All hvac formulas pdf

If outside air is provided through a mechanical system, then at least 15 cubic feet per minute cfm of outside air must be provided for each occupant. A typical classroom with 30 people requires a minimum of 15 x 30 or cfm of outside air. In spaces where the number of occupants is highly variable such as gyms, auditoriums and multipurpose spaces, demand controlled ventilation DCV systems can be used to vary the quantity of outside air ventilation in these spaces in response to the number of occupants.

One technique for doing this is to install carbon dioxide CO 2 sensors that measure concentrations and vary the volume of outside air accordingly. If an auditorium fills up for school assembly, then CO 2 concentrations will increase, a signal will be provided to the HVAC system and outside air volumes will be increased accordingly.

When the spaces served by an air handler have highly variable occupancy, this type of control can both save energy and help control moisture and mold by reducing the quantity of humid outside air when it is not needed for ventilation. CO 2 and other sensors must be periodically calibrated and maintained.

In addition to "atmospheric dust," airborne particulates can include pollen, mold fungal spores, animal dander, insect proteins, pesticides, lead and infectious bacteria and viruses. Designers can integrate features into the ventilation system that will provide benefits for the school occupants as well as the efficiency and longevity of the HVAC system. In addition, these features can reduce the need for expensive cleaning of the duct work and air handling units.

The most effective means of reducing exposure of occupants to gases and VOCs is to manage and control potential pollution sources.

Filters are available to remove gases and volatile organic contaminants from ventilation air; however, because of cost and maintenance requirements, these systems are not generally used in normal occupancy buildings or schools. In specially designed HVAC systems, permanganate oxidizers and activated charcoal may be used for gaseous removal filters. Some manufacturers offer "partial bypass" carbon filters and carbon impregnated filters to reduce volatile organics in the ventilation air of office environments.

Gaseous filters must be regularly maintained replaced or regenerated in order for the system to continue to operate effectively.

Although a typical HVAC system has many controls, the control of outdoor air quantity that enters the building can have a significant impact on IAQ, yet typically is not part of standard practice. Demand controlled ventilation is addressed as a method of humidity control, but is not otherwise discussed here because its primary use is to reduce the supply of outdoor air below the recommended minimum for the purposes of saving energy, not for improving IAQ.

Supplying acceptable quantities of outdoor air to occupied spaces is a critical component of good indoor air quality. Yet nearly all school ventilation systems cannot indicate whether outdoor air is even being supplied to the school, much less gauge the quantity of that air.

Virtually all existing school ventilation systems rely upon a fixed damper to regulate the amount of outdoor air. Yet wind, stack effect, unbalanced supply and return fans and constantly changing variable air volume VAV systems can cause significant under- or over-ventilation, which can affect IAQ and energy costs.

Combinations of these effects can even cause the intake system to actually exhaust air. Uncontrolled moisture indoors can cause major damage to the building structure, as well as to furnishings and to finish materials like floors, walls and ceilings. Uncontrolled moisture can trigger mold growth which not only damages the school facility, but can lead to health and performance problems for students and staff. Controlling moisture entry into buildings and preventing condensation are critical in protecting buildings from mold and other moisture-related problems, including damage to building components.

Dirt and moisture should not be present in duct systems and must be controlled to prevent mold growth. However, it is not always possible to assure that ducts remain dirt and moisture free. In many existing schools, sheet metal ducts, as well as those constructed of or lined with insulation products, are often contaminated with mold because dirt and moisture found their way into the system.

Duct board and duct liner are widely used in duct systems because of their excellent acoustic, thermal and condensation control properties. If the HVAC system is properly designed, fabricated, installed, operated and maintained, these duct systems pose no greater risk of mold growth than duct systems made of sheet metal or any other materials. However, the very properties that make duct board and duct liner superior insulators e.

While there is an ongoing debate about the wisdom of using insulation materials in duct systems that might retain moisture longer, all sides agree that extraordinary attention to preventing moisture contamination of the duct work should be the primary strategy for preventing mold growth.

As a secondary strategy, designers should consider methods of reducing the potential for future problems to occur due to unforeseen moisture contamination by investigating insulation products now on the market that minimize the potential for moisture to penetrate the insulation material.

