Agricultural Engg Formula (2) PDF

AGRICULTURAL ENGINEERING FORMULA Alexis T. Belonio Department of Agricultural Engineering and Environmental Management College of Agriculture Central Philippine University Iloilo City, Philippines 2006 About the Author...

AGRICULTURAL ENGINEERING FORMULA Alexis T. Belonio Department of Agricultural Engineering and Environmental Management College of Agriculture Central Philippine University Iloilo City, Philippines 2006 About the Author Alexis T. Belonio is a Professional Agricultural Engineer. Presently, he is an Associate Professor and Chairman of the Department of Agricultural Engineering and Environmental Management, College of Agriculture, Central Philippine University, Iloilo City. He finished his Bachelor of Science in Agricultural Engineering and Master of Science degrees from Central Luzon State University, Muñoz, Nueva Ecija. He has been deeply involved in teaching, research, project development, and entrepreneurial activity on various agricultural engineering projects since 1983. He was awarded by the Philippine Society of Agricultural Engineers (PSAE) as Most Outstanding Agricultural Engineer in the Field of Farm Power and Machinery and by the Professional Regulation Commission (PRC) as Outstanding Professional in the Field of Agricultural Engineering in 1993. In 1997, he was awarded by the TOYM Foundation and the Jerry Roxas Foundation as the Outstanding Young Filipinos (TOYF) in the Field of Agricultural Engineering. He is presently a PSAE Fellow Member. As a dedicated professional, he serves as technical consultant to various agricultural machinery manufacturers in Region VI. He also serves as a Reviewer of the TGIM Foundation Review Center on the field of Agricultural Machinery and Allied Subjects, and Agricultural Processing and Allied Subjects since 1998. He has written and published several research and technical papers. Other Books Available: Dictionary of Agricultural Engineering Agricultural Engineering Design Data Hanbook Problems and Solutions in Agricultural Engineering Agricultural Engineering Reviewer: Volume I Agricultural Engineering Reviewer: Volume II Rice Husk Gas Stove Handbook Small Farm Irrigation Windpump Handbook Axial Flow Biomass Shredder Handbook AGRICULTURAL ENGINEERING FORMULA Alexis T. Belonio Department of Agricultural Engineering and Environmental Management College of Agriculture Central Philippine University Iloilo City, Philippines 2006 Revised Edition Copyright © 2006 by Alexis T. Belonio No part of this book is allowed to be photocopied or reproduced in any form without written permission from the author. Acknowledgement: The author is very much thankful to the Lord God Almighty who inspired him to prepare this material for the benefit of those who are called to serve in the agricultural engineering profession. He also wishes to acknowledge the following for the motivation and encouragement during the preparation of this material: (1) Dr. Norbert Orcullo of the TGIM Foundation Review Center, Manila who is persistent to fully equip students to pass the Professional AE Board Examination; and (2) Dr. Reynaldo Dusaran of the College of Agriculture, Central Philippine University, Iloilo City who is always supportive to his students and Department to obtain higher percentage passing in the board examination. To his friends in the Philippine Society of Agricultural Engineers in the Regional and National Chapters who also encouraged me to collect all the information and materials needed in the preparation of this Handbook. To Salve and their children: Mike, Happy, Humble, Jireh, Justly, Tenderly, and Wisdom, for their prayer and inspiration.  