Hydraulics Engineering deals with the mechanical properties of liquids or fluid at rest. Fluids exert pressure normal to any contacting surface. Fluids at rest indicate that there exists a force, known as pressure that acts upon its surroundings. This pressure is not constant throughout the body of fluid.
Pressure, ‘p’, increases with an increase in depth. Where the upward force on a body acts on the base and can be found by equation: , Where h is the height of the liquid column; ρ is liquid the constant and g = specific gravity.
Archimedes Law of Buoyancy: Discovery of the principle of buoyancy is attributed to Archimedes.
When anybody of arbitrary shape is immersed, partly or fully, in a fluid, it will experience the action of a net force in the opposite direction of the local pressure gradient. If this pressure gradient arises from gravity, the net force is in the vertical direction opposite that of the gravitational force. This vertical force is termed buoyancy or buoyant force and is equal in magnitude, but opposite in direction, to the weight of the displaced fluid. Example: In the case of a ship, its weight is balanced by shear force from the displaced water allowing it to float. If more cargo is loaded onto the ship, it would sink more into the water displacing more water and thus receive a higher buoyant force to balance the increased weight.
Properties of perfect gases (Ideal gas): A perfect gas (or an ideal gas) is a state of a substance, whose evaporation from its liquid state is complete.
Laws of perfect gas: The physical properties of a gas are controlled by the following three variables: (i) Pressure exerted by the gas. (ii) Volume occupied by the gas. (iii) Temperature of the gas.
Avogadro's law: Avogadro's law is stated mathematically as:
Where, V is the volume of the gas. n is the amount of substance of the gas. k is proportionality constant.
Molar volume: Taking STP to be 101.325 kPa and 273.15 K, we can find the volume of one mole of a gas:
For 100.000 kPa and 273.15 K, the molar volume of an ideal gas is 22.414 dm3 mol-1.
Boyle's law: Boyle’s law is relation to Kinetic Theory and Ideal Gases and states that at constant temperature for a fixed mass, the absolute pressure and the volume of a gas are inversely proportional. The law can also be stated in a slightly different manner, that the product of absolute pressure and volume is always constant. The mathematical equation for Boyle's law is:
1
P or, P V = constant
OR;
P1 V1 = P2 V2 = P3 V3 = k
V
Where, p denotes the pressure of the system; V denotes the volume of the gas; k is a constant value representative of the pressure and volume of the system and 1, 2, 3 refer to the different sets of conditions. Examples: The Change of Pressure in a Syringe, the popping of a Balloon, increase in size of bubbles as they rise to the surface, death of deep sea creatures due to change in pressure and popping of ears at high altitude are the examples.
Charles's law: Charles's law states that at constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same factor as its temperature on the absolute temperature scale (i.e. the gas expands as the temperature increases). This can be written as,
Where V is the volume of the gas; and T is the absolute temperature. The law can also be usefully expressed as follows:
The equation shows that as absolute temperature increases, the volume of the gas increases in proportion at a constant pressure.
Relation to the ideal gas law: French physicist Emile Clapeyron combined Charles's law with Boyle's law to produce a single equation which would become known as the ideal gas law:
Where, t is the Celsius temperature; and p0, V0 and t0 are the pressure, volume and temperature of a sample of gas under some standard state. The figure of 267 came directly from Gay-Lussac's work.
The modern figure would be 273.15. For any given sample of gas, p0 V0 ⁄ 267+ t0 is a constant (Clapeyron denoted this constant R, and it is closely related to the modern gas constant); if the pressure is also constant, the equation simplifies to
The thermodynamic properties of an ideal gas law are:
Where, P is the pressure; V is the volume; n is the amount of substance of the gas (in moles); R is the gas constant (8.314 J·K−1mol-1) and T is the absolute temperature
Absolute Zero: Charles's law appears to imply that the volume of a gas will descend to zero at a certain temperature (−266.66 °C according to Gay-Lussac's figures) or -273°C.
However, the "absolute zero" on the Kelvin temperature scale was originally defined in terms of the second law of thermodynamics.
Relation to kinetic theory: Where, N is the number of molecules in the gas sample. If the pressure is constant, the volume is directly proportional to the average kinetic energy and hence to the temperature for any given gas sample. The kinetic theory of gases relates that the temperature being
proportional to the average kinetic energy of the gas molecules.