These include foil vapor retarders, tightly bonded non-woven vapor retarders, butt or shiplap edges and other techniques that have been developed by insulation manufacturers to address concerns about moisture. Nearly all schools currently use the mixed-airflow method for distribution and dilution of the air within the occupied space. Designers should investigate a method called vertical displacement ventilation or thermal displacement ventilation.

This approach successfully uses natural convection forces to reduce fan energy and carefully lift air contaminants up and away from the breathing zone. Quick removal of concentrated air contaminants and building pressurization are two ways that exhaust systems affect IAQ. These areas should be maintained under negative pressure relative to adjacent spaces. To help ensure that proper operation and maintenance of HVAC system components will be performed, it is critical that the designer makes the components easily accessible.

AHUs, controls and exhaust fans should not require a ladder, the removal of ceiling tiles, or crawling to gain access. Rooftop equipment should be accessible by way of stairs and a full-sized door, not a fixed ladder and a hatch. The labels should be easy to read when standing next to the equipment and durable to match the life of the equipment to which they are attached. At a minimum, the following components should be labeled in each ventilation zone of the school and should correspond with the HVAC diagrams and drawings.

The filter pressure gauge and the recommended filter change pressure Filter Pressure, max 0. Other pertinent access doors such as to energy recovery ventilation wheels or plates Energy Recovery Ventilation Unit. The outdoor air damper OA Damper , with special marks noting when the damper is in the fully closed Closed , fully opened open and minimum designed position Min.

Log in with Facebook Log in with Google. Remember me on this computer. Enter the email address you signed up with and we'll email you a reset link. Need an account? Click here to sign up. Download Free PDF. JZ cls. A short summary of this paper. Linear Equation in one unknown lb Simple Transposition Latent of water vapor in air and flue gases average 2. Linear Equations in two or more unknowns a.

Elimination kg lb c. Determinants 3. Factoring if factorable b. Completing the Square 4. Quadratic Equations in two more unknowns a. Substitution b. Elimination c. Cubic Equation 7. Number Problem Synthetic division, trial and error Two consecutive numbers have a difference of 1; two Possible roots are the factors of the constant consecutive odd and even numbers have a difference of 2.

Interest Problem 6. Lever Problem 7. Direct Variation: x varies directly as y x y 2. Inverse Variation: x varies inversely as y 3. Mixture Problem c. Integration by Algebraic Substitution dy A new variable is used to substitute the original variable to y2 make the integrand integrable. Volume of Solid Revolution 4. Integration by Partial Fractions Cylindrical Disk This is applied when the integrand becomes integrable when dx expressed into its partial functions.

Order of differential equation — the order of the highest derivative that occurs in the equation. Degree of a differential equation — the algebraic degree in the highest-ordered derivative present in the equation.

Put the given equation into the standard form; differential equation. Apply the integrating factor to the equation in a. General Solution — solution that contains arbitrary its standard form. Solve the resulting exact equation. Particular Solution — solution that does not contain any more arbitrary constants.

Statics — branch of Mechanics which studies forces on II. This is a type of differential equation in which all the terms II. Dynamics — branch of Mechanics which considers the are of the same degree. The substitution will make the equation variable separable.

Elinematics: deals with pure motion 2. Kinetics: relates motion to the applied forces III. Physical Depreciation — type of depreciation caused by the bond which is the price at which the bond is first bought lessening of the physical ability of the property to produce results, such as physical damage, wear and tear. Depletion — the decrease in value of a property due to the 2.

Functional Depreciation — type of depreciation caused by gradual extraction of its contents, such as mining properties, oil lessening in the demand for which the property is designed wells, timber lands and other consumable resources. Straight Line Method worth of a physical property for specific reasons. Declining-Balance Method also called Diminishing-Balance 1.

Sum-of-the-Years-Digits Method 1. Private Corporation b. Semi-Public Corporation Basic investment studies are made to determine whether an d. Quasi-Public Corporation investment should be made or not, based on the following e.

Non-Profit Corporation criteria: Stock — certificate of ownership of corporation 1. Rate of Return a. Mortgage bond — type of bond in which the security behind are the asset of the corporation b. Collateral bond — type of bond in which the security behind are the assets of a well known subsidiary. Future Worth Studies on selection of alternatives are made to determine in This is applicable when the alternatives involve expenses what manner an investment should be undertaken, based on any of the whose future worth is the more suitable basis of following criteria: comparison.

