Contributed by:

Fluid, Fluid vs Solid mechanics, Important terms, Surface tension, Metric to US system conversions

1.
Fluid Mechanics (CE-201)

Course Instructor

Prof. Dr. A R Ghumman

abdulrazzaq@uettaxila.edu.pk 051-9047638

03005223338

Associate

Dr Usman Ali Naeem-Ghufran Ahmed Pasha

(Lecturer, CED)

ghufran.ahmed@uettaxila.edu.pk

Ph : 051-9047658

Course Instructor

Prof. Dr. A R Ghumman

abdulrazzaq@uettaxila.edu.pk 051-9047638

03005223338

Associate

Dr Usman Ali Naeem-Ghufran Ahmed Pasha

(Lecturer, CED)

ghufran.ahmed@uettaxila.edu.pk

Ph : 051-9047658

2.
Recommended Books

Text Book:

Fluid Mechanics With Engineering Applications (10th

Edition)

by E. John Finnemore & Joseph B. Franzini

Reference Books:

A textbook of Hydraulics, Fluid Mechanics and Hydraulic

Machines (19th Edition) by R.S. Khurmi

Applied Fluid Mechanics (6th Edition) by Robert L. Mott

Fluid Mechanics by A.K Jain

Text Book:

Fluid Mechanics With Engineering Applications (10th

Edition)

by E. John Finnemore & Joseph B. Franzini

Reference Books:

A textbook of Hydraulics, Fluid Mechanics and Hydraulic

Machines (19th Edition) by R.S. Khurmi

Applied Fluid Mechanics (6th Edition) by Robert L. Mott

Fluid Mechanics by A.K Jain

3.
Marks Distribution

Sessionals - 40%

Attendance – 2%

Assignments – 8%

Practicals - 15%

Quizes – 10 %

Class Project/ Presentation – 5%

Mid Term - 20%

Final Exam - 40%

Sessionals - 40%

Attendance – 2%

Assignments – 8%

Practicals - 15%

Quizes – 10 %

Class Project/ Presentation – 5%

Mid Term - 20%

Final Exam - 40%

4.
Properties of Fluids

Lecture - 1

Lecture - 1

5.
Fluid

A fluid is defined as:

“A substance that continually deforms (flows) under

an applied shear stress regardless of the magnitude

of the applied stress”.

It is a subset of the phases of matter and includes

liquids, gases, plasmas and, to some extent, plastic

solids.

A fluid is defined as:

“A substance that continually deforms (flows) under

an applied shear stress regardless of the magnitude

of the applied stress”.

It is a subset of the phases of matter and includes

liquids, gases, plasmas and, to some extent, plastic

solids.

6.
Fluid Vs Solid Mechanics

Fluid mechanics:

“The study of the physics of materials which take the shape of

their container.” Or

“Branch of Engg. science that studies fluids and forces on them.”

Solid Mechanics:

“The study of the physics of materials with a defined rest shape.”

Fluid Mechanics can be further subdivided into fluid statics, the

study of fluids at rest, and kinematics, the study of fluids in motion

and fluid dynamics, the study of effect of forces on fluid motion.

In the modern discipline called Computational Fluid Dynamics

(CFD), computational approach is used to develop solutions to fluid

mechanics problems.

Fluid mechanics:

“The study of the physics of materials which take the shape of

their container.” Or

“Branch of Engg. science that studies fluids and forces on them.”

Solid Mechanics:

“The study of the physics of materials with a defined rest shape.”

Fluid Mechanics can be further subdivided into fluid statics, the

study of fluids at rest, and kinematics, the study of fluids in motion

and fluid dynamics, the study of effect of forces on fluid motion.

In the modern discipline called Computational Fluid Dynamics

(CFD), computational approach is used to develop solutions to fluid

mechanics problems.

7.
Distinction between a Solid and a Fluid

Solid Fluid

Definite Shape and definite Indefinite Shape and Indefinite

volume. volume & it assumes the shape

Does not flow easily. of the container which it

occupies.

Molecules are closer. Flow Easily.