The kinetic theory equivalent of the ideal gas law relates pV to the average kinetic energy:
iii) General Gas Equation: In order to deal with all practical cases, the Boyles’ law and Charles’ law are combined together, which give us a general gas equation as below;
P1 V1 P2 V2 P3 V3 = = = ……. = Constant T1 T2 T3
Viscous Flow: A viscous fluid will deform continuously under a shear force, whereas an ideal fluid doesn't deform. Both pneumatics and hydraulics are applications of fluid power. Pneumatics fluid is an easily compressible, such as, gas or air, while hydraulic fluid is relatively incompressible liquid media such as water or oil. Most industrial applications of pneumatic fluid pressures are about 80 to 100 pounds per square inch (550 to 690 kPa). Hydraulics applications commonly use from 1,000 to 5,000 psi (6.9 to 34 MPa) with specialized applications up to 10,000 psi (69 MPa). Hydraulic systems use an incompressible fluid, such as oil or water, to transmit forces from one location to another within the fluid. Most aircraft use hydraulics in the braking systems and landing gear.
Pneumatic systems use compressible fluid, such as air, in their operation. Some aircraft utilize pneumatic systems for their brakes, landing gear and movement of flaps.
Pascal's law: Pascal's law states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container. There is an increase in pressure as the length of the column of liquid increases, due to the increased mass of the fluid above. Pascal's law allows forces to be multiplied.
Affinity laws: The affinity laws are used in hydraulics and HVAC to express the relationship between variables involved in pump or fan and turbine performance, such as, head, flow rate, shaft speed, and power. In rotary implements, the affinity laws apply both to centrifugal and axial flows.
The affinity laws are useful as they allow prediction of the head discharge characteristic of a pump or fan from a known characteristic measured at a different speed or impeller diameter.
Quantity of Discharge through a pipe = Q = Cross Section Area of Pipe x Velocity = A V, Where, V = C r S and, C = 2 g / ---(i)
= 0.01 (1+1 / 12 d) for old pipes. And, = 0.005 (1+1 / 12 d) for new pipes. ---(ii)
Where d is the inside diameter of pipe.
Pipe Friction:
h f= 4 L V2 / 2 g d; Where, = 0.0056; and d = H. M. D. =Inside diameter of pipe ----(iii)
For old pipes For new pipes
Velocity = V = 39 d S
Inside Diameter = d = 0.2545 x 5 Q2 /g
Velocity = V = 55 d S
Inside Diameter = d = 0.222 x 5 Q2 /g
Loss of head in pipe: Head loss is calculated with,
Where, hf is the head loss due to friction (SI units: m); L is the length of the pipe (m); D is the hydraulic diameter of the pipe (for a pipe of circular section, this equals the internal diameter of the pipe) (m); V is the average velocity of the fluid flow, equal to the volumetric flow rate per unit cross-sectional wetted area (m/s); g is the local acceleration due to gravity (m/s2); f is a dimensionless coefficient called the Darcy friction factor. It can be found from a Moody Diagram or more precisely by solving the Colebrook Equation.
Pressure loss: The head loss hf expresses the pressure loss Δp as the height of a column of fluid,
Where ρ is the density of the fluid, the Darcy–Weisbach equation can also be written in terms of pressure loss:
Where the pressure loss due to friction Δp (units: Pa or kg/ms2) is a function of: the ratio of the length to diameter of the pipe, L/D; the density of the fluid, ρ (kg/m3); the mean velocity of the flow, V (m/s), as defined above; a (dimensionless) coefficient of laminar, or turbulent flow, f.
Components of hydraulic head: A mass free falling from an elevation (in a vacuum) will reach a speed,
When
Where, g is the acceleration due to gravity.
When arriving at elevation z = 0 or when we rearrange it as a head.
Head Loss due to Sudden Head Loss due to Sudden
Enlargement Contraction
Head Loss = (V1 - V2) 2 / 2g Head Loss = 0.5 V22 / 2g
Head Loss due to Obstruction
Head Loss due to Change of direction
Head Loss = A / Cc (A-Q) - 1 x V22 / 2g
Head Loss = K V22 / 2g; For 900 bend K = 1.
Where, K depends upon bend type.
Bernoulli’s Theorem: For a non-viscous, incompressible fluid in steady flow, the sum of pressure, potential and kinetic energies per unit volume is constant at any point. A centrifugal pump converts the input power to kinetic energy in the liquid by accelerating the liquid by a revolving device - an impeller. The energy created by the pump is kinetic energy according the Bernoulli Equation. The energy transferred to the liquid corresponds to the velocity at the edge or vane tip of the impeller. The faster the impeller revolves or the bigger the impeller is the higher will the velocity of the liquid energy transferred to the liquid be. This is described by the Affinity Laws.
A special form of the Euler’s equation derived along a fluid flow streamline is often called the Bernoulli Equation:
Where, v = flow speed; p = pressure; ρ = density; g = gravity; h = height.