Studies usually involve alternatives are: to replace the old equipment with anew one or to the selection between alternative designs, material or continue using the old equipment. Two criteria commonly used are: methods. Rate of return 2. Payout Period 2. In computing the depreciation and interest of the old 4.

Pure Substance — a working substance whose chemical composition remains the same even if there is a change in Perfect Vac. Temperature — the degree of hotness or coldness of a Positive Temperature substance. Time The most efficient operating cycle is the Carnot Cycle. Definition: A pure substance is a working substance that has a homogeneous and invariable chemical composition even though there 1.

Mass or Gravimetric Analysis: is a change of phase. The Mollier h-s Diagram of Steam is usually useful in determining the final enthalpy of steam after an isentropic process. Simplify: ANS. Working together, they can do to the work in 6 days?

How long would it take Dan to do it alone? Combine into a single fraction: ANS. Maria is 36 years old. Maria was twice as old as Ana was x-1 Maria was when Maria was as old as Ana is now. How old is Ana now? Two cars start at the same time from two nearby towns km ANS. After how many hours will they meet on the A man leaving his office one afternoon noticed the clock at road and how many km each car has traveled when they meet?

Between two to three hours, he returned to ANS. At what time did he leave the office and the time that he returned to the 4. A Cesna single engine airplane has an airspeed speed in still office? A west wind of 25 KPH is blowing. The ANS. How far east can it go if the round trip is to consume 4 hours? When two times a certain number is added to thrice its ANS. Find the number. A car travels from A to B, a distance of km, at an average speed of 30 km per hour.

At what speed must it travel back A company has a certain number of machines of equal capacity from B to A in order to average 45 km per hour for the round that produced a total of pieces each working day. If two trip of km? Find the number of machines. Leave the same point and travel in opposite directions. In how many minutes would they be miles A rectangular field is surrounded by a fence meters long.

The diagonal distance from a corner to corner is meters. A machine foundation has a trapezoidal cross-section whose A man bought 20 calculators for P20, There are three area is 21 square feet. The shorter base of the trapezoid must be types of calculators bought, business type costs P3, each, twice its height and the longer base must exceed the height by scientific type costs P1, each and basic type costs P 5 feet. Find the height and the two base lengths the bases are each.

How many calculators of each type were purchased? A production supervisor submitted the following report ion the average rate of production of printed circuit boards PCB in an Solve for x: How many layers are there in the pile?

A rectangular lot has a perimeter of meters and an area of ANS. Find the length and width of the lot. In a racing contest, there are cars which will have fuel provisions that will last for 15 hours. Assuming a constant A meter pole is held by three guy wires in its vertical hourly consumption for each car, how long will the fuel position. Tow of the guy wires are equal length. The third wire provisions last if 8 cars withdraw from the race every hour is 5 meters longer than the other two and is attached to the after the first?

Find the length of the wires. Find the length of the side of the 1. Two points lie on a horizontal line directly south of a building square. The angles of depression to the points are ANS.

Determine: a. The distance between the points. The distance between the building and the nearest point. The distance between the building and the farthest 9. Solve for x: casts a shadow 9. Find the length of the pole. Find the largest angle.

Find the side of the ANS. The opposite side of angle B is meters. Using trigonometric function and not using calculator, find Tan ANS. A right circular conical vessel is constructed to have a volume ANS. Find the diameter and the depth of the depth is to be 1. Give the answers in meters. If the diameter AD of the semi-circle is 2. Find the area of the triangle. Hint: ANS. Two ships started sailing from the same point. After 3 hours, how far apart are the 3.

A hollow sphere with an outer radius of 32cm is made of a ships? The weight of the sphere ANS. Find the inner radius. A circular cylindrical tank, axis horizontal, diameter 1 meter, 8. Find the area of the circle shown: and length 2 meters, is filled with water to a depth of 0.

How much water is in the tank? A machine foundation has the shape of a frustrum of a pyramid with lower base 6mx2m, upper base 5. Find the volume of the foundation. The total height of the tank is 5 meters. Water is pumped into the tank at ANS. How long will it take to full fill the tank starting from empty?

Find the area of the shaded portion: 1. A straight line passes through 2,2 such that the length of the line segment intercepted between the coordinate axes is equal to the square root of 5. Find the equation of the straight line. Find the equation of the circle with center at 2,-3 and radius of 4.