Attractive forces between the

molecules are large enough to

Molecules are far apart.

retain its shape. Attractive forces between the

An ideal Elastic Solid deform molecules are smaller.

under load and comes back to Intermolecular cohesive forces

original position upon removal of in a fluid are not great enough to

load. hold the various elements of

Plastic Solid does not comes back fluid together. Hence Fluid will

to original position upon removal flow under the action of applied

of load, means permanent stress. The flow will be

deformation takes place. continuous as long as stress is

applied.

Solid Fluid

Definite Shape and definite Indefinite Shape and Indefinite

volume. volume & it assumes the shape

Does not flow easily. of the container which it

occupies.

Molecules are closer. Flow Easily.

Attractive forces between the

molecules are large enough to

Molecules are far apart.

retain its shape. Attractive forces between the

An ideal Elastic Solid deform molecules are smaller.

under load and comes back to Intermolecular cohesive forces

original position upon removal of in a fluid are not great enough to

load. hold the various elements of

Plastic Solid does not comes back fluid together. Hence Fluid will

to original position upon removal flow under the action of applied

of load, means permanent stress. The flow will be

deformation takes place. continuous as long as stress is

applied.

8.
Distinction between a Gas and Liquid

The molecules of a gas are A liquid is relatively

much farther apart than incompressible.

those of a liquid. If all pressure, except that

Hence a gas is very of its own vapor pressure,

compressible, and when is removed, the cohesion

all external pressure is between molecules holds

removed, it tends to expand them together, so that the

indefinitely. liquid does not expand

A gas is therefore in indefinitely.

equilibrium only when it is Therefore a liquid may

completely enclosed. have a free surface.

The molecules of a gas are A liquid is relatively

much farther apart than incompressible.

those of a liquid. If all pressure, except that

Hence a gas is very of its own vapor pressure,

compressible, and when is removed, the cohesion

all external pressure is between molecules holds

removed, it tends to expand them together, so that the

indefinitely. liquid does not expand

A gas is therefore in indefinitely.

equilibrium only when it is Therefore a liquid may

completely enclosed. have a free surface.

9.
SI Units

10.
FPS Units

11.
Important Terms

Density ():

Mass per unit volume of a substance.

kg/m3 in SI units

m

Slug/ft3 in FPS system of units

V

Specific weight ():

Weight per unit volume of substance.

N/m3 in SI units w

lbs/ft3 in FPS units

V

Density and Specific Weight of a fluid are related as:

g

Where g is the gravitational constant having value 9.8m/s2 or

32.2 ft/s2.

Density ():

Mass per unit volume of a substance.

kg/m3 in SI units

m

Slug/ft3 in FPS system of units

V

Specific weight ():

Weight per unit volume of substance.

N/m3 in SI units w

lbs/ft3 in FPS units

V

Density and Specific Weight of a fluid are related as:

g

Where g is the gravitational constant having value 9.8m/s2 or

32.2 ft/s2.

12.
Important Terms

Specific Volume (v):

Volume occupied by unit mass of fluid.

It is commonly applied to gases, and is usually expressed in

cubic feet per slug (m3/kg in SI units).

Specific volume is the reciprocal of density.

SpecificVo lume v 1 /

Specific Volume (v):

Volume occupied by unit mass of fluid.

It is commonly applied to gases, and is usually expressed in

cubic feet per slug (m3/kg in SI units).

Specific volume is the reciprocal of density.

SpecificVo lume v 1 /

13.
Important Terms

Specific gravity:

It can be defined in either of two ways:

a. Specific gravity is the ratio of the density of a substance

to the density of water at 4°C.

b. Specific gravity is the ratio of the specific weight of a

substance to the specific weight of water at 4°C.

l l

s liquid

w w

Specific gravity:

It can be defined in either of two ways:

a. Specific gravity is the ratio of the density of a substance

to the density of water at 4°C.

b. Specific gravity is the ratio of the specific weight of a

substance to the specific weight of water at 4°C.

l l

s liquid

w w

14.
Example

The specific wt. of water at ordinary temperature and

pressure is 62.4lb/ft3. The specific gravity of mercury is

13.56. Compute density of water, Specific wt. of mercury,

and density of mercury.

1. water water / g 62.4/32.2 1.938 slugs/ft3

2. mercury s mercury water 13.56 x62.4 846lb / ft 3

3. mercury s mercury water 13.56 x1.938 26.3slugs / ft 3

(Where Slug = lb.sec2/ ft)

The specific wt. of water at ordinary temperature and

pressure is 62.4lb/ft3. The specific gravity of mercury is

13.56. Compute density of water, Specific wt. of mercury,

and density of mercury.