H = h + V2 / 2g + P / W
Total energy = E pot + E kin + E press
Specific energy = Static energy + Kinetic energy. E = d + V2 / 2g
Depth for minimum energy is called critical path.
V2= g x d; Frauds number = V/ g d
Kennedy’s Equation for Critical Velocity at top of channel = Vo = C x Dn ft/sec
Where, C = 0.84; n = 0.64; and D = depth of channel.
1.5 Chemistry
Chemistry is the science of study of interaction of chemical substances, such as, the composition, behaviour, reaction, structure, and properties of atoms, the subatomic particles, protons, electrons and neutrons, molecules or crystals and the changes it undergoes. These include inorganic chemistry;
organic chemistry; biochemistry; physical chemistry; and analytical chemistry.
Chemical Substance: A chemical substance is a mixture of compounds, elements. Example: air, alloys, biomass, etc.
Compound: A compound is a substance with a particular ratio of atoms of particular elements which determines its composition, and chemical properties. Example: water is a compound containing hydrogen and oxygen in the ratio of two to one, with one oxygen atom between the two hydrogen atoms. Compounds are formed by chemical reactions.
Inorganic Compound: Inorganic compounds are considered to be of a mineral with no biological origin.
Organic compound: An organic compound is chemical compounds whose molecules contain carbon.
Methane is one of the simplest organic compounds.
Molecule: A molecule is the smallest indivisible portion of a pure chemical substance that has its unique set of chemical properties and its potential to undergo a certain set of chemical reactions with other substances. Molecules are typically a set of atoms bound together by covalent bonds and electrically neutral. All valence electrons are paired with other electrons either in bonds or in lone pairs. One of the main characteristic of a molecule is its geometry often called its structure.
Mole: Mole is a SI Unit to measure amount of substance (chemical amount). A mole is the amount of a substance that contains as many elementary entities as there are atoms in 0.012 kilogram (or 12 grams) of carbon-12, where the carbon-12 atoms are unbound, at rest and in their ground state.
Element: The element is a particle which is composed of a single atom and is associated by a particular number of protons in the nuclei of its atoms. It is known as the atomic number of the element. Example: All atoms have 6 protons in their nuclei in the chemical element carbon, and all atoms have 92 protons in their nuclei in the element uranium. Ninety–four different chemical elements exist naturally and another 18 have been recognized as existing artificially only. All the nuclei of all atoms of one element will have the same number of protons, but they may not necessarily have the same number of neutrons and such atoms are termed isotopes. In fact several isotopes of an element may exist. Some Chemical Elements are given in the periodic table, which is grouped by atomic number.
Atom: The atom is the smallest entity of the chemical substance that retains the chemical properties of the element, such as electro negativity, ionization potential, preferred oxidation state, coordination number, and types of bonds e.g. metallic, ionic or covalent. An atom is the basic unit of chemistry, which consists of a positively charged core called the atomic nucleus, which contains protons and neutrons, and maintains a number of electrons to balance the positive charge in the nucleus. The atoms belonging to one element will have the same number of protons in all the particles of that Element, but they may not necessarily have the same number of neutrons and thus are termed isotopes.
Atomic Number: The element is composed of a single atom with a particular number of protons in its nuclei, which is called the Atomic Number of the Element. Example: carbon has 6 protons in nuclei of their atoms of the element and thus the Atomic Number is 6. In an atom of neutral charge, the number of electrons typically equals the atomic number.
Atomic mass unit: The atomic mass unit (amu) or unified atomic mass unit (u) or Dalton (Da), is a small unit of mass used to express the atomic masses and molecular masses. It is defined to be 1/12 of the mass of one atom of Carbon-12. Accordingly,
1 u = 1/NA gram = 1/(1000 NA) kg (where NA is Avogadro's number) = 1.66053886 x 10-27 kg Pico metre: Pico metre (pm) is a measure of length that is commonly used in measuring the atomic-scale distances or the atom diameters, which are in the range from approximately 30 to 600 pm. 1 pm
= 1 × 10−12 metre. 1 pm = 1000 femtometre. 100 pm = 1 angstrom. 1000 pm = 1 nanometre. 1 nm = 1000.
Nucleus: The nucleus of most atoms consists of protons and neutrons. As exception, the Isotope of Hydrogen consists of a single proton without any neutron. Outside the nucleus, neutrons are unstable and have a mean lifetime of 886 seconds (15 minutes), decaying by emitting an electron and antineutrino to become a proton. Neutrons in this unstable form are known as free neutrons. Particles inside the nucleus are in resonances between neutrons and protons, which transform into one another by the emission and absorption of Pions.