A cable supporting a pipeline has a span of feet. The 2. If tangents to the graph have slope of 9. A rectangular field to contain a given area is to be fenced off ANS. If no fencing is needed along the river, show that the least amount of fencing will be required when the 6. Find the area of an ellipse whose equation is length of the field is twice its width.

Find the shape of the largest rectangle that can be inscribed in a 7. It passes through points given circle. Square specific equation of the given curve. Divide the number 60 into two parts so that the product P of one part and the square of the other is a maximum. Find the volume of the solid which is formed by revolving the ANS. When a load is uniformly distributed horizontally, a suspension 7. A square sheet of galvanized iron, cm x cm will be bridge cable hangs in parabolic arc.

If the bridge is m long used in making an open-top container by cutting a small square and the towers 40m high and the cable is 15m above the floor from each corner and bending up the sides.

Determine how of the bridge at the mid-point, find the equation of the parabola large the square should be cut from each corner in order to using mid-point of the bridge as origin. The sum of two positive numbers is What are the numbers if their product is to be the largest possible? Find the equation of the tangent and normal to the ellipse ANS. A bus company charges P Two posts, one 8 meters high and the other 12 meters high, Baguio for or less passengers.

For group tours, the stand 15 meters apart. They are to be stayed by wires attached company allows for P0. How many passengers will give the of the posts. How far from the shorter post should the stake be maximum income? A tinsmith wishes to make a gutter of maximum cross-section A cylindrical glass jar has a metal top.

If the metal costs three carrying capacity whose bottom and sides are each 6 inches times as much as the glass per unit area, find the proportions of wide and whose sides have the same slope. What will be the the least costly jar that holds a given amount.

The parcel post regulations limit the size of a package to such a A lot is in the shape of a quadrant of a circle of radius size that the length plus the girth equals 6 feet. Determine the meters. Find the area of the largest rectangular building that dimensions and the volume of the largest cylindrical package can be constructed inside the lot. The cost of setting up a geothermal plant is P10M for the first The material for the sides costs other expenses Land rights, design fee, etc.

P per square meter and for the ends P per square meter. A boat is towed toward a pier which is 20 feet above the water. How fast is the boat If the fuel cost to run a boat is proportional to the square of her approaching the base of the pier when 25 feet of rope remain to speed and is P A water tank is in the form of a right circular cone with vertex ANS.

How fast is the The strength of a rectangular beam is proportional to the surface of the water in the tank rising when the water is 5 feet breadth and the square of the depth. Find the dimensions of the deep? A helicopter is rising vertically from the ground at a constant 2. An ellipsoidal tank measuring 6 ft by 12 ft has its axis vertical, rate of 25 ft per second. When it is feet of the ground, a the axis of rotation being the major axis.

It is filled with water jeep passed beneath the helicopter traveling in a straight line at to a depth of 7 feet. Find the amount of water in the tank. Determine how fast is ANS. Work with the part of the volume lying in the first An elevated light rail transit on a track 4. Since the curve of the intersection lie on the cylinder, it ground crosses a street station at 6.

How ANS. A plane flying north at km per hour passes over a certain ANS. If the planes 5. An open cylindrical tank 3 feet in diameter and 4. It is then tilted until one-half of its bottom is at PM? How many gallons of water was spilled out? The height of a cylindrical cone is measured to be four 4 6. The parabolic reflector of an automobile headlight is 12 inches meters which is equal to its radius with a possible error of 0.

What is the surface area in Determine the percentage error in computing the volume. A cistern in the form of an inverted right circular cone is 20 one pair, plus one-third the product of another pair, plus one- meters deep and 12 meters diameter at the top. If the kilojoules fourth the product of the third pair may seem to be a maximum in pumping out the water to a height of 10 meters above the top value.

Clue: use partial differentiation of the cistern. A flour bag originally weighing 60 kilograms is lifted through 6. While the bag is being lifted, of brine wherein lbs of salt are dissolved. If the amount of salt in the tank at the end of minutes.

A body weighing kilos is suspended by a cable 20 meters 1. Solve the differential equation long and pulled 5 meters to one side by a horizontal force.

The rate of population growth of a country is proportional to 2. The arm ABC, weighing 60 kg per meter carries a load of 15kg the number of inhabitants. Compute the population 20 years from now? In drying copra by a certain process, the moisture is removed at a rate proportional to the actual moisture present.

