Environmental Physics Term 1
Lecture 1: 17/7/23
N/A
Lecture 2-3: 18/7/23-19/7/23
Units
Unit: A standard measure used to express a physical quantity. Units are well-defined and internationally accepted. Units are invariant with time and place. Units must be easily accessible.
International System of Units (SI)
Meter = distance
Kilogram = mass
Second = time
Ampere = electric current
Kelvin = temperature
Mole = amount of substance
Candela = intensity of light
Derived Units
Expression of denominators
The solidus, a horizontal line, or negative powers may be used to express a derived unit formed from two others by division. Only one solidus should be used in a combination of units. Parentheses are used to avoid ambiguity.
Example: A car accelerates from 0 km/hr to 100km/hr in 60 seconds. The rate of acceleration is 100 km/hr over 60 seconds.
Scientific Notation
Expressing very large or very small numbers in a compact from that is easy to use in computations
Rules:
Base: 10
Exponent: Non-zero (Negative or positive)
Coefficient:
Positive or negative
Whole or decimal
Magnitude between 1 and 10
Approach
Large numbers:
Locate the decimal place point. Move the decimal place leftward until one non-zero digit remains on the left. Count how many digits passed on the way. That is the positive exponent. Find the coefficient, carrying significant figures of the number.
Small numbers:
Locate the decimal place point. Move the decimal place rightward until one digit remains on the left. Count how many digits passed on the way. That is the negative exponent. Find the coefficient, carrying significant figures of the number.
Significant figures
Significant figures of a number are those digits that carry meaning contributing to its precision. For example a weight of 253g implies that the weight is between 252 and 254 grams, therefore it carries 3 significant figures.
Rules:
All non zeros are significant
Zero’s between two non zeros are significant
Leading zeros are not significant
Trailing zeros in a number containing a decimal point are significant
Trailing zeros in a number without a decimal point are not significant
Exact numbers have infinite number of significant figures
Lecture 4: 24/7/23
Measurement error
Most experiments require scientists to make measurements. Measurements are rarely exactly the same
Systematic errors are reproducible and cause a bias in the same direction each measurement
Poorly trained operator
Miscalibrated instrument
Random errors are caused by the natural uncertainty that occurs with any measurement
Noise
Careless measurements
Low-resolution instruments
Accuracy is the closeness of a measured value to the accepted value. Affected by systematic errors. Percent error is used to estimate the accuracy of a measurement
Precision is the agreement between repeated measurements of the same sample. Precision is independent of accuracy. Precision is mostly affected by random errors. Precision is usually expressed as a standard deviation.
Accuracy vs Precision
Accuracy and precision are mutually independent
A set of measurements can be
Accurate
Precise
Both
Neither
Matter
Solid: maintain a fixed shape and a fixed size even if a large force is applied.
Liquid: cannot maintain a fixed shape when a large force is applied. Liquids take on the shape of the container, but like a solid, they are not readily compressible.
Gas: gasses have neither a fixed shape nor a fixed volume. They will expand to fill its container.
Properties
Density: The mass of a matter compared to its volume. Simply expressed as Mass/Volume.
SI Units: kg/m^3 , Mg/m^3 , g/cm^3
Surface Area
Measured in m^2
Porous Media
Materials containing pores such as soil, rock, and timber. Empty spaces between solid particles are called pores. In natural porous systems, all three phases coexist. Solids are immobile, while liquid and gasses are mobile and transient, and mutually share the pore space. Transfer processes of energy and mass in nature through porous systems require knowledge about the characteristics of the pore system.
Density of most mineral soils are close to the density of the primary or secondary minerals they derived from.
The dry bulk density is primarily affected by the texture and structure of porous media.
Porosity (Φ)
Pore volume (PV)
Represents the total volume of the pores (Vv, m3) in a porous medium.
1PV = Vv = Φ x Vt m^3
If a dissolved contaminant is present in soil pores, the soil pores need to be flushed to remove contaminants. How much water to be supplied is denoted by no. of pore volumes to be flushed.
