1. LECTURE UNIT NO. 1
References:
- Fluid Mechanics with Engineering Applications by Daugherty and Franzini
- Fluid Mechanics with Applications by Anthony Esposito
- Elementary Fluid Mechanics, 7th Ed. By Vernard and Street
- Fundamentals of Fluid Mechanics by Munsoon, Okiishi and Young
Introduction
Fluid Mechanics is the study of the behavior of fluids (liquid and gasses) and the application where
fluids are used.
Branches of Fluid Mechanics
1. Fluid statics – study of the mechanics of fluids at rest
2. Kinematics of fluids – deals with velocities and streamlines without considering forces or energy
3. Fluid dynamics – concerned with the relations between velocities and accelerations and the forces
exerted by or upon fluids in motion
Two categories of Fluid dynamics:
i. Hydrodynamics – deals with flow systems where the fluid density does not change
significantly
ii. Gas dynamics – deals with flow systems where fluid density changes significantly.
4. Aerodynamics – deals with the effect of airflow on immersed bodies such as airplanes and
automobiles regardless of whether it is a low-speed incompressible flow or high speed compressible
flow
Compressible and Incompressible Fluids
Liquids are considered to be incompressible so that their volume does not change with pressure
changes. This is not exactly true, but the change in volume due to pressure changes is so small that it is
ignored for most engineering applications. This is usually the case with liquids. Gasses, on the other hand,
are fluids that are readily compressible. Gasses are greatly influenced by the pressure to which they are
subjected.
Distinction Between a Gas and a Liquid
A fluid may be either a gas or a liquid. The molecules of a gas are much further apart than those of
a liquid. A liquid may have a free surface. A vapor is a gas whose temperature and pressure are such that
it is very near the liquid phase.
FUNDAMENTAL UNITS AND NOMENCLETURE:
Nomenclature Parameter English Engineering Units Metric SI Units
l length ft m
F, W force lbf N
m mass lbm, slugs kg or kgm
A area ft2 m2
V volume or total volume ft3 m3
v velocity ft/sec m/s
a . acceleration ft/sec2 m/s2
m. mass flow rate lbm/sec kg/s
V, Q volume flow rate ft3/sec m3/s
P pressure lbf/in2, psi N/m2, Pa
WP, P power hp Watt
E energy Btu N-m, J
Total values (Capital Letters) Specific values (Small Letters)
Total Enthalpy H (kJ) Specific Enthalpy h (kJ/kg)
Total Volume V (m3) Specific Volume v (m3/kg)
Total Internal Energy U (kJ) Specific Internal Energy u (kJ/kg)
Isaac Newton’s Second Law of Motion
States that of an unbalanced force acts in a body: (1) the body will accelerate in the direction of
the unbalanced force, and (2) the acceleration will be proportional to the unbalanced force and inversely
proportional to the mass of the body
Illustration:

2. Where:
F = force of gravity
m = mass of the substance, slugs or lbm, kg
go = observed or local gravitational acceleration, ft/sec 2, m/s2
gc = proportionality constant
gs = standard gravitational acceleration
Note:
Use standard gravitational acceleration gs if the observed or local gravitational acceleration go is
not given
1. Given: 5 lbm (Eng’g units)
Required: F
2. Given: 5 slugs (Eng’g units)
Required: F
Note: 1 slug = 32.2 lbm = 14.594 kgm
3. Given: 5 kg (SI units)
Required: F
FORMS OF ENERGY
Energies possessed by a body which has to be considered when analyzing a thermodynamic system
Types or Forms of Energy
A. Stored energy
Energies stored within the body which goes or dependent upon the flow of the mass.
1. Potential energy (PE) – energy stored due to its elevation above any arbitrary datum line.
Note: 1 Btu = 778 ft - lbf = 0.252 kcal
2. Kinetic Energy (KE) – stored energy of a body by virtue of its motion