Find the minimum force P required to roll the kg wheel 5. The coefficient of P static friction is 0. Prevent the block from sliding down the plane. A steam pipe weighing kg per meter will cross a road by suspension on a cable anchored between supports 6 meters 4.

A force P on top of the 30 kg block as shown in the figure. If apart. The maximum allowable sag of the cable is 50cm. Calculate the tension in the cable 0. Calculate the length o the cable. A parabolic cable has a span of feet. The difference in 50cm elevation of the supports is 10 feet and the lowest point of the A 30kg B cable is5 feet below the lower support.

If the load supported by the cable is 12 lbs per horizontal foot, find the maximum 25cm tension in the cable. A tripod whose legs are each 4 meters long supports of horizontal. The angle of static friction between the body and kilograms. The feet of the tripod are vertices of a horizontal the plane is 15 degrees. What horizontal force P is necessary to equilateral triangle whose side is 3. Determine the hold the body from sliding down the plane?

The coefficient of friction Two cars A and b accelerate from a stationary start. If B was a. Just prevent the crate from sliding down the inclined originally 20 feet behind A, how long will it take B to overtake ramp. Start the crate moving up the ramp. In how may seconds will B overtake A? How far will each car have traveled before coming ANS. If the bomb hits the ground in 20 seconds, calculate: In a 25 storey office building, the elevator starting from rest at a.

The vertical height of the bomber when it released the first floor, is accelerated at 0. The horizontal distance traveled by the bomb before it stopped in 3 seconds with constant deceleration. If the floors hit the ground, in meters. The vertical velocity of the bomb as it hit the ground, in ANS. A stone is dropped from a cliff into the ocean. The sound of the ANS. The velocity of sound is 1, fps. How A flywheel starting from rest develops a speed of RPM in high is the cliff?

What is the angular acceleration? How many revolutions did the flywheel make in 30 Water drips from a faucet at the rate of 8 drops per second. The seconds it took to attain RPM? When one drop strikes the sink, how far is the next drop above the sink? Bombs from a plane drop at a rate of one 1 per second. If the slight melting of the ice renders Calculate the vertical distance between two 2 bombs after the the surfaces frictionless, calculate the velocity at the foot of the first had dropped for 7 seconds.

Assume freely falling body incline. A body weighing kg is being dragged along a rough 4. A tank with its content weighs kg. It will be supported by horizontal plane by a force of 45 kg. Calculate the diameter of each post in meters? What constant thrust drawbar pull parallel to the ANS.

A steel wire 20 feet long, hanging vertically supports a load of ANS. Neglecting the weight of the wire, determine the required diameter if the stress is not to exceed 20, psi and the total elongation is not to exceed 0. A reactor weighing 1, metric tons is placed on a 10 sq. A copper-rolled wire 10 meters long and 1. A spherical tank is supported by four steel pipes each having ANS. Determine the maximum thickness of metal plate in which a maximum weight of tank, in KN, can be supported?

A single bolt is used to lap join two steel bars together. Tensile ANS. Determine the diameter of the bolt if the allowable shearing stress in it is 10, psi. A rectangular beam with a span of 20 feet is simply supported 3. The amount of P52, was deposited in a fund earning at both ends. If the beam is to be leaded at mid- ANS. An engineering student borrowed P5, He promised to repay the loan How stress is 6, psi? A cantilever beam 3 meters long by 30centimeters depth by 10 5. A savings and loan association requires that loans be repaid by centimeters breadth has a single 45 kg load art the unsupported uniform monthly payments which include monthly interest end.

If P5, a. Draw the shear and moment diagram is borrowed to be repaid in 10 years, what must be the monthly b. Determine the maximum moment payment? Determine the maximum flexural stress ANS. A young engineer buys a television set from a merchant who 7. A man will buy a house and lot worth P, The subdivision in Metro Manila. His year-end installments is engineer wishes to pay immediately and the merchant offers to P34, What is the cash price today?

Five years ago you paid P, for a house and lot. If you 8. Prove you answer by the mathematical solution. A firm plans to market a new minicomputer that will sell for The direct labor cost and material cost of a certain product are P, Fixed charges are balance to be settled by equal monthly payments for 5 years.