Lecture 5-6: 25/7/23-31/7/23
Velocity, Acceleration, Force
Distance, displacement: a measure from the initial to the final position of a point (m)
Velocity: speed and direction (ms^-1)
Acceleration: rate of change in velocity (ms^-2)
Force: Mass x acceleration (kg ms^-2 or N)
Weight: a measurement of gravitational force acting on an object (N)
Acceleration of gravity = g = 9.91ms^-2
Weight = mass x acceleration of gravity
W = m g
Mass vs Weight
Mass is a measure of the amount of inertia or matter an object contains.
Inertia is the tendency of a body to resist motion.
Weight is the force with which a body is attracted towards the earth/celestial body by gravity.
The unit for mass is kg, the unit for weight is N, g = 9.81ms^-1
Velocity, acceleration, time
Velocity is a vector quantity that describes how fast an object is moving and the direction it is headed.
Acceleration is the rate at which velocity is changing (increasing, decreasing, or changing direction).
A positive acceleration means an increase in velocity; a negative acceleration means a decrease.
Acceleration of gravity
All bodies in free fall near the earth's surface have the same downward acceleration of gravity = 9.8ms^-2.
Newton's Laws of Motion
1: A body at rest will remain at rest and a body in motion will remain in motion at a constant velocity in a straight line if no net force acts on it.
2. The net force acting on a body is proportional to the mass of the body and to its acceleration; the direction of the force is the same as that of the body’s acceleration.
F=ma
N=kg ms^-2
3. When a body exerts a force on another body, the second exerts an equal force in the opposite direction of the first, Thus for every action force, there is an equal and opposite reaction force; no force can occur all by itself.
Gravity
Newton's Law of Gravitation: every massive particle in the universe attracts every other massive particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
G = Gravitational Constant = 6.673 x 10^-11 Nm^2 kg^-2
The gravitation of Earth
Earth's actual gravity field differs from the gravity field of a uniform, featureless Earth surface. Gravity anomalies are often due to unusual concentrations of mass in a region.
Presence of mountain ranges cause high gravitatiovectoscnal force
The presence of ocean trenches, and depression of landmass causes lower gravity force
Microgravity
In microgravity, we are nearly weightless. Occurs in the space international space stations, or controlled microgravity settings. Long exposure to microgravity has physiological consequences.
Microgravity Physics g=0
Changes in moisture configuration in microgravity
Capillary-dominated movement
Uniform moisture distribution
Increased resistance to gas flow
High liquid-induced tortuosity for gas for has diffusion
Plants in Microgravity
Plants play a key role in advanced life support systems (ALS): a key element in NASA’s future space missions. Plants provide both functional and psychological support in a remote human base. Growing plants in space is challenging due to microgravity effects.
Vectors
A quantity that has both a magnitude and a direction. If it is a vector, we require two independent properties to characterize it: Magnitude and direction.
Solving a problem that has a combination of vectors acting on an object requires the use of vector addition. Vector addition uses geometric methods such as Pythagoras’ rule, sine, cosine, and tangent.
The vector addition of two vectors acting on an object begins by drawing a parallelogram with the two vectors drawn to scale as the adjacent sides directed away from the object.
Dimensional Analysis
Helps to keep track of units.
Helps to transfer units from one system to another.
Enable to find the consistency of an equation.
Enable to derive the relation between physical quantities in physical phenomena.
Lecture 7-8: 1/8/23-2/8/23
Mass, volume and density
Viscosity
Described as ‘resistance to flow’
Denote by η
Measured in ‘Pa.s’
Thick fluids have higher viscosity
Changes with temperature
r4
Effect of temperature on viscosity
Archimedes’ principle
“Any object, wholly or partly immersed in a fluid, is buoyed up by force equal to the weight of the fluid displaced by the object”
Example with equations
Stokes’ Law
“The force that retards a sphere moving through a viscous fluid is directly proportional to the velocity of the sphere (v), the radius of the sphere (r), and the viscosity (η) of the fluid”.
Assumptions
Rigid, spherical, and smoot particles
Steady state
No acceleration (exclude large particles)
No Brownian motion (exclude small particles)
Constant temperature
No collision (dilute suspension)
Same particle density
Fluid flow around the particles is laminar
Applications
Sedimentation analysis
Fall of raindrops
Bubbles in beer
Jumping with a parachute
Change of Density of water
Soil formation
How is soil formed?