Proton: The Proton is a subatomic particle with an electric charge of one positive fundamental unit (1.602 × 10−19 coulomb) and a mass of 938.3 MeV/c2 (1.6726 × 10−27 kg, or about 1836 times the mass of an electron). The proton is observed to be stable, with a lower limit on its half-life of about 1035 years, although some theories predict that the proton may decay. The nuclei of the atoms are composed of protons and neutrons held together by the strong nuclear force. The number of protons in the nucleus determines the chemical properties of the atom or the chemical element. Protons are classified as Baryons and are composed of two “up quarks” and one “down quark”, which are also held together by the strong nuclear force, mediated by Gluons. The proton's antimatter equivalent is the antiproton, which has the same magnitude charge as the proton but the opposite sign.
Because the electromagnetic force magnitude is stronger than the gravitational force, the charge on the Proton is equal and opposite of the charge on the Electron. Otherwise, the net repulsion of having an excess of positive or negative charge would cause an expansion effect on the universe, and indeed any gravitationally aggregated matter like planets or stars.
Neutron: The Neutron is a subatomic particle with no net electric charge and a mass of 939.6 MeV/c² (kg, slightly more than a proton). Its spin is ½. A neutron is classified as a baryon and consists of two “down quarks” and one “up quark”. The neutron's antimatter equivalent is the antineutron.
Proton Neutron
Mass 938 MeV/c² Mass: 940 MeV/c²
Electric Charge 1.6 × 10−19 C Electric charge: 0 C
Spin 1/2 Spin: ½
Quark
Composition 1 Down, 2 Up Quark
composition: 2 Down, 1 Up
Ions and Salts An ion is a charged atom or molecule that has lost or gained one or more electrons.
Positively charged cations (e.g. sodium cation Na+) and negatively charged anions (e.g. chloride anion Cl−) can form a crystalline lattice of neutral salts (e.g. sodium chloride NaCl). The polyatomic ions that do not split up during acid-base reactions are hydroxide (OH−) and phosphate (PO43−).
Ions in the gaseous phase are often known as plasma.
Acid and Base: An acid is a substance that produces hydronium ions when it is dissolved in water, and a base is one that produces hydroxide ions when dissolved in water. Acids donate a positive hydrogen ion to another substance in a chemical reaction. A base receives the hydrogen ion. An acid is a substance which is capable of accepting a pair of electrons from another substance during the process of bond formation, while a base can provide a pair of electrons to form a new bond.
Oxidants & Reductant: It is a concept related to the ability of atoms of various substances to lose or gain electrons. Substances that have the ability to oxidize other substances are said to be oxidative and are known as oxidizing agents, oxidants or oxidizers. An oxidant removes electrons from another substance. Similarly, substances that have the ability to reduce other substances are said to be reductive and are known as reducing agents, reductants, or reducers. A reductant transfers electrons to another substance, and is thus oxidized itself.
Chemical Equilibrium: Chemical Equilibrium is a stage of chemical reaction when the chemical composition of the substance remains unchanged over time.
Chemical laws: Chemical reactions are governed by certain laws, which have become fundamental concepts in chemistry. Some of them are: Avogadro’s law; Beer-Lambert law; Boyle’s law (relating pressure and volume); Charles’s law (relating volume and temperature); Fick’s law of diffusion; Gay-Lussac’s law (relating pressure and temperature); Le Chatelaine’s Principle; Henry’s law; Hess’s Law; Law of conservation of energy; Law of conservation of mass; Law of definite composition;
Law of multiple proportions and Fault’s Law.
Conservation of energy: The law of conservation of energy states that the total amount of energy in a system remains constant over time. A consequence of this law is that energy can neither be created nor destroyed. It can only be transformed from one state to another.
Einstein’s theory of relativity: Albert Einstein’s theory of relativity states that mass is a form of energy and can transform one into another with the conservation of the total energy of a system to other system of energy.
The first law of thermodynamics: Entropy is a function of a quantity of heat which shows the possibility of conversion of that heat into work.
Conservation of mass: The law of conservation of mass states that the mass of a closed system will remain constant over time because of a result of processes acting inside the system. The mass cannot be created or destroyed, although it may be rearranged in space and changed into different types of particles for any chemical process in a closed system. The mass of the reactants must be equal to the mass of the products.
Biomass: Biomass is a renewable energy source and is a biological material from living or recently living organisms, such as, wood, waste, hydrogen gas and alcohol fuels. Biomass is commonly plant
Biomass: Biomass is a renewable energy source and is a biological material from living or recently living organisms, such as, wood, waste, hydrogen gas and alcohol fuels. Biomass is commonly plant