If the product is sold at P per unit, how many units monthly payment? A P10, The agreement cost of P per unit, material cost of P per unit, fixed provides for paying of the mortgage in a lump sum at any time charges of P, per month and variable cost of P per with an amount equal to the unpaid balance including interest.

The net selling price of each stove is P1, , wholesale. What single amount have to be paid to discharge the mortgage Determine the monthly break even sales volume in pesos. P7, A total of P62, is donated by a wealthy man to provide an A manufacturing firm has just installed standby power annual scholarship to deserving students.

It is proposed that an generating unit at a first cost of P, The projected annual grant of P10, will be drawn from this fund. How many years from today should be the of first cost. Determine the following: scholarship grant given so that the scholarship will last a. Annual depreciation charges using straight line method forever? Annual depreciation charges using sinking fund method ANS. You purchased a P5, bond for P5, The bond pays P ANS.

P24, b. P8, It is redeemable for P5, after 10 years. What is the net rate of interest on your investment? A machine which cost P10, If the scrap value was P Total depreciation at the end of the 5th year.

How much should the man be b. Book value at the end of the 5th year. An air compressor has been purchased at a cost of P18, A manufacturing company is faced with the choice of repairing The compressor will be retired at the end of 5 years, at which an old machine at a cost of P12, or replaces it with a new time it is expected to have a salvage value of P2, based on one at P50, It is estimated that the repaired machine will current prices.

The compressor will then be replaced with an last for 5 years after which replacement will be necessary. The firm plans to establish a reserve fund to Present salvage value of the old machine is P10, and its accumulate the capital needed to replace the compressor.

If an salvage value after 5 years will be P5, It is estimated that average annual rate of inflation of 3 percent is anticipated, how the new machine will last for 20 years and will have a salvage much capital must be accumulated? The yearly maintenance of the new machine ANS.

P18, will be P less than the old. Use uniform annual cost. In the manufacture of a certain product, two processes are ANS. Process B will produce 87 units of the finished product per P worth of raw materials A contain heat exchanger costs P30, installed and has an and will cost P0. If the estimated life of 6 years.

By the addition of certain auxiliary selling price per unit of the finished product is P2. Process B the estimated life of the heat exchanger can be doubled.

A chemical plant needs a generating set. The engineering staff for the auxiliary equipment? A boiler installed where the atmospheric pressure is mm Salvage Value 30, 5, Hg has a pressure of 12 kg per sq cm. What is the absolute Useful life, years 12 8 pressure in MPa?

Show your computations with the itemized cost. An oil storage tank contains oil specific gravity of 0. What is the hydrostatic pressure at the ANS. What is the absolute pressure in KPa? A boiler feed pump delivers , kg of water per hour at 3. What is the ANS. Express in KPa? The radiator of a heating system was filled with dry and ANS. As a result of heat transfer to the room, 4.

What percentage of steam has ANS. A throttling calorimeter receives a sample of steam from a ANS. What is the quality of steam in 6. What is the temperature difference in ANS. Steam at 2. If the process occurs 7. The velocity leaving the nozzle b. The exit area of the nozzle 8. Determine the specific volume, enthalpy and entropy of water or steam in the given states: ANS. What d. Determine the quality if saturated or temperature if superheated of steam in the given states: a.

If the steam flow rate is , c. The enthalpy after expansion b. The turbine power ANS. An air compressor delivers air to an air receiver having a 7. Circle — a closed plane curve every point of which is equally volume of 2 m3. After 5 minutes, 8. What is the capacity of the compressor in 9. Diagonal — a line joining any two nonconsecutive vertices of a polygon At the suction of an air compressor, in which the conditions are Hypotenuse — the side opposite the right triangle of a right What is the triangle.

Isosceles triangle — a triangle which has two equal sides. Locus — a figure containing all the points, and only those points, which fulfill a given requirement Polygon — a closed plane figure bounded by straight lines 1. Axiom — a statement accepted as true Triangle, quadrilateral, pentagon, hexagon, etc Postulate — a statement assumed to be true, as a basis for Quadrilateral — a polygon with four sides square, rectangle, argument parallelogram, trapezoid Hypothesis — an unapproved theory tentatively accepted to Rectangle — a parallelogram whose angles are right angles explain certain facts Regular Polygon — a polygon all of whose angles are equal and Theorem — a proposition that can be proven from accepted all of whose sides are equal premises Rhomboid — a parallelogram with oblique angles and only the Corollary — a proposition that follows from one already proved opposite sides equal Rhombus — an equilateral parallelogram, 2.

