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ME 262 BASIC FLUID MECHANICS
Assistant Professor Neslihan Semerci
Lecture 1
(Introduction to Fluid Mechanics, weight and mass, dimensions, dimensional
homogeneity and units, unit systems, pressure, compressibility, density, specific
weight and specific gravity)
1. INTRODUCTION
Fluid mechanics is the study of fluids and forces on them.
Fluids : liquids,gases, and plasmas
FLUID MECHANICS
Fluid Dynamics
The study of fluids in motion
Fluid Statistics
The study of fluids at rest
Both liquid and gases are classifed as fluids.
Fluid engineering applications  breathing, blood flow, swimming pump, fans, turbine,
airplane, ships, rivers, pipes, icebergs, filters, jets
Almost everything in this planet either is a fluid or moved within or near a fluid.
The concept of fluid: From the point of view of fluid mechanics, all matter consists of only
two states: fluid or solid
Technical distinction lies with the reaction of the two to an applied shear or tangential stress.
“A solid can resist a shear stress by a static deformation”
“Any shear applied to a fluid, no matter how small, will result in movement of that fluid.”
“A fluid moves and deforms continuously as long as the shear stress applied.”
MOLECULAR STRUCTURE OF SOLID: A solid has a regular arrangement of particles
(atoms, ions or molecules). The particles are close together and cannot move around so
the shape of a solid is fixed.
MOLECULAR STRUCTURE OF LIQUID: A liquid has an arrangement of particles that
are close together (like a solid) but the particles are free to move because the
force of attraction between the particles is weaker than it is in a solid. A liquid will flow to
take the shape of its container.
MOLECULAR STRUCTURE OF GASES: A gas has no order, its particles are arranged
at
random.
The particles in
a gas are
so
far
apart
that
there
is
no force of attraction between them. A gas will fill the whole volume of its container.
A gas is easily compressed.
2. WEIGHT AND MASS
An understanding of fluid properties requires a careful distinction between mass and weight.
Mass: Property of a body of fluid that is a measure of its inertia or resistance to a change in
motion. It’s also a measure of the quantity of fluid. Mass does not change with the body’s
position, movement or alteration of its shape unless material is added or removed.
Weight: Gravitational force acting on a body mass. Force with which a body is attracted
toward the earth by gravitation.
mass, kg
𝐹 = 𝑚. 𝑎
acceleration, m/s2
Force (N)
𝑊 = 𝑚. 𝑔
Weight (N)
g
acceleration of gravity, m/s2
mass, kg
= 9.81 m/s2 in SI system
= 32.2 ft/s2 in U.S. Customary System
3. DIMENSIONS, DIMENSIONAL HOMOGENITY AND UNITS
Primary dimensions: In fluid mechanics there are only four primary dimensions from which
all other dimensions can be derived. These are mass, length, time and temperature.
Qualitative: Identify the nature, or type, of the characteristics (such as length, time, stress, and
velocity).
Quantitative: Numerical measure of the characteristics (such as 10 meter).
Primary dimensions: Length, temperature, time, mass
Secondary dimensions: Velocity, length/time, Area, ∀olume.
4. UNIT SYSTEMS
English System
(United States Customary System)
(English Gravitational Unit System)
(British Units)
Metric SI
(International System)
SI system
English System
Mass, kg
Mass, Ibm
Length, m
Length, foot(m)
Time, s
Time, second(s)
Force in English System:
Force is usually considered to be one of the primary dimensions. This is the source of confusion
and error that necessitates the use of a dimensional constant (gc) in many formulas.
Force = (mass) (acceleration)
= m.a
In SI system, the force unit is Newton (N). One Newton is equal to the force needed to
accelerate a mass of one kilogram one meter per second per second.
In English system, the force unit is the pound-force (Ibf) and is defined as the force required to
accelerate a mass of 32.174 (1 slug) at a rate of 1 ft/s2.
m= 1 kg
m= 32.174 Ibm
a=1 m/s2
F= 1 N
a=1 ft/s2
1 N= 1 kg.m/s2
1 Ibf= 32.174 Ibm.ft/s2
F= 1 Ibf
A force of 1 N is roughly equivalent to the weight of a small apple (m=102 g) whereas a
force of 1 pound-force is roughly equivalent to the weight of 4 medium apples (mtotal=454
g). Another force a unit is commonly used in many European countries is the kg-f
(kilogram-force which is the weight of 1 kg mass at sea-level.
Force (kg-force) = 1 kg. 9.807 m/s2
=9.807 N
At sea level a mass of 1 kg weighs 9.807 N. A mass of 1 Ibm however weighs 1 Ibf.