Note the five soil forming factors
Parent material
Climate
Biota
Topography
Time
Soil Particle
AWESOME Soil Architecture
Air - 25%
Water or soil solution - 25%
Solids - 45%
Organic Matter - 5%
Minerals
Ever changing nature
Particle Size
Soils contain a complex ‘spectrum’ of particle size and distribution
The concept of texture to characterize the particle size
Split into 3 ranges
Sand: 2mm to 20μm
Slit: 20μm to 2μm
Clay: <2μm
Soil texture
Sand
Feels gritty when touched
Made of mineral quartz
No cohesion among particles (except wet)
Freely drained
But have poor water retention for plants
Fine sand s very susceptible to erosion, by water or wind
Silt
Feels ‘FLOURY, SMOOTH, and SOAPY’
Medium size pores
Weak cohesion between particles
High water holding capacity and high water availability
Clay
Feels STICKY when wet
Small size pores
Large surface area
High surface charge (predominantly negative)
Charge leads to strong forces
Cohesion - stick to themselves
Adhesion - stick to other surfaces
Texture Triangle
Represents mixes of sand, silt, and clay in different proportions. Altogether 12 textural classes.
Loam: “balance” of sand, silt, and clay
How to find the textural class? Follow the arrows
Clay 15%
Sand 20%
Silt 60%
Lecture 9-10: 8/8/23-9/8/23
Work and energy
Work
“The transfer of energy by a force acting on an object as it is displaced”
Work = force x displacement
J (Jule) = N x m
Both force and displacement are vector quantities
One joule is the work done by a force of one newton moving a meter along the direction of the force. 1J = 1N x 1m
Accordingly, a force of 20N pushing an object 5m in the direction of the force does 100J of work
Other units: 1 Cal = 4.186J
Energy
“Ability to work”
SI unit - Joule (J)
The yield of little boy, the atomic bomb that was dropped on Hiroshima at the end of WW2, was 15,000tons of TNT (trinitrotoluene). One ton of TNT releases 63,100,000 joules of energy. Thus little boy released 9.5 x 10^11 joules
Kinetic and potential energy
Gravitational potential energy
“Energy an object possesses because of its position in a gravitational field. Measured always with respect to a reference elevation (h(o))
Ep = mg x h(o)
Kinetic energy
The energy of motion, observable as the movement of an object
Ek = 1.2mv^2
An object at rest (v=0) has no kinetic energy
Total mechanical energy
Total energy = Potential energy + Kinetic Energy
Et = (mg x h(o)) + (½ x m x v^2)
The total mechanical energy of an object remains constant as the object moves, provided that the net work done by the external forces is 0.
Conservation of energy
“Energy in an isolated system cannot be created or destroyed. All one can do is change energy from one form to another”
Ep + Ek = constant
Net work done (W) is equal to the change in Energy of an object
W = ΔEp + ΔEk
W = 0 -ΔEp = ΔEk
Pressure
“The force applied perpendicular to the surface of an object per unit area over which that force is distributed
Expressed by Pa (Pascals)
1Pa = 1 Nm^-2 = 1 kgs^-2 m^02
1kPa = 1000 Pa, 1 Mpa = 1000kPa
1 bar = 100kPa
Pressure of a column of water 2m high
Force = mg
Mass water = 2(m^3) x 1000(kgm^-2) = 2000(kg)
F = m x g = 2000(kg) x 9.8(m.s^-2) = 19600(N)
Pressure = F/A = 19600(N) / 1 (m^2) = 19.6kPa
Water pressure is exerted from all directions
Hydrostatic pressure (HP)
Hydro - water
Static - at rest
“The pressure exerted by a fluid at equilibrium at any point of time due to the force of gravity
HP = ρgh
ρ = density of water (kg m^-3)
g = gravity
H - height of water column (m)
Fluid flow
When water flows water pressure is no longer hydrostatic. Energy of moving water explained by Bernoulli’s Equation
Groundwater moves in response to differences in fluid pressure and elevation. Groundwater velocity is typically very small and can be ignored.