Altitude of a Triangle — a perpendicular from any vertex of a Similar Polygons — polygons whose corresponding angles are triangle to the side opposite equal and whose corresponding sides are proportional 3. Angle — the opening between two straight lines drawn from the Apothem — the radius of the inscribed circle of a polygon Tangent — a straight line which meets a curve only at one point 5.

Area — the number of unit squares of a plane figure. Trapezoid — a quadrilateral two and only two of whose sides 6. Center of Polygon — the common center of the inscribed and are parallel circumscribed circles of a regular polygon Vertical Angles — opposite angles of two intersecting lines Two points each equally distant from the extremities of a line 1.

If two parallel lines are cut by a transversal: determines the perpendicular bisector of the line. Alternate interior angles are equal b. Exterior-interior angles are equal c. The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side. If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side; and conversely.

If tow sides of a triangle are equal an isosceles triangle , the 2. If a line is perpendicular to one of two parallel lines, it is angles opposite these sides are equal; and conversely.

The bisectors of the angles of the angles of a triangle meet at a point which is the center of the inscribed circle. The perpendicular bisectors of the sides of a triangle meet at a point which is the center of the circumscribed circle.

The medians of a triangle are concurrent at a point which is two-thirds of the distance from any vertex to the midpoint of the opposite side. Two triangles are congruent if two angles and the included side of one are equal, respectively, to two angles and the included 3.

Any point in the perpendicular bisector of a line is equally side of the other. Two triangles are congruent if two sides and the included angle perpendicular bisector of the line of one are equal, respectively, to two sides and the included angle of the other. Two triangles are congruent if the three sides of one are equal, respectively, to the three sides of the other.

Theorem of Pythagoras: In any right triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. Two right angles are equal if a side and the hypotenuse of one are equal, respectively, to a side and the hypotenuse of the other.

Two right triangles are equal if the hypotenuse and an adjacent POLYGONS angle of one are equal, respectively, to the hypotenuse and an adjacent angle of the other. Corresponding parts of congruent figures are equal. Two triangles are similar if the angles of one are respectively 1.

Through three points not in a straight line one circle and only equal to the angles of the other; or if two angles of one are one can be drawn. A tangent to a circle is perpendicular to the radius at the point 2. Two triangles are similar if their sides are in the same ratio. Two triangles are similar if their sides are respectively parallel 3. The tangents to a circle drawn from an external point are equal, each to each. Two triangles are similar if their sides are respectively center.

An inscribed angle is measured by one-half the intercepted arc. An angle inscribed in a semicircle is a right angle. If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other. The circumference of two circles are in the same ratio as their radii, and the arcs of two circles subtended by equal central angles are in the same ratio as their radii. Coke, wood, charcoal, bagasse, coconut shells a SG at Higher heating value gross calorific value — the Properties of Fuels and Lubricants: heating value obtained when the water in the products of combustion is in the liquid state.

Analysis of composition: b. Lower heating value net calorific value — the heating a. Proximate analysis — analysis of the composition of fuel value obtained when the water in the products of which gives, on mass basis, the relative amounts of combustion is in the vapor state.

Instruments used in measuring heating value of fuels: b. Ultimate chemical analysis — analysis of the a. Oxygen bomb calorimeter: for solid and liquid fuels composition of fuel which gives, on mass basis, the b. Gas calorimeter: for gaseous fuels relative amounts of Carbon, Hydrogen, Oxygen, Nitrogen, Sulfur, Ash and Moisture Calculating heating value by formulas: a.

Water Tube Tubulous Boiler — type of boiler in which the 9. Thermal Eff. Fire Tube Tubular Boiler — type of boiler in which the hot gases pass inside the tubes while the water is outside the tubes. Net Boiler eff. Ideal P-V Diagram Steam cut-off through which the steam is released in case of excessive P temperature which is usually caused by low water level Baffles — direct the flow of the hot gases to effect efficient heat transfer between the hot gases and the heated water Furnace — encloses the combustion equipment so that the heat generated will be utilized effectively Soot Blower — device which uses steam or compresses air to remove the soot that has accumulated in the boiler tubes and drums V Draft Fans forced draft and induced draft fans — supply air VD needed for combustion and create the draft required for the flow of gases in the boiler Blowdown Valve — valve through which the impurities that settle in the mud drum are removed 2.