W=mg
= 1 Ibm.32.22 ft/s2 = 1 Ibf
1 Ibm ≠ 1 Ibf
5. PRESSURE
Pressure defined as the amount of force exerted on a unit area of a substance.
Pressure =
Force
Area of which the force is applied
P=
= N/m2
F
A
Unit : N/m2 or Pascal (Pa)
(Also frequently used is “bar”, where 1 bar = 105 Pa)
Two important principles about pressure (Pascal’s Principles)

Pressure act uniformly in all directions on a small volume of a fluid.

In a fluid confined by solid boundaries, pressure acts perpendicular to the boundary.
6. COMPRESSIBILITY : Change of volume (V) of a substance that is subjected to a change
in pressure on it. Quantity used to measure : bulk modulus of elasticity or, simply, bulk
modulus, E.
𝐸=
−∆𝑃
(∆𝑉)/𝑉
The units are same as those for the pressure.
Liquids are very slightly compressible. It would take a large change in pressure to produce a
small change in volume.
“ LIQUIDS IS CONSIDERED AS INCOMPRESSIBLE”
Example 1: Compute the change in pressure that must be applied to change its volume
1 %.
E = ∆P × [∆V/V]
Water 316.000 psi =∆P × [0.01]
E = 316 000 psi
∆P = 3160 psi
7. DENSITY, SPECIFIC WEIGHT AND SPECIFIC GRAVITY
Density: Amount of mass per unit volume of substance
𝜌=
𝑚
𝑚𝑎𝑠𝑠 𝑘𝑔
=
,
𝑉 𝑣𝑜𝑙𝑢𝑚𝑒 𝑚3
Units are kilograms per cubic meter in SI system and slugs per cubic foot in the U.S. customary
units.
Specific Weight: The amount of weight per unit volume of a substance
S𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑤𝑒𝑖𝑔ℎ𝑡 =
𝑊 𝑊𝑒𝑖𝑔ℎ𝑡
𝑁
=
= 3
𝑉 𝑉𝑜𝑙𝑢𝑚𝑒 𝑚
The units for specific weight Newton per cubic meters (N/m3) in the SI system and pounds per
cubic foot in the U.S. customary system.
Specific gravity: Ratio of the density of a substance to the density of water at 40C.
Ratio of the specific weight of a substance to the specific weight of the water
at 40C.
s𝑔 (𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑔𝑟𝑎𝑣𝑖𝑡𝑦) =
At 4℃ ρwater =1000
𝛾𝑠
𝛾𝑤 𝑎𝑡 4℃
𝜌𝑠
= 𝜌𝑤 𝑎𝑡 40𝐶
Example 2: A load of 200 Ib is exerted on a piston confining an oil in a circular cylinder
with an inside diameter 2.5 inches. Compute the pressure.
P=
Area =
P=
F
A
π×(2.5)2
4
200 Ib
4.91 in2
= 4.91 in2
= 40.7 Ib/in2
Example3 :a) Calculate the weight of a reservoir of oil if it has a mass of 825 kg.
w=m×g
= 825 kg × 9.81 m/s2
= 8093 kg. m/s2 (N) = 8093 N = 8.093 kN
b) If the reservoir has a volume of 0.917 m3 . Find its density, specific weight and
specific gravity =?
m
Density=ρ =
γ=
Specific weight
Specific gravity s. g =
ρoil
ρwater at 4℃
V
w
V
=
=
=
825 kg
0.917 m3
8.093 kN
0.917 m3
γoil
γwater at 4℃
= 8.93 kN/m3
900 kg/m3
=
1000
kg
m3
at 4℃
= 0.9
Density of water at 20 ℃ → 998 kg/m3 , at 4 ℃ → 1000 kg/m3
Example 4: Glycerine at 20 ℃ has a specific gravity of 1.26. ρglycerine = ? γglycerine = ?
s. g =
1.26 =
γgly. =
w
∀
=
mg
∀
ρgly.
1000
=
1260kg
m3
ρglycerine
γwater at 4 ℃
ρgly. = 1260 kg/m3
m
kg
× (9.81 s2 ) = 12360 m2 s2=12.36 kN
Example 5: A container has a 5 m3 volume capacity and weights 1500 N when empty
and 47 000 N when filled with a liquid.
ρliquid = ?
(s. g)liquid = ?
γliquid = ?
weight of liquid = 47 000 – 1500 N =45 500 N
w=m×g
45 500 = m × (9.81 m/s2 )
m = 4638.12 kg
ρ=
γ=
w
∀
=
m
∀
mg
∀
=
46.38.12 kg
5 m3
= 928 kg/m3
kg
= 928 m3 × 9.81m/s 3 = 9103 N/m3
s. g =
928 kg/m3
1000 at 4 ℃
= 0.928