FLUID MECHANICS
SPECIFIC VOLUME
 a physical science dealing with the action of FLUIDS
 the volume occupied by a unit mass of fluid
 UNITS: ft3/slugs (English), cm3/gram (Metric), m3/kg (SI)
AT REST or IN MOTION, and with applications and
devices in engineering using fluids
It is subdivided into two major areas:
FLUID STATICS – deals with fluids AT REST
FLUID DYNAMICS – deals with fluids IN MOTION
TYPES OF FLUIDS
IDEAL FLUIDS
» assumed to have no viscosity (hence, no resistance
to shear)
» incompressible
» have uniform velocity when flowing
» no friction between moving layers of fluid
» no eddy currents of turbulence
REAL FLUIDS
» exhibit infinite viscosities
» non-uniform velocity when flowing
» compressible
» experiencing friction and turbulence in flow
COMMON TERMS:
M = mass of fluid
V = volume of fluid
W = weight of the fluid (mg)
g = acceleration due to gravity
𝑽𝑺 = 𝟏⁄𝝆
𝑽𝑺 = 𝑽⁄𝑴
UNIT WEIGHT or SPECIFIC WEIGHT
 the weight of a unit volume of a liquid
 UNITS: lbf/ft3 (English), dyne/cm3 (Metric), KN/ N/m3 (SI)
𝜸 = 𝑾⁄𝑽
𝜸 = 𝝆𝒈
SPECIFIC GRAVITY
 a dimensionless ratio of a fluid’s density to some
standard reference density
 For liquids and solids, the reference density is WATER at
4◦C (39.2 ◦F)
𝒔=
𝝆𝒍𝒊𝒒𝒖𝒊𝒅
⁄𝝆𝒘𝒂𝒕𝒆𝒓
FOR WATER AT 4 ◦C:
 Unit Weight, 𝜸 = 62.4 lbf/ft3 = 9.81 kN/m3
 Density, 𝝆 = 1.94 slugs/ft3
= 1000 kg/m3
 s = 1.0
In gases, the standard reference to calculate the
specific gravity, s is the density of air
𝒔=
𝝆𝒈𝒂𝒔
⁄𝝆𝒍𝒊𝒒𝒖𝒊𝒅
𝝉
MASS DENSITY


𝝆 = 𝑴⁄𝑽
the density of a fluid is MASS per unit of VOLUME
UNITS: slugs/ft3 (English), gram/cm3 (Metric), kg/m3 (SI)
𝝆
𝝆𝒔𝒍𝒖𝒈𝒔 = 𝒍𝒃 𝒎⁄𝒈
g = 9.81 m/s2 / 32.2 ft/s2
DYNAMIC VISCOSITY 𝝁 = 𝑼
⁄𝒚
 the property of a fluid which determines the amount
of its resistance to shearing forces
For an ideal gas, its density can be found from the
specific gas constant and ideal gas law:
𝒑
𝝆 = ⁄𝑹𝑻
Where:
p = absolute pressure of gas, Pa
R = gas constant, Joule/kg - ◦K
For air:
R = 287 J/kg - ◦K
R = 1,716 lb-ft/slug - ◦R
T = absolute temperature in ◦Kelvin or ◦Rankine
◦K = ◦C + 273
◦R = ◦F + 460
TABLE 1: Approximate Room – Temperature Densities
of Common Fluids
𝝁
KINEMATIC VISCOSITY 𝒗 = ⁄𝝆
 the weight of a unit volume of a liquid
Where:
𝝁 = absolute viscosity in Pa-sec
𝝆 = Density of Fluid in kg/m3
COMMON UNITS OF VISCOSITY
1 poise = dyne-s/cm2 = 0.1 Pa-sec
1 dyne = 10-5 N
1 Stoke = 0.0001 m2/sec
SURFACE TENSION 𝝈
»
»
»
the membrane of "skin" that seems to form on the
free surface of a fluid is due to the intermolecular
cohesive forces
it is the reason that insects are able to sit on water
and a needle is able to float on it
it also causes bubbles and droplets to take on a
spherical shape, since any other shape would have
more surface area per unit volume
COMPRESSIBILITY 𝜷

known as the coefficient of compressibility is the
fractional change in the volume of a fluid per unit
change in pressure in a constant-temperature
process
∆𝑽
𝜷=
Where:
𝑤ℎ𝑒𝑟𝑒:
𝜎 = surface Tension in N/m
d = diameter of the droplet in m
p = gage pressure in Pa
𝑉