3. 3. Internal Energy (U) – stored energy die to its motion of molecules and forces of attraction between
them.
4. Flow work (Wf) – is the energy required to move the fluid across the boundary of the system
Enthalpy (H) – combination energy or useful energy.
B. Transition energy
Energies in transit (on the move) which are not dependent upon the flow of mass.
5. Heat (Q) – is the energy crossing a system boundary because of a temperature differences
between the system and surroundings.
6. Mechanical work (W) – when force acts in the direction of motion
Note: 1 hp = 745.7 Watts
(+) W = work is done by the system (direction is going out of the system)
(-) W = work is done on the system (direction is going into the system)

4. (+) Q = heat is added on the system (direction is going into the system)
(-) Q = heat is rejected by the system (direction is going out of the system)
PROPERTIES OF FLUIDS
1. Mass Density or simply “Density”, ρ
- Mass per unit volume
- Usually used to solve the mass
Mass Density of Common Fluid at Sea Level when it is at standard Temperature and Pressure
Density of water: 1000 kg/m3
62.4 lbm/ft3
Mass density of water at any temperature
Note: 1ft3 = 7.281 Gal 1 m3 = 1000 L
1 gal = 8 pt
1 drum = 55 gal (petroleum, unrefined)
1 barrel = 42 gal (refined petroleum products and other liquids)
2. Specific volume, ν
- Volume occupied by a unit mass
3. Specific Weight or weight density or unit weight, γ
- Weight per unit volume
Weight density of water: 9810 N/m3 SI Units
62.4 lbf/ft3 Eng’g Units
4. Specific Gravity (SG) or Relative density (RD)
- The ratio of the mass density of a substance to a mass density of an equal volume of water
at 4°C (temperature of water at its maximum density)
For Liquid Substance:

5. For Gaseous Substance:
Where: MW = molecular weight of gas or air
Ideal Gas Law
- Equation of state for an ideal gas. This equation closely predicts the behavior of real gasses
when gasses are not approaching the point where they condense into a liquid.
In terms of mass
In terms of moles (mol)
R = gas constant, each ideal gas has its own gas constant.
Rair = 0.287 kJ/ kg-K SI Units
Rair = 1716 _ft - lbf_ Eng’g Units
lbm °R
Note:
A gas can be considered ideal if the pressure is very low and the temp is much higher than its
critical temperature
Gas Constants:
Where: MW = molecular weight
Element is defined by:
n Cx
Compound Element is defined by:
n Cx Hy

6. Common Elements Used
Elements Atomic Weight (AW) Number of Atoms Molecular Weight (MW)
C (Carbon) 12 1 12
H2 (Hydrogen) 1 2 2
O2 (Oxygen) 16 2 32
N2 (Nitrogen) 14 2 28
S (Sulfur) 32 1 32
Common Compound Elements Used
Elements Atomic Weight (AW) Number of Atoms Molecular Weight (MW)
CO2 (Carbon dioxide)
CO (Carbon monoxide)
H2O (Water Vapor)
SO2 (sulfur Dioxide)
SO (Sulfur Monoxide)
Universal Gas Constant
According to Avogadro’s Law
n V t P___________
1 pmole 359 ft3 32°F 14.7 psia
1 kgmole 22.4 m3 0 °C 101.325 kPa_____
R = universal gas constant = 8.314 kJ/ kgmole-K = 1545 1716 _ft lb__
pmole °R
5. Temperature
- Used to indicate the amount of energy within the molecules of the substance
- Measures the hotness or coldness of the substance
Arbitrary scale: t
Fahrenheit (°F)
Centigrade or Celcius (°C)
Absolute scale:
Rankine (°R) = °F + 460
Kelvin (K) = °C + 273
6. Pressure
- Amount of force exerted by the fluid per unit area of surface.

