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Lecture 2

Properties of FluidsUnits and Dimensions

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• The elemental volume must be much larger than the free random path of a molecule. 2/19

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Density Dimensions and Units

• Dimensions

• Units:

3L

M

Vol

M

SI C.G.S Gravitational (MKpS)

kg m-3 g cm-3 UMM m-3

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Specific Weight, Dimensions and Units

• Dimensions

• Units:

33

2

LF

LMLT

VolMg

g

SI C.G.S Gravitational (MKpS)

N m-3 dine cm-3

(gcms-2)cm-3

(10-3kg*10-2ms-2)(10-2m)-3

dine cm-3

= 10 Nm-2= 1 kgm-2

kg m-3

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Other properties

• Temperature, is a measure of molecule kinetic energy,

• Specific Gravity (dimensionless)

SI C.G.S Gravitational (MKpS)

k k k

12

OH

SG

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Viscosity

When a fluid is sheared, it begins to move at a strain rate inversely proportional to a property called its coefficient of viscosity, .

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Viscosity is responsible for the shear stress which opposes to the relative movement of elemental fluid volumes. Is null if there is no velocity gradient, so it destroys gradients, i.e. generates momentum diffusion.

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Viscosity Units

SI C.G.S Gravitational (MKpS)

N m-2s=kgm-1s-1

(Poiseuille)

dine cm-2s = gcm-1s-1

(Poise=10 Poiseuille)

kg m-2s=kgm-1s-1

1

2

T

FL

dydu

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Kinematic Viscosity

SI C.G.S Gravitational (MKpS)

m2s-1 cm2s-1 m2s-1

121

223

1

23

TLT

LMLT

M

L

T

FL

M

L

12

12

61

55.1

smE

smE

water

air

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Flow between two plates

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Viscosity variability

• Varies much with temperature and weekly with pressure.

• In liquids:– Decreases with temperature,

• In gases:– Increases with temperature.

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No Slip Condition

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Surface Tension

• Exists because intermolecular attraction forces between liquid molecules are higher than between the liquid molecules and air.

• Is responsible for drop formation and for pressure increase inside the drop.

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Spherical droplet

• Surface tension decreases with temperature. This is why solubility increases with temperature.

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Capilarity

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Summary

• We have seen the main fluid properties, their dimensions and units.

• Viscosity is relevant only when there is movement and velocity gradients are present.

• In the next lecture we will see properties of the flow field.

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Velocity, momentum, kinetic energy

dA

dQV

A

QV

L

TL

TL

LL

T

LV

2

13

2

2.

TL

FT

L

MLT

T

L

L

MV

33

2

3

Momentum is the Force applied to a volume multiplied by the action time. A small force acting for long can generate big momentum.

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Dimensions consistency/homogeneity

• In one equation all terms must have the same dimensions.

• In Fluid mechanics this norm is usually respected.

• In many empirical laws (often in natural sciences) it is not, being a source of errors.

• Manning formula for friction is a tricky example of a non-homogeneous formula.

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Other properties computed from velocity

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Momentum and kinetic energy

VVddtVoldtVd

Mdt

Vol

F

• Momentum is often called impulse

22

2

2

1

2.

...2

1

VV

dVdV

dtVdt

Vdld

dt

VdldFV

Volume

Work

L

LMLT

T

L

L

MV

3

2

2

2

32

2

1