1. water water / g 62.4/32.2 1.938 slugs/ft3

2. mercury s mercury water 13.56 x62.4 846lb / ft 3

3. mercury s mercury water 13.56 x1.938 26.3slugs / ft 3

(Where Slug = lb.sec2/ ft)

15.
Example

A certain gas weighs 16.0 N/m3 at a certain temperature and

pressure. What are the values of its density, specific volume,

and specific gravity relative to air weighing 12.0 N/m3

1. Density ρ γ /g

ρ 16/9.81 16.631 kg/m 3

2. Specific volume υ 1/ρ

u 1/1.631 0.613 m 3 /kg

3. Specific gravity s γ f /γ air

s 16/12 1.333

A certain gas weighs 16.0 N/m3 at a certain temperature and

pressure. What are the values of its density, specific volume,

and specific gravity relative to air weighing 12.0 N/m3

1. Density ρ γ /g

ρ 16/9.81 16.631 kg/m 3

2. Specific volume υ 1/ρ

u 1/1.631 0.613 m 3 /kg

3. Specific gravity s γ f /γ air

s 16/12 1.333

16.
Example

The specific weight of glycerin is 78.6 lb/ft3. compute its density

and specific gravity. What is its specific weight in kN/m3

1. Density / g

78.6/32.2 2.44 slugs/ft 3

2. Specific gravity s l / w

s 78.6/62.4 1.260

so 1.260x1000kg/m 3

1260 Kg/m 3

3. Specific weight in kN/m 3

x g

9.81x1260 12.36 kN/m 3

The specific weight of glycerin is 78.6 lb/ft3. compute its density

and specific gravity. What is its specific weight in kN/m3

1. Density / g

78.6/32.2 2.44 slugs/ft 3

2. Specific gravity s l / w

s 78.6/62.4 1.260

so 1.260x1000kg/m 3

1260 Kg/m 3

3. Specific weight in kN/m 3

x g

9.81x1260 12.36 kN/m 3

17.
Example

Calculate the specific weight, density, specific volume and

specific gravity of 1litre of petrol weights 7 N.

Given Volume = 1 litre = 10-3 m3

Weight = 7 N

1. Specific weight,

w = Weight of Liquid/volume of Liquid

w = 7/ 10-3 = 7000 N/m3

2. Density, = /g

= 7000/9.81 = 713.56 kg/m3

Calculate the specific weight, density, specific volume and

specific gravity of 1litre of petrol weights 7 N.

Given Volume = 1 litre = 10-3 m3

Weight = 7 N

1. Specific weight,

w = Weight of Liquid/volume of Liquid

w = 7/ 10-3 = 7000 N/m3

2. Density, = /g

= 7000/9.81 = 713.56 kg/m3

18.
Solution (Cont.):

3. Specific Volume = 1/

1/713.56

=1.4x10-3 m3/kg

4. Specific Gravity = s =

Specific Weight of Liquid/Specific Weight of Water

= Density of Liquid/Density of Water

s = 713.56/1000 = 0.7136

3. Specific Volume = 1/

1/713.56

=1.4x10-3 m3/kg

4. Specific Gravity = s =

Specific Weight of Liquid/Specific Weight of Water

= Density of Liquid/Density of Water

s = 713.56/1000 = 0.7136

19.
Example

If the specific gravity of petrol is 0.70.Calculate its Density,

Specific Volume and Specific Weight.

Solution:

Given

Specific gravity = s = 0.70

1. Density of Liquid, s x density of water

= 0.70x1000

= 700 kg/m3

2. Specific Volume = 1/

x-3

3. Specific Weight, = 700x9.81 = 6867 N/m3

If the specific gravity of petrol is 0.70.Calculate its Density,

Specific Volume and Specific Weight.

Solution:

Given

Specific gravity = s = 0.70

1. Density of Liquid, s x density of water

= 0.70x1000

= 700 kg/m3

2. Specific Volume = 1/

x-3

3. Specific Weight, = 700x9.81 = 6867 N/m3

20.
Compressibility

It is defined as:

“Change in Volume due to change in Pressure.”