7. Where: F = normal force exerted by the fluid, lbf , N (kN)
A = area normal to the force, in2 , m2
Units pressure, all in absolute:
1 bar = 105 Pa = 100 kPa = 0.1 Mpa = 0.9869 atm
1 mbar = 100 Pa
1 torr = 1 mm Hg = 133.322 N/m2
Bourdon Gage – Commonly used to measure gage pressure
Manometer – used to measure gage or vacuum pressure
Compound gage – can measure either gage or vacuum pressures
Graphical representation of absolute pressure:
1. Absolute pressure when it is greater than Atmospheric or Barometric pressure:
Absolute pressure = Atmospheric pressure + Gage pressure
2. Absolute pressure when it is less than Atmospheric or Barometric pressure:
Absolute pressure = Atmospheric pressure - Vacuum pressure
Standard atmospheric or Barometer (at sea level)
Eng’g SI units
14.7 psia 101.325 kPaa
29.92 in Hg abs 760 mm Hg abs
1 atm
Note:
Absolute pressure must be used in engineering problems, because most of thermal
properties are functions of actual pressure of the fluid
7. Bulk Modulus, E
- Measures the incompressibility of a fluid. The higher the value of the bulk modulus, the less
compressible and thus stiffer the fluid.
Coefficient of Compressibility, β
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PROBLEMS:
1. The volume of a tetrachloride having a mass of 1200 kg is 0.952 m3. Compute the following:
a. Mass density
b. Specific weight
c. Specific Gravity
2. Calculate the density, specific weight, and specific volume of carbon dioxide at 700 kPa and 90C.
3. A cubic metre of air at 101 kPa and 15C weighs 12.0 N. What is its specific volume?
4. Calculate the temperature of methane (CH4) at 202.6 kPa if its density is 1.05 kg / m3 .

8. 5. The specific volume of a certain perfect gas at 200 kPa and 40C is 0.65 m3/kg. Calculate its gas
constant and molecular weight.
6. Calculate the density, specific weight, and specific volume of chlorine gas (Cl 2) at 25C and
pressure of 600 kN/m2 , abs. Molecular weight of chlorine (Cl 2) = 71.
7. For the fluid power automotive lift system shown below, the hydraulic piston has a diameter of 10
in. How much oil pressure (psi) is required to lift a 3000 lb automobile?
Control Valve Automobile
Air from
compressor Piston
Air
Oil
8. If 5.6 m3 of oil weighs 46,800 N, calculate the following (a) Unit weight N/m 3 (b) Density (c)
Specific gravity
9. A gallon of water weighs 4.08 lb. Compute the following (a) Mass in slugs (b) Mass in kg (c)
Volume in ft3
10. A 10 m. diameter cylindrical tank has a height of 5 m. and is full of water at 20°C (unit weight of
water = 9.789 kN/m3). If the water us heated to a temperature of 50°C (unit weight of water =
9.689 kN/m3) (a) compute the weight of water (b) What is the final volume of when heated to a
temperature of 50°C. (c) Determine the volume of water that will spill over the edge of the tank.
11. A gas at 40°C under a pressure of 20,000 mbar, abs, has a unit weight of 340 N/m 3. What is the
value of R for the gas? What gas might this be?
12. A volume of one cu. meter of water is subjected to a pressure increase of 14 Mpa. (a) compute the
change in its volume if it has a bulk modulus of elasticity of 2200 Mpa (b) Compute the percentage
of volume decreased (c) Compute the coefficient of compressibility
13. A rigid container is partly filled with a liquid at 1520 kPa. The volume of the liquid is 1.232 liters. At
a pressure of 3039 kPa, the volume of the liquid is 1.231 liters (a) compute the average bulk
modulus of elasticity of the liquid (b) Compute the coefficient of compressibility (c) If the liquid has
a density of 1593 kg/m3, find velocity of sound.
14. Calculate the gas constant of CO2 in SI and Eng’g Units.
15. If the specific weight of a liquid is 10 kN/m3, what is its density, specific volume, and specific
gravity.
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