Useful Concepts
A net force acting on a body causes it to accelerate. Force is a vector, meaning that it has magnitude and direction. The units of force are newtons or pounds. Force is more explicitaly defined as the derivative of momemtum (mass times velocity) with respect to time. In Newtonian physics, F = ma, where F is force in newtons, m is mass in kilograms and a is acceleration in meters per second squared.
With regard to portable water filters, one might be interested in the force required to depress a piston or lever or squeeze a water bottle.
In Newtonian physics, momentum is the product of mass and velocity. It is a vector, with units of newton-seconds or kg-meters / second.
Energy exists in many forms, including kinetic energy, heat, potential energy, chemical energy, electrical energy, electromagnetic radiation, and mass. Each type of energy is associated with specific equations that can be used to quantify energy in a particular way. One very important use for the concept of energy is the estimation of work. The unit of energy and work is the joule (J), named in honor of James Prescott Joule. One joule is one newton-meter. An erg is 0.0000001 joule.
The stress at a point in a material is the applied force per unit area. The stress unit is the Pascal (Pa), one newton / square meter. The stress in a bolt with cross-sectional area = 0.01 square meter subjected to a force of 10 newtons along it length is 10/0.01 = 1,000 Pa.
Pressure is a measure of force per unit area, often expressed as a Pascal (Pa) or in the units of pounds / square-inch (psi). Pressure is often used to describe force exerted by liquids or gasses. Pressure can be measured in inches or mm of mercury or water, i.e., the the pressure exerted by the weight of a height of fluid under the influence of gravity. Standard density and gravity are assumed when reporting pressure in this way. The standard atmosphere (atm), the pressure exerted by the atmosphere at sea level, is assumed to equal 101,325 Pa or 14.696 psi. One millibar (mb) = 100 Pa.. Thus, one bar is approximately an atmosphere.
Pressure is sometimes measured not as an absolute pressure, but as the pressure above atmospheric pressure, also called gauge pressure. An example of this is the air pressure in a car tire, which might be said to be "thirty psi", but is actually thirty psi above atmospheric pressure. In technical work, this would be written as "30 psig", note the "g" added to indicate gauge pressure.
In Newtonian mechanics, work is a measure of energy expended in applying force over a distance. Common units of work are Newton meters (i.e., joules) or foot pounds. If the force is constant, W equals the dot product of the force and distance, where W is work in joules, F is the force in newtons, and d is the distance in meters. Force and distance are both vectors. The dot product is the product of the force magnitude, the distance magnitude and the cosine of the angle between the two vectors. If the force and distance vectors are in the same direction, the work is simply F times d. When the Force is not constant, but is in the same direction as the distance vector, Work is the integral of F over the distance. This can be estimated as the area under the force versus distance curve, it travel is along a straight line.
Work can also be measured in watt hrs or kilowatt hrs (a kilowatt equals 1000 watts), see Power for an explanation of watts.
In physics, power is the amount of work done per unit of time. This is equivalent to the rate of change of the energy in a system, or the time rate of doing work, or the derivative of energy with respect to time. Common units of power are ergs per second or joules per second or foot-pounds per minute. The SI unit of power is the watt, which is equal to one joule per second.
Non-SI units of power include horsepower (hp). One unit of horsepower is equivalent to 33,000 foot-pounds per minute, or the power required to lift 550 pounds one foot in one second, and is equivalent to about 746 watts. One hp is approximately the power that a single horse can generate. The power consumption of a human is on average roughly 100 watts, ranging from 85 W during sleep to 800 W while playing a strenuous sport.
For direct current (DC) the instantaneous power consumed by a product is the voltage across the terminals, V, times the current passing through the device, I, i.e.,
P = VI
P is in watts, V is in volts, and I is in amperes.
In electricity, current is any flow of charge, usually through a metal wire or some other electrical conductor. Conventional current was defined early in the history of electrical science as a flow of positive charge, although we now know that, in the case of metallic conduction, current is caused by a flow of negatively charged electrons in the opposite direction. Despite this understanding, the original definition of conventional current still stands. The symbol typically used for the amount of current (the amount of charge flowing per unit of time) is I, and the SI unit of electrical current is the ampere, A . The unit of electric charge, the coulomb, is defined in terms of the ampere: 1 coulomb is the amount of electric charge carried in a current of 1 ampere flowing for 1 second.
In metallic conductors, such as wires, currents are caused by a flow of electrons (negatively charged particles), but this is not the case in most non-metallic conductors. Electric currents in electrolytes (e.g., water containing dissolved ions) are flows of electrically charged atoms (ions), which exist in both positive and negative varieties. For example, an electrochemical cell may be constructed with salt water (a solution of sodium chloride) on one side of a membrane and pure water on the other. If the membrane lets the positive sodium ions pass, but not the negative chlorine ions, a net current results. Electric currents in plasma are flows of electrons as well as positive and negative ions. In water ice and in certain solid electrolytes, flowing protons constitute the electric current.