Artesian well: groundwater flows from a well without the aid of a pump
Blood pressure
Pressure of circulating blood against the walls of blood vessels. Most of this pressure results from the heart pumping blood through the circulatory system. Two types: systolic (when heart beats) and diastolic (when heat rests). Blood pressure counterbalances the atmospheric pressure on the body.
Atmospheric pressure
The weight of 5.7 x 10^16 tons of air is spread over the entire surface of the earth, creating relatively small pressure. Atmospheric pressure involves the collisions of millions of air molecules with the surface. Atmospheric pressure decreases by 50% for every 5.5km ascent in elevation.
Spacewalk spacesuit
NASA calls a spacewalk an Extra-Vehicular Activity or EVA. EVA suit is a multi-layered costume specially designed for different purposes. Three layers closest to the astronaut’s skin, the cooling garment. One top of this garment is the bladder layer which is filled with gas to create proper pressure for the body.
Ideal Gas Law
The pressure of any gas, including air, can be predicted from the kinetic theory of gasses. The pressure which a gas exerts on the surface of a liquid or solid is a measure of the rate at which momentum is transferred to the surface from the molecules which strike it and rebound.
Gas molecules (O2, N2,etc.) and atoms (He, Ar, etc.) are very small relative to the distances apart.
Force of attraction between molecules negligible
Kinetic energy causes gasses to bump into each other. These collisions (momentum transfer) are elastic and random
Relation between the pressure P, volume V, and temperature T of a gas in the limit of low pressure and high temperatures, such that the molecules of the gas move almost independently of each other
P is the absolute pressure of the gas (Pa)
V is the volume in which the gas is confined (m^3)
n is the number of moles of gas present in volume
R is the universal gas constant, 8.3144J Mol^-1 (K)
T is the temperature in K
Partial pressure
Dalton's law of partial pressure
“The total pressure of a mixture of gasses is the sum of the partial pressure”. Partial pressure is the pressure which each gas would have if it alone occupied a volume
Lecture 11-12: 14/8/23-15/8/23
Transport principles
“ the movement of mass or energy through space due to a gradient”
Transport essentially occurs along a gradient
Examples:
-water and gas movement in porous materials
Heat flow in a metal
Current flow in a circuit
Component of transport
Q = qAt
Q = quantity of flow
Q = flux
A = area
T = time
Flux “amount of material (expressed in units of energy, mass, or volume) moved per unit cross-sectional area per unit time.
Gradient
“Changes of driving force per unit distance
Temperature gradient - heat flow
Voltage gradient - current flow
Pressure gradient - water and gas flow by advection
Partial pressure/concentration gradient - flow by diffusion
Transport coordinates
Flow is the movement of mass or energy through space due to a gradient. Flow is measured between two points established in a grid system. The gradient will be positive if the flow direction is downwards or to the left. The gradient will have negative values if the flow is upwards or to the right.
Gradients
Thermal gradient ΔT/ ΔZ
Temperature per change in distance, (℃/m). Direct measurement of kinetic thermal energy of the molecules.
Concentration gradient ΔC/ Δx
Change in concentration (mol m^-3 , g m^-3, mg/L) per change in distance, this is usually associated with diffusuion.
Hydraulic gradient ΔH/ Δz
Change in driving force or pressure per change in distance (Pa/m, m/m).
Transport parameters
Conductivity
Thermal conductivity (λ, W m^-1 ℃^-1
The ability of the material to conduct heat. Hot molecules vibrate at higher energies and their vibration iis transferred to adjacent molecules.
Fourier’s Law
Hydraulic conductivity Ks, ms^-1
Ability of water to flow through a porous medium such as soil
Darcy’s Law
Function of both the fluid and the porous material
Ks and Soil Texture
Poiseuilles’ Law
Laminar flow
Diffusion
Diffusion coefficient (D. m^2 s^-1)
Movement of chemicals from high concentration to low concentration. A key mechanism of mass transfer in environmental systems
Ficks law
Electricity
Ohm’s law
Current through a conductor between two points is directly proportional to the voltage across the two points.
Lecture 13: 16/8/23
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