The compressibility of a liquid is inversely proportional to Bulk

Modulus (volume modulus of elasticity).

Bulk modulus of a substance measures resistance of a substance to

uniform compression. dp

Ev

(dv / v)

v

Ev dp

Where; v is the specific volume and p is the pressure. dv

Units: Psi, MPa , As v/dv is a dimensionless ratio, the units of E

and p are identical.

It is defined as:

“Change in Volume due to change in Pressure.”

The compressibility of a liquid is inversely proportional to Bulk

Modulus (volume modulus of elasticity).

Bulk modulus of a substance measures resistance of a substance to

uniform compression. dp

Ev

(dv / v)

v

Ev dp

Where; v is the specific volume and p is the pressure. dv

Units: Psi, MPa , As v/dv is a dimensionless ratio, the units of E

and p are identical.

21.
Example

At a depth of 8km in the ocean the pressure is 81.8Mpa. Assume

that the specific weight of sea water at the surface is 10.05 kN/m 3

and that the average volume modulus is 2.34 x 10 3 N/m3 for that

pressure range.

(a) What will be the change in specific volume between that at the

surface and at that depth?

(b) What will be the specific volume at that depth?

(c) What will be the specific weight at that depth?

At a depth of 8km in the ocean the pressure is 81.8Mpa. Assume

that the specific weight of sea water at the surface is 10.05 kN/m 3

and that the average volume modulus is 2.34 x 10 3 N/m3 for that

pressure range.

(a) What will be the change in specific volume between that at the

surface and at that depth?

(b) What will be the specific volume at that depth?

(c) What will be the specific weight at that depth?

22.
(a) v1 1 / p1 g / 1

Using Equation :

9.81 / 10050 0.000976m 3 / kg

p

6 9

v 0.000976(81.8 x10 0) /( 2.34 x10 ) Ev

(v / v)

-34.1x10 -6 m 3 / kg dv p

v Ev

(b) v 2 v1 v 0.000942 m 3 / kg v2 v1 p 2 p1

v1 Ev

(c) 2 g / v2 9.81 / 0.000942 10410 N / m 3

Using Equation :

9.81 / 10050 0.000976m 3 / kg

p

6 9

v 0.000976(81.8 x10 0) /( 2.34 x10 ) Ev

(v / v)

-34.1x10 -6 m 3 / kg dv p

v Ev

(b) v 2 v1 v 0.000942 m 3 / kg v2 v1 p 2 p1

v1 Ev

(c) 2 g / v2 9.81 / 0.000942 10410 N / m 3

23.
Viscosity

Viscosity is a measure of the resistance of a fluid to deform

under shear stress.

It is commonly perceived as thickness, or resistance to flow.

Viscosity describes a fluid's internal resistance to flow and may be

thought of as a measure of fluid friction. Thus, water is "thin",

having a lower viscosity, while vegetable oil is "thick" having a

higher viscosity.

The friction forces in flowing fluid result from the cohesion and

momentum interchange between molecules.

All real fluids (except super-fluids) have some resistance to shear

stress, but a fluid which has no resistance to shear stress is known

as an ideal fluid.

It is also known as Absolute Viscosity or Dynamic Viscosity.

Viscosity is a measure of the resistance of a fluid to deform

under shear stress.

It is commonly perceived as thickness, or resistance to flow.

Viscosity describes a fluid's internal resistance to flow and may be

thought of as a measure of fluid friction. Thus, water is "thin",

having a lower viscosity, while vegetable oil is "thick" having a

higher viscosity.

The friction forces in flowing fluid result from the cohesion and

momentum interchange between molecules.

All real fluids (except super-fluids) have some resistance to shear

stress, but a fluid which has no resistance to shear stress is known

as an ideal fluid.

It is also known as Absolute Viscosity or Dynamic Viscosity.

24.

25.
Dynamic Viscosity

As a fluid moves, a shear stress is developed in

it, the magnitude of which depends on the

viscosity of the fluid.

Shear stress, denoted by the Greek letter (tau),

τ, can be defined as the force required to slide

one unit area layer of a substance over another.

Thus, τ is a force divided by an area and can be

measured in the units of N/m2 (Pa) or lb/ft2.

