values of average, maximum, etc.

8-Jan-13 TK3201

DGA/7

Boundary Conditions

No slip at solid-fluid interfaces

Continuity on flux and velocity at a liquid-

liquid interfacial plane

Zero flux at a liquid-gas interfacial plane

8-Jan-13 TK3201

DGA/8

Flow of a falling film

8-Jan-13 TK3201

DGA/9

Flow Through A Circular Tube

8-Jan-13 TK3201

DGA/10

Average Velocity

dr

d

d r

r d dA = r dr d

2

0 0 0 0 0

2

0 0 0 0 0

V L A R

z z z

z V L A R

v dV v dzdA v rdrd

v

dV dzdA rdrd

8-Jan-13 TK3201

DGA/11

Cannon-Fenske Viscometer

From analysis of flow in a circular tube

attVL

hRg

QL

hRg

L

RhgQ

8

88

)(

4

44

Taking into account kinetic energy

= at + b/t (note: b/t at)

8-Jan-13 TK3201

DGA/12

Cone-Plate Viscometer

Shear rate:

dvx/dy = / sin , sin = c / r (by manufacturer) Shear stress:

yx = Tp / [(2/3) r3]

8-Jan-13 TK3201

DGA/13

Homework II

1. Problem 2B.3

2. Problem 2B.11

3. Problem 2C.7

R. B. Bird et al, Transport phenomena, John

Willey & Sons, 2002.

8-Jan-13 TK3201

DGA/14