CAPILLARITY



The rise or fall or a fluid in a capillary tube is caused
by surface tension and depends on the relative
magnitudes of the cohesion of the liquid and the
adhesion of the liquid to the walls of the containing
vessel
Liquids rise in tubes they wet (adhesion › cohesion)
and fall in tubes they do not wet (cohesion ›
adhesion)
Capillary is important when using tubes smaller than
about 3/8 inch (9.5 mm) in diameter
∆𝒑
𝜷=
𝒅𝒑
BULK MODULUS OF ELASTICITY 𝑬𝑩
expresses the compressibility of the fluid
the ratio of the change in unit pressure to the
corresponding volume change per unit volume
∆𝒑
⁄∆𝑽
=
𝑬𝑩 =
𝒅𝒑
⁄𝒅𝑽
𝑽
imposed on a fluid move in waves. The velocity or
celerity, 𝑐 of pressure wave (also known as acoustical
or sonic velocity) is expressed as:
𝑬
𝝆
=
𝒄 = √ 𝑩
𝟏
𝜷𝝆
𝒄 = √
PROPERTY CHANGES IN IDEAL GAS
 For any ideal gas experiencing any process, the
𝒑𝟏 𝑽𝟏
𝒑 𝑽
equation of state is given by:
= 𝟐 𝟐
𝑻𝟏

𝑻𝟐
When temperature is held constant, the equation of
state reduces to (Boyle’s Law): 𝒑𝟏 𝑽𝟏 = 𝒑𝟐 𝑽𝟐
When pressure is held constant, the equation of state
reduces to (Charle’s Law):
𝑽𝟏
𝑻𝟏
For Adiabatic or Isentropic Conditions
𝑽
For complete wetting, as with water on clean glass, the
angle 𝜃. Hence the formula becomes
Where:
h = capillary rise or depression in m
𝜎 = surface Tension in N/m
d = diameter of the tube in m
𝛾 = unit weight of liquid in N/m3
𝜃 = contact angle between the tube and the liquid in
degrees
CONTACT ANGLES
𝑽⁄
PRESSURE DISTURBANCES 𝒄


𝒉 = 𝟒𝝈𝒄𝒐𝒔𝜽⁄𝒚𝒅
𝒅𝑽
𝑽

CAPILLARY RISE OR FALL
−
= change in volume (usually in percent)
𝑬𝑩 =
CAPILLARITY ACTION – the name given to the behavior of
the liquid in a thin-bore tube
=
∆𝑉 = change in volume
𝑉 = original volume
∆𝑝 = change in pressure
𝑑𝑉
Pressure Inside a Droplet of Liquid 𝒑 = 𝟒𝝈⁄𝒅
𝑽⁄
𝒌
𝒑𝟏 𝑽𝟏 𝒌 = 𝒑𝟐 𝑽𝟐 𝒌 OR ( 𝟏) =
𝑽𝟐
𝒑𝟐
𝒑𝟏
=
𝑽𝟐
𝑻𝟐
𝒑
= CONSTANT AND ( 𝟏)
𝒑𝟐
𝒌−𝟏
𝒌
=
Where:
𝑝1 = initial absolute pressure of gas
𝑝2 = final absolute pressure of gas
𝑉1 = initial volume of gas
𝑉2 = final volume of gas
𝑇1 = initial absolute temperature of gas in oK
𝑇2 = final absolute temperature of gas in oK
𝑘 = ratio of the specific heat at constant pressure to the
specific heat at constant volume (adiabatic exponent)
𝑻𝟐
𝑻𝟏