As a fluid moves, a shear stress is developed in

it, the magnitude of which depends on the

viscosity of the fluid.

Shear stress, denoted by the Greek letter (tau),

τ, can be defined as the force required to slide

one unit area layer of a substance over another.

Thus, τ is a force divided by an area and can be

measured in the units of N/m2 (Pa) or lb/ft2.

26.
Dynamic Viscosity

Figure shows the velocity gradient in a moving fluid.

U

F, U

Y

Experiments have shown that: AU

F

Y

Figure shows the velocity gradient in a moving fluid.

U

F, U

Y

Experiments have shown that: AU

F

Y

27.
Dynamic Viscosity

The fact that the shear stress in the fluid is directly

proportional to the velocity gradient can be stated

mathematically as F U du

A Y dy

where the constant of proportionality (the Greek letter miu)

is called the dynamic viscosity of the fluid. The term absolute

viscosity is sometimes used.

The fact that the shear stress in the fluid is directly

proportional to the velocity gradient can be stated

mathematically as F U du

A Y dy

where the constant of proportionality (the Greek letter miu)

is called the dynamic viscosity of the fluid. The term absolute

viscosity is sometimes used.

28.
Kinematic Viscosity

The kinematic viscosity ν is defined as:

“Ratio of absolute viscosity to density.”

The kinematic viscosity ν is defined as:

“Ratio of absolute viscosity to density.”

29.
Newtonian Fluid

A Newtonian fluid; where stress is directly

proportional to rate of strain, and (named for Isaac

Newton) is a fluid that flows like water, its stress versus

rate of strain curve is linear and passes through the origin.

The constant of proportionality is known as the viscosity.

A simple equation to describe Newtonian fluid behavior is

du

Where =

absolute viscosity/Dynamic viscosity or

dy

simply viscosity

= shear stress

A Newtonian fluid; where stress is directly

proportional to rate of strain, and (named for Isaac

Newton) is a fluid that flows like water, its stress versus

rate of strain curve is linear and passes through the origin.

The constant of proportionality is known as the viscosity.

A simple equation to describe Newtonian fluid behavior is

du

Where =

absolute viscosity/Dynamic viscosity or

dy

simply viscosity

= shear stress

30.

31.
Example

Find the kinematic viscosity of liquid in stokes whose specific

gravity is 0.85 and dynamic viscosity is 0.015 poise.

Solution:

Given S = 0.85

= 0.015 poise

= 0.015 x 0.1 Ns/m2 = x-3 Ns/m2

We know that S = density of liquid/density of water

density of liquid = S x density of water

0.85 x 1000kg/m3

Kinematic Viscosity ,

x-3

x -6m2/s = x 10-6 x4cm2/s

= x 10-2 stokes.

Find the kinematic viscosity of liquid in stokes whose specific

gravity is 0.85 and dynamic viscosity is 0.015 poise.

Solution:

Given S = 0.85

= 0.015 poise

= 0.015 x 0.1 Ns/m2 = x-3 Ns/m2

We know that S = density of liquid/density of water

density of liquid = S x density of water

0.85 x 1000kg/m3

Kinematic Viscosity ,

x-3

x -6m2/s = x 10-6 x4cm2/s

= x 10-2 stokes.

32.
Example

A 1 in wide space between two horizontal plane surface is

filled with SAE 30 Western lubricating oil at 80 F. What

force is required to drag a very thin plate of 4 sq.ft area

through the oil at a velocity of 20 ft/mm if the plate is 0.33

in from one surface.

A 1 in wide space between two horizontal plane surface is

filled with SAE 30 Western lubricating oil at 80 F. What

force is required to drag a very thin plate of 4 sq.ft area

through the oil at a velocity of 20 ft/mm if the plate is 0.33

in from one surface.