PREFACE This book is a compilation of the various formula that are commonly used in agricultural engineering curriculum. Students who are taking the course as well as those who are preparing for the Professional Agricultural Engineer Board Examination may find this book useful. Practicing Agricultural Engineers and those other Engineers working in the field of agriculture will find this book as a handy reference material for design, estimate, testing, and evaluation activities. The presentation of the formula in this book covers the different subject matter as follows: agricultural power and energy, agricultural machinery and equipment, agricultural processing and food engineering, farm electrification and instrumentation, agricultural buildings and infrastructures, agricultural waste utilization and environmental pollution, and soil and water engineering. The subject areas are arranged in alphabetical manner for ease of finding the formula needed. The parameters and units for each formula are specified in the book and can be converted to either English, Metric, or SI system using the conversion constants given at the end of the book. This book is still in draft form. Additional subject matter and formula will be included in the future to make this material more comprehensive. Comments and suggestions are welcome for the future improvement of this book. God bless and may this book become useful to you! ALEXIS T. BELONIO  TABLE OF CONTENTS Page Air Moving Devices........................ 1 Agricultural Building Construction............ 4 Agricultural Economics..................... 9 Algebra................................. 14 Animal Space Requirement (Minimum)........ 20 Bearings................................. 24 Biogas................................... 26 Biomass Cookstove........................ 29 Biomass Furnace.......................... 31 Boarder Irrigation.......................... 33 Chain Transmission......................... 34 Conveyance Channel....................... 38 Corn Sheller.............................. 40 Cost Return Analysis........................ 42 Cyclone Separator......................... 45 Differential Calculus........................ 48 Drip Irrigation............................. 50 Electricity................................ 52 Electric Motor............................. 56 Electrification............................. 58 Engine................................... 60 Engine Foundation......................... 65 Flat and V-Belt Belt Transmission............ 66 Fluid Mechanics........................... 70 Furrow Irrigation.......................... 75 Gas Cleaning............................. 76 Gasifier.................................. 77 Gears.................................... 79 Grain Dryer............................... 80 Grain Engineering Properties................. 84 Grain Seeder.............................. 87 Grain Storage Loss......................... 90 Grain Storage Structure..................... 92 Heat Transfer............................. 95 Human and Animal Power................... 97 Hydraulic of Well.......................... 99 Hydraulics............................... 100 Hydro Power............................. 101 Infiltration, Evaporation and Transpiration...... 102 Integral Calculus........................... 104 Irrigation Efficiency........................ 108 Irrigation Requirement...................... 110 Material Handling.......................... 112 Pipe Flow................................ 115 Power Tiller............................... 116 Pump.................................... 119 Pump Laws............................... 121 Rainfall and Runoff........................ 123 Reaper Harvester.......................... 124 Refrigeration.............................. 125 Rice Milling............................... 127 Rice Thresher............................. 129 Shaft, Key, and Keyway..................... 131 Soil, Water, Plant Relation.................. 134 Soil and Water Conservation Engineering....... 136 Solar Thermal System...................... 152 Solid Geometry........................... 154 Sprayer.................................. 156 Sprinkler Irrigation......................... 158 Statistics................................. 160 Temperature.............................. 163 Tillage................................... 164 Tractor.................................. 167 Trigonometry............................. 171 Water Treatment........................... 174 Weir, Flumes, and Orifice................... 175 Wind Energy............................. 177 CONVERSION CONSTANTS................ 179 REFERENCES............................ 