Thermal Efficiency a. Power 2. Power 4. Engine Efficiency of Turbine a. Output ms h1 — h2 Cooling Water 7. Surface Condenser - type of condenser in which the steam and cooling water do not mix; commonly used design is the shell-and-tube. By heat balance: 2. Magma — molten metal within the earth which is basically nickel-iron in composition whose stored energy heats the surrounding water thereby producing steam or hot water. Well-bore product — the effluent coming out from the geothermal well as produced after drilling.

This can be purely 3. Geothermal Plant 3. Steam-dominated geothermal field — refers to a geothermal plant with its well producing all steam, as the well-bore product.

Liquid-dominated geothermal field — the well-bore product for this type of field is practically all hot water pressurized. Sources of geothermal energy: a. Hot spring b. Steam vent c. Geyser 6.

Fumarole — a crack in the earth through which geothermal substance passes. Pressurized Water Reactor PWR Control Rods — Boron-coated steel rods used to control the This type of reactor uses high pressure light or heavy water reactor as both moderator and coolant.

This is the type which is constructed in Morong, Bataan with capacity of MW Reflector — made of lead or carbon which surrounds the core to and intended to supply power to the Luzon area.

In bounce back any leakage of neutrons the Philippine government decided to stop the completion of the plant because of the controversy regarding its safety Thermal Shield — prevents escape of radiation from reactor and economic features.

The feedwater from the power turbine goes directly into the reactor and Biological Shield — concrete or lead which absorbs any leakage picks up the heat from the fuel core. Thus the feedwater of radiation and protects operators from exposure to also serves as the coolant. The first experimental reactor radioactivity installed in Diliman, Quezon City is of this type. It has a capacity of 1 MW. Control Cubicle — contains the meters that show the operating quantities in the reactor 3.

Gas-Cooled Power Reactor GCPR Coolants — absorbs the heat from the fuel core and then release The gas coolant used in this type of reactor is carbon the heat to the water in the steam generator dioxide. Nuclear power plants in the Philippines: Coolant Pump — circulates the coolant 1. Brake Power c. Output kw-hr the torque; Tachometer measures the speed Power kw-hr b. Output kw-hr effective pressure, kPa Generator Speed 7.

Thermal Efficiency Exhaust Loss………………………. Power Friction, Radiation, Etc……………. Specific Fuel Consumption 1. Engine-driven compressor a. Exhaust-driven compressor turbo-charger Ind. Power kw-hr 3. Separately-driven compressor b. Intake and Exhaust System: Air filter, intake pipe, exhaust pipe, silencer 5.

Low fuel cost 2. High Efficiency 3. Needs no large water supply 4. No long warm-up period 5. Impulse Pelton Turbine Tailrace — a channel which leads the water from the turbine to the tailwater Tailwater — the water that is discharged from the turbine 2. Reaction turbine a. Propeller Kaplan Turbine Pumped Storage Plant is a hydro-electric plant which involves the use of off-peak energy to store water and to use the stored water to generate extra energy to cope with the peak load.

Specific speed of hydraulic turbine: 7. Specific Speed Vs. Dutch sail type 5. A basin is required to catch the sea water during high tide Types of Solar Collectors: while the water drives a turbine. During low tide, the water in the 1. Flat Rate basin discharges back to the sea while driving the turbine. Concentrating 3. Focusing Low Thermal Head Plant Low thermal head plant, otherwise known as Ocean Thermal Photovoltaic Cell — a device which converts solar energy to energy Conversion, makes use of the temperature difference between electric energy the ocean surface water and the water at the sea bottom.

Thermoinic Converter Thermoinic converter is a device which converts heat energy directly to electrical energy. Knowing the weight of the machine, WM, determine the Functions of Machine Foundation: required weight of the foundation, WF, by any of the following methods: 1.

To support the weight of the machine, and to distribute the a. To absorb the vibrations produced by the machine.

Volume of foundation can be computed based on HP Grouting — process of filing a small clearance between machine and of the engine, Table 2. Weight of foundation can be computed based on the hardening mixture. HP of the engine, Morse, Table , p. The safe bearing capacity is computed using a factor of safety of 5. To dispose the exhaust gases at suitable height so that no 2 bL pollution will occur in the vicinity.