33.
0.0063 lb.sec/ft 2 ( From A.1)

F U du

A Y dy

1 0.0063 * (20 / 60) /(0.33 / 12) 0.0764lb / ft 2

2 0.0063 * (20 / 60) /(0.67 / 12) 0.0394lb / ft 2

F1 1 A 0.0764 * 4 0.0305lb

F2 2 A 0.0394 * 4 0.158lb

Force F1 F2 0.463lb

F U du

A Y dy

1 0.0063 * (20 / 60) /(0.33 / 12) 0.0764lb / ft 2

2 0.0063 * (20 / 60) /(0.67 / 12) 0.0394lb / ft 2

F1 1 A 0.0764 * 4 0.0305lb

F2 2 A 0.0394 * 4 0.158lb

Force F1 F2 0.463lb

34.
Example

Assuming a velocity distribution as shown in fig., which is a

parabola having its vertex 12 in from the boundary,

calculate the shear stress at y= 0, 3, 6, 9 and 12 inches.

Fluid’s absolute viscosity is 600 P.

Assuming a velocity distribution as shown in fig., which is a

parabola having its vertex 12 in from the boundary,

calculate the shear stress at y= 0, 3, 6, 9 and 12 inches.

Fluid’s absolute viscosity is 600 P.

35.
Solution

600 P= 600 x 0.1=0.6 N-s/m2 =0.6 x (1x2.204/9.81 x 3.282)

=0.6 x 0.020885=0.01253 lb-sec/ft2

Parabola Equation Y=aX2

120-u= a(12-y) 2

u=0 at y=0 so a= 120/122=5/6

u=120-5/6(12-y) 2 du/dy=5/3(12-y)

= du/dy

y (in) 0 3 6 9 12

du/dy 20 15 10 5 0

0.251 0.1880 0.1253 0.0627 0

600 P= 600 x 0.1=0.6 N-s/m2 =0.6 x (1x2.204/9.81 x 3.282)

=0.6 x 0.020885=0.01253 lb-sec/ft2

Parabola Equation Y=aX2

120-u= a(12-y) 2

u=0 at y=0 so a= 120/122=5/6

u=120-5/6(12-y) 2 du/dy=5/3(12-y)

= du/dy

y (in) 0 3 6 9 12

du/dy 20 15 10 5 0

0.251 0.1880 0.1253 0.0627 0

36.
Ideal Fluid

An ideal fluid may be defined as:

“A fluid in which there is no friction i.e Zero viscosity.”

Although such a fluid does not exist in reality, many fluids

approximate frictionless flow at sufficient distances, and so

their behaviors can often be conveniently analyzed by

assuming an ideal fluid.

An ideal fluid may be defined as:

“A fluid in which there is no friction i.e Zero viscosity.”

Although such a fluid does not exist in reality, many fluids

approximate frictionless flow at sufficient distances, and so

their behaviors can often be conveniently analyzed by

assuming an ideal fluid.

37.
Real Fluid

In a real fluid, either liquid or gas, tangential or

shearing forces always come into being whenever

motion relative to a body takes place, thus giving

rise to fluid friction, because these forces oppose

the motion of one particle past another.

These friction forces give rise to a fluid property

called viscosity.

In a real fluid, either liquid or gas, tangential or

shearing forces always come into being whenever

motion relative to a body takes place, thus giving

rise to fluid friction, because these forces oppose

the motion of one particle past another.

These friction forces give rise to a fluid property

called viscosity.

38.
Surface Tension

Cohesion: “Attraction between molecules of same surface”

It enables a liquid to resist tensile stresses.

Adhesion: “Attraction between molecules of different

surface” It enables to adhere to another body.

“Surface Tension is the property of a liquid, which enables it

to resist tensile stress”.

At the interface between liquid and a gas i.e at the liquid

surface, and at the interface between two immiscible (not

mixable) liquids, the attraction force between molecules form

an imaginary surface film which exerts a tension force in the

surface. This liquid property is known as Surface Tension.

Cohesion: “Attraction between molecules of same surface”

It enables a liquid to resist tensile stresses.

Adhesion: “Attraction between molecules of different

surface” It enables to adhere to another body.

“Surface Tension is the property of a liquid, which enables it

to resist tensile stress”.

At the interface between liquid and a gas i.e at the liquid

surface, and at the interface between two immiscible (not

mixable) liquids, the attraction force between molecules form

an imaginary surface film which exerts a tension force in the

surface. This liquid property is known as Surface Tension.

39.
Surface Tension

As a result of surface tension, the liquid surface has a

tendency to reduce its surface as small as possible. That is

why the water droplets assume a nearly spherical shape.

