Fluid statics : fluid at rest

force/ pressure/ head

Fluid dynamics :

hydrodynamics/

aerodynamics

Motion transport (flow)

Fluid statics

• Pressure = normal force exerted by fluid

/ unit area

• Absolute, gauge, vacuum pressure

• Pressure measurement devices: U-tube

manometer, barometer

• Hydrostatic force, buoyant force

Fluid dynamics

Motion transport (flow)

Internal flow, velocity profile, pressure drop, friction loss

Bernoulli’s equation

https://www.accessengineeringlibrary.com/content/book/9780071422949/toc-chapter/chapter6/section/section2#/p200139d889206_6014

Classification of fluid flows

• Viscous flow region/ inviscid flow region

• Internal flow/ external flow

• Compressible /incompressible flow

• Laminar / turbulent flow

• Natural/forced flow

• Steady /unsteady flow

https://www.theengineerspost.com/types-of-fluid-flow/

TYPES OF FLUID FLOW AND REYNOLDS NUMBER

• Two types of fluid flow : laminar and turbulent flow.

– Laminar flow: flow at low velocities where the layers

of fluid seem to slide by one another without eddies

or swirls being present (viscous flow)

– Turbulent flow: flow at higher velocities where

eddies are present giving the fluid a fluctuating

nature

• The Reynolds number used to characterize the regimes

of flow.

• As the velocity was increased, laminar flow becomes

turbulent flow.

– The velocity at which the flow changes is known as

the critical velocity

TYPES OF FLUID FLOW AND REYNOLDS NUMBER

The experiments of Reynolds

https://theconstructor.org/practical-guide/hydraulics-lab/reynolds-experiment/2052/

https://www.aps.org/publications/apsnews/202003/history.cfm

TYPES OF FLUID FLOW AND REYNOLDS NUMBER

• Transition from laminar to turbulent in tubes is function of:

– velocity, density, viscosity of the fluid

– the tube diameter

• These variables are combined into the Reynolds number, which is

dimensionless:

– NRe is the Reynolds number

– D is the diameter in m

– is the fluid density in kg/m3

– is the fluid viscosity in Pas

– v is the average velocity of the fluid in m/s

• Units in the cgs system, D in cm, in g/cm3, in g/cms, v in cm/s.

• Units in the English system, D is in ft, in lbm/ft3, in lbm/fts, v in

ft/s.

DvN Re

TYPES OF FLUID FLOW AND REYNOLDS NUMBER

• For a straight circular pipe

– Reynolds number less than 2100 - the flow will be laminar.

– Reynolds number over 4000, the flow will be turbulent.

– In between, which is called the transition region, the flow can be

viscous or turbulent, depending upon the apparatus details.

ExampleWater at 303 K is flowing at the rate of 10 gal/min in a

pipe having an inside diameter (ID) of 2.067 in.

Calculate the Reynolds number using both English

units and SI units.

• Solution:

s/ft957.0ft 0233.0

1

s

ft0223.0 pipe,in velocity

ft 0233.04

)172.0(

4

D pipe of area sectional-cross

ft 172.012

2.067 D diameter, pipe

s/ft 0223.0s 60

min1

gal 7.481

ft 1

min

gal0.10rate flow

2

3

222

33

v

SolutionWater at 303 K (30°C),

density, = 0.996(62.43) lbm/ft3

viscosity, = (0.8007 cp)(6.719710-4 lbm/ftscp = 5.3810-4 lbm/fts

Finally,

Hence, the flow is turbulent

If using SI unit:

density, = 0.996(100) kg/m3 = 996 kg/m3

D = (2.067 in.)(1 ft/12 in.)(1 m/3.2808 ft) = 0.0525 m

v = (0.957 ft/s)(1 m/3.2808 ft) = 0.2917 m/s

= (0.8007 cp)(110-3 kg/mscp = 8.00710-4 kg/ms = 8.00710-4

Pas

4

m

4-

3

mRe 10905.1

s/ftlb105.38

)/ftlb 43.62996.0(ft/s) 957.0(ft) 172.0(

DvN

4

4-

3

Re 10905.1skg/m108.007

)kg/m 996(m/s) 2917.0(m) 0525.0(

DvN