184  AIR MOVING DEVICES Specific Speed Ns – specific speed, dmls N - speed of air moving unit, rpm Ns = [ N Q 0.5 ] / [Ps 0.75] Q - airflow, cfm Ps – pressure requirement, in. H2O Impeller Diameter D - diameter of impeller, in. Ps – pressure requirement, in. H2O (2.35) 108 Ps ψ - pressure coefficient, 0.05 to 2.0 D= N - speed of impeller, rpm ψ N2 Pitch Angle for Axial Fan α - pitch angle, deg Q - airflow, cfm 350 Q N - speed of impeller, rpm α = Sin –1 D - diameter of impeller, in. φ N D3 φ - flow coefficient, 0.01 to 0.80 Impeller Width (centrifugal and mixed W – width of impeller, in. flow blower) Q - airflow, cfm N - speed of impeller, rpm 175 Q D - diameter of impeller, in. W = φ - flow coefficient, 0.01 to 0.80 φ N D2 Impeller Width (traverse flow) W – width of impeller, in. Q - airflow, cfm 550 Q N - speed of impeller, rpm W = D - diameter of impeller, in. φ N D2 φ - flow coefficient, 0.01 to 0.80 for 0.5 ≤ W/D ≤ 10 1  AIR MOVING DEVICES Casing Dimension (Forward Curved Centrifugal) Hc – height of casing, in. Hc = 1.7 D Bc - breath of casing, in Bc = 1.5 D Wc – width of casing, in. Wc = 1.25 W + 0.1 D D – diameter of impeller, in W - width of impeller, in Casing Dimension (Narrow Backward Curved Hc – height of casing, in. Centrifugal) Bc - breath of casing, in Hc = 1.4 D Wc – width of casing, in. Bc = 1.35 D D – diameter of impeller, in Wc = W + 0.1 D W - width of impeller, in Casing Dimension (Wide Backward Curved Hc – height of casing, in. Centrifugal) Bc - breath of casing, in Hc = 2.0 D Wc – width of casing, in. Bc = 1.6 D D – diameter of impeller, in Wc = W + 0.16 D W - width of impeller, in Casing Dimension (Mixed Flow) Hc – height of casing, in. Hc = 2.0 D Bc - breath of casing, in Bc = 2.0 D Wc – width of casing, in. Wc = 0.46 D D – diameter of impeller, in Casing Dimension (Traverse Flow) Hc – height of casing, in. Hc = 2.2 D Bc - breath of casing, in Bc = 2.2 D Wc – width of casing, in. Wc = W + [D/4] D – diameter of impeller, in Casing Dimension (Vane Axial Flow) Wc – width of casing, in. Wc = 1.2 D D – diameter of impeller, in Casing Dimension (Tube Axial Flow) Wc – width of casing, in. Wc = 1.0 D D – diameter of impeller, in Casing Dimension (Partially Cased Fan) Wc – width of casing, in. Wc = 0.5 D D – diameter of impeller, in 2  AIR MOVING DEVICES Air Horsepower AHP - air horsepower, hp Q - airflow rate, cfm Q V H V - specific weight of air, lb/ft3 AHP = ------------ H - total head, ft 33,000 Brake Horsepower BHP - brake horsepower, hp Q - airflow rate, cfm Q Pa Pa - static pressure, in. water BHP = -------------- ξf - fan efficiency, decimal 6360 ξf Mechanical Efficiency ξf - fan efficiency, decimal AHP - air horsepower, hp ξf = AHP / BHP BHP - brake horsepower, hp Propeller Fan Pitch P - pitch in. r - fan radius, in. P = 2 π r tan α α - angle of fan blade twist, deg Fan Laws D – impeller diameter, in. H1 1/4 Q2 1/2 H - fan head, in. H20 D2 = D1 --------- --------- Q - air flow rate, cfm Q1 1/2 H2 ¼ Fan Laws N – impeller speed, rpm Q1 1/2 H2 3/4 H - fan head, in. H20 N2 = N1 --------- --------- Q - air flow rate, cfm H1 3/4 Q2 ½ Fan Laws HP – fan horsepower, hp D2 5 N2 3 D - fan diameter, in. HP2 = HP1 -------- --------- N - speed of impeller, rpm D1 5 N1 3 3  AGRICULTURAL BUILDING CONSTRUCTION Volume of Cement/Sand/Gravel (1:2:3) Vc - volume of cement, bags Vs - volume of sand, m3 Vc = 10.5 Vco Vg - volume of gravel, m3 Vs = 0.42 Vco Vco – volume of concrete, m3 Vg = 0.84 Vco Volume of Cement/Sand/Gravel (1:2:4) Vc - volume of cement, bags Vs - volume of sand, m3 Vc = 7.84 Vco Vg - volume of gravel, m3 Vs = 0.44 Vco Vco – volume of concrete, m3 Vg = 0.88 Vco Volume of Cement/Sand/Gravel (1:3:6) Vc - volume of cement, bags Vs - volume of sand, m3 Vc = 5.48 Vco Vg - volume of gravel, m3 Vs = 0.44 Vco Vco – volume of concrete, m3 Vg = 0.88 Vco Volume of Cement/Sand/Gravel Vc - volume of cement, bags (1:3.5:7) Vs - volume of sand, m3 Vg - volume of gravel, m3 Vc = 5.00 Vco Vco – volume of concrete, m3 Vs = 0.45 Vco Vg = 0.90 Vco Number of Hallow Blocks per m2 NHB - number of hallow blocks, pieces Wall Area ( 8 in. x 16 in.) Aw – area of wall, m2 NHB = 13 Aw 4  AGRICULTURAL BUILDING CONSTRUCTION Volume of Cement and Sand for Mortar and Vc - volume of cement, bags Plaster per m3 of Mixture (1:2) Vm – volume of mixture, m3 Vs - volume of sand, m3 Vc = 14.5 Vm Vs = 1.0 Vm Volume of Cement and Sand for Mortar and Vc - volume of cement, bags Plaster per m3 of Mixture (1:3) Vm – volume of mixture, m3 Vs - volume of sand, m3 Vc = 9.5 Vm Vs = 1.0 Vm Volume of Cement and Sand for