This property of surface tension is utilized in manufacturing

of lead shots.

Capillary Rise: The phenomenon of rising water in the tube of

smaller diameter is called capillary rise.

As a result of surface tension, the liquid surface has a

tendency to reduce its surface as small as possible. That is

why the water droplets assume a nearly spherical shape.

This property of surface tension is utilized in manufacturing

of lead shots.

Capillary Rise: The phenomenon of rising water in the tube of

smaller diameter is called capillary rise.

40.
Metric to U.S. System Conversions,

Calculations, Equations, and Formulas

Millimeters (mm) x 0.03937 = inches (")(in)

Centimeters (cm) x 0.3937 = inches (")(in)

Meters (m) x 39.37 = inches (")(in)

Meters (m) x 3.281 = feet (')(ft)

Meters (m) x 1.094 = yards (yds)

Kilometers (km) x 0.62137 = miles (mi)

Kilometers (km) x 3280.87 = feet (')(ft)

Liters (l) x 0.2642 = gallons (U.S.)(gals)

Calculations, Equations, and Formulas

Millimeters (mm) x 0.03937 = inches (")(in)

Centimeters (cm) x 0.3937 = inches (")(in)

Meters (m) x 39.37 = inches (")(in)

Meters (m) x 3.281 = feet (')(ft)

Meters (m) x 1.094 = yards (yds)

Kilometers (km) x 0.62137 = miles (mi)

Kilometers (km) x 3280.87 = feet (')(ft)

Liters (l) x 0.2642 = gallons (U.S.)(gals)

41.
Calculations, Equations & Formulas

Bars x 14.5038 = pounds per square inch (PSI)

Kilograms (kg) x 2.205 = Pounds (P)

Kilometers (km) x 1093.62 = yards (yds)

Square centimeters x 0.155 = square inches

Liters (l) x 0.0353 = cubic feet

Square meters x 10.76 = square feet

Square kilometers x 0.386 = square miles

Cubic centimeters x 0.06102 = cubic inches

Cubic meters x 35.315 = cubic feet

Bars x 14.5038 = pounds per square inch (PSI)

Kilograms (kg) x 2.205 = Pounds (P)

Kilometers (km) x 1093.62 = yards (yds)

Square centimeters x 0.155 = square inches

Liters (l) x 0.0353 = cubic feet

Square meters x 10.76 = square feet

Square kilometers x 0.386 = square miles

Cubic centimeters x 0.06102 = cubic inches

Cubic meters x 35.315 = cubic feet

42.
Calculations, Equations & Formulas

Inches (")(in) x 25.4 = millimeters (mm)

Inches (")(in) x 2.54 = centimeters (cm)

Inches (")(in) x 0.0254 = meters (m)

Feet (')(ft) x 0.3048 = meters (m)

Yards (yds) x 0.9144 = meters (m)

Miles (mi) x 1.6093 = kilometers (km)

Feet (')(ft) x 0.0003048 = kilometers (km)

Inches (")(in) x 25.4 = millimeters (mm)

Inches (")(in) x 2.54 = centimeters (cm)

Inches (")(in) x 0.0254 = meters (m)

Feet (')(ft) x 0.3048 = meters (m)

Yards (yds) x 0.9144 = meters (m)

Miles (mi) x 1.6093 = kilometers (km)

Feet (')(ft) x 0.0003048 = kilometers (km)

43.
Calculations, Equations & Formulas

Gallons (gals) x 3.78 = liters (l)

Cubic feet x 28.316 = liters (l)

Pounds (P) x 0.4536 = kilograms (kg)

Square inches x 6.452 = square centimeters

Square feet x 0.0929 = square meters

Square miles x 2.59 = square kilometers

Acres x 4046.85 = square meters

Cubic inches x 16.39 = cubic centimeters

Cubic feet x 0.0283 = cubic meters

Gallons (gals) x 3.78 = liters (l)

Cubic feet x 28.316 = liters (l)

Pounds (P) x 0.4536 = kilograms (kg)

Square inches x 6.452 = square centimeters

Square feet x 0.0929 = square meters

Square miles x 2.59 = square kilometers

Acres x 4046.85 = square meters

Cubic inches x 16.39 = cubic centimeters

Cubic feet x 0.0283 = cubic meters