Current can be measured by connecting an amp meter to a circuit. Break the circuit, then complete the circuit with the leads of the amp meter. Battereis are typically rated in terms of Amp hours, i.e., how many hours they can provide 1 amp. Most manufacturers provide specification sheets on their websites. For batteries in series, add the amp hours for each batterry. Estimate how long batteries will last in a given application using a service hours versus discharge current curve (usually included in a battery datasheet). Multiply the service life estimated from the curve by the number of batteries in series.
In electrical engineering, the potential difference between two points in an electrical circuit is equal to the difference in their electrical potentials. It is defined as the amount of work per charge needed to move electric charge from the second point to the first, or equivalently, the amount of work that unit charge flowing from the first point to the second can perform. A potential difference between two points gives rise to a "force" called an electromotive force (emf) that tends to push electrons or other charge-carriers from one point to the other. Common sources of emf are the battery, the electrical generator, and the capacitor. In the SI system of units, potential difference, electrical potential and electromotive force are measured in volts, leading to the commonly used term voltage and its abbreviation V. Named after Alessandro Volta, one volt is defined to be one joule of energy per coulomb of charge, i.e., newton meter / coulomb. According to Ohm's law (named after Georg Ohm),
V = IR
where R is the resistance in ohms. Resistance is a measure of how "easy" current can flow through a current carrier. Resisters are devices designed to have specific values of resistance. The ohm is the SI unit of electrical resistance. Its symbol is the Greek capital letter omega. By Ohm's Law, an ohm equals a volt divided by an ampere. In other words, a device has a resistance of 1 ohm if a voltage of 1 volt causes a current of 1 ampere to flow. An ohm is the reciprocal of a siemens (also called mho), the SI unit of electrical conductance. Note that 'siemens' is both singular and plural.
Potential can be measured by connecting the leads of a volt meter to a closed circuit just before and after a power source, such as a battery. Most batteries have their voltage listed right on the casing. For batteries in series, add the voltages.
One event occurs after another event. Furthermore one can measure how much one event occurs after another. The answer to "how much" is the amount of time between the those two events. One way of defining the idea of 'after' is based on the assumption of causality. The work humanity has done to increasingly understand the nature and measurement of time, through the work of making and improving calendars and clocks, has been a major engine of scientific discovery.
Mechanical advantage (MA) is a term used in physics and engineering that describes how much a machine multiplies the force put into it. The mechanical advantage can be calculated for the following simple machines by using the following formulas:
Lever: MA = length of effort arm ÷ length of resistance arm.
Wheel and Axle: A wheel is essentially a lever with one arm the distance between the axle and the outer point of the wheel, and the other the radius of the axle. Typically this is a fairly large difference, leading to an equally large mechanical advantage. This is why even simple wheels with wooden axles running in wooden blocks will still turn freely, because the friction is overwhelmed by the rotational force of the wheel multiplied by the mechanical advantage.
Pulley: Pulleys are wheels that are connected together with ropes. In doing so the direction of the force on the rope can be changed, with little loss in force due to friction (for the same reasons as the wheel). However pulleys can be "added together" to create additional mechanical advantage by having the rope looped over several pulleys in turn. A pulley with one rope (single fixed pulley) has an MA = 1, that is, no advantage (or disadvantage). A pulley with two ropes (single moveable pulley) has a MA = 2. A pulley with 6 ropes (block and tackle) has a MA = 6.
Inclined Plane: MA = length of slope ÷ height of slope
Most generally, the mechanical advantage is:
MA = (the distance over which force is applied) ÷ (the distance over which the load is moved)
Analogies can be made between the flow of water and electricity. Voltage, or potential, is analogous to pressure. Current is analogous to flow. Resistance is analogous to headloss.
If velocity and elevation are the same at the beginning and end, the hydraulic power needed to move water through a hydraulic system (e.g., pipes or a portable water treatment device) can be determined as
P = 0.1152 p Q
where P = power in watts, p = the pressure change in psi, and Q = flowrate in L/min.
Yes, the units are strange, but they'll work well for the experiment we plan to do in this class. If one used a pump to move the water, one would have to input more power into the pump than the hydraulic power, to overcome internal energy losses in the pump.
Web resources are plentiful. For example go to the free encyclopedia at "en.wikipedia.org" and search any of the terms described here. Much of the material on this page was adopted from "en.wikipedia.org".