Mortar and Vc - volume of cement, bags Plaster per m3 Mixture (1:4) Vm – volume of mixture, m3 Vs - volume of sand, m3 Vc = 7.0 Vm Vs = 1.0 Vm Volume of Cement and Sand for Mortar and Vc - volume of cement, bags Plaster per m3 Mixture (1:5) Vm – volume of mixture, m3 Vs - volume of sand, m3 Vc = 6.0 Vm Vs = 1.0 Vm Quantity of Cement and Sand for Plastering Vc - volume of cement, bags per Face (50kg Cement-Class B) Vs - volume of sand, m3 Vc = 0.238 Aw Aw – area of wall, m2 Vs = 0.025 Aw 5  AGRICULTURAL BUILDING CONSTRUCTION Quantity of Cement and Sand for Vc - volume of cement, bags Plastering per Face (50kg Cement-Class Vs - volume of sand, m3 C) Aw – area of wall, m2 Vc = 0.170 Aw Vs = 0.025 Aw Quantity of Cement and Sand for Vc - volume of cement, bags Plastering per Face (50kg Cement-Class Vs - volume of sand, m3 D) Aw – area of wall, m2 Vc = 0.150 Aw Vs = 0.025 Aw Quantity of Cement and Sand per 100 - 4 Vc - volume of cement, bags in. CHB Mortar (50kg Cement-Class B) Vs - volume of sand, m3 NHB – number of hallow blocks Vc = 3.328 NHB/100 Vs = 0.350 NHB /100 Quantity of Cement and Sand per 100 - 6 Vc - volume of cement, bags in. CHB Mortar (50kg Cement-Class B) Vs - volume of sand, m3 Vc = 6.418 NHB/100 NHB – number of hallow blocks Vs = 0.675 NHB /100 Quantity of Cement and Sand per 100 - 8 Vc - volume of cement, bags in. CHB Mortar (50kg Cement-Class B) Vs - volume of sand, m3 NHB – number of hallow blocks Vc = 9.504 NHB/100 Vs = 1.000 NHB /100 6  AGRICULTURAL BUILDING CONSTRUCTION Quantity of Cement and Sand per 100 - 8 Vc - volume of cement, bags in. CHB Mortar (50kg Cement-Class B) Vs - volume of sand, m3 NHB – number of hallow blocks Vc = 9.504 NHB /100 Vs = 1.000 NHB /100 Weight of Tie Wire (No. 16 GI wire) Wtw – weight of tie wire, kg Wrb - weight of reinforcement bar, tons Wtw = 20 Wrb Vertical Reinforcement Bar Requirement Lb - length of vertical bar needed, m Aw - area of wall, m2 Lb = 3.0 Aw (0.4 m spacing) Lb = 2.1 Aw (0.6 m spacing) Lb = 1.5 Aw (0.8 m spacing) Horizontal Reinforcement Bar Lb - length of vertical bar needed, m Requirement Aw - area of wall, m2 Lb = 2.7 Aw (every 2 layers) Lb = 1.9 Aw (every 3 layers) Lb = 1.7 Aw (every 4 layers) 7  AGRICULTURAL BUILDING CONSTRUCTION Board Feet of Lumber BF - number of board foot, bd-ft T – thickness of wood, in. T W L W - width of wood, in. BF = L - length of wood, ft 12 Number of Board Foot that can be BF - number of board foot, bd-ft Obtained from Log D – small diameter of log, in. L - length of log, ft (D – 4) 2 L BF = 16 Volume of Paint Needed for Wood Pv - volume of paints needed, liters Aw - area of wall, m2 Pv = 3.78 Aw / 20 (1st coating) Pv = 3.78 Aw / 25 (2nd coating) Nails Requirement Wn - weight of nail needed, kg BFw – number of board foot of wood, bd-ft Wn = 20 BFw / 1000 Wood Preservation Vp - volume of preservatives, gal As - area of surface, m2 Vp = As / 9.3 8  AGRICULTURAL ECONOMICS Elasticity E – elasticity % ΔQd Qd – quantity of demand E = P - Price % ΔP Point Elasticity Q – quantity ΔQ P - price ΔQ – change in quantity Q + Q2 / 2 ΔP – change in price Έpa = ΔP P1 + P2 / 2 Simple Interest I – total interest earned for N period I=PiN i – interest rate N – number of interest period F=P+I P – principal or the present value F – future value or the total amount to be repaid Compound Interest F – future value or the total amount to be repaid F = P(1 + i)n P – principal or the present value i – interest rate n – number of interest period Effective Interest Rte EIR – effective interest rate F – future value or the total EIR = F – P amount to be repaid P P – principal or the present EIR= (1 + i)n - 1 value i – nominal interest rate n – interest period 9  AGRICULTURAL ECONOMICS Perpetuity P – principal or present value 1. To find for P given A: A – annuity i – interest rate P = (1 + i)n -1 n – interest period i (1 + i)n F – Future value or the total amount to be repaid 2. T find for A given P: i (1 + i)n A=P (1 + i)n - 1 3. To find for F given A: (1 + i)n - 1 A=P i 4. To find for A given F: A=F i (1 + i)n - 1 10  AGRICULTURAL ECONOMICS Perpetuity and Capitalized Cost P – capitalized value of A x – amount needed to provide P= x i for replacement or maintenance i (1 + i)n – 1 for K period Arithmetic Gradient A – uniform periodic amount equivalent to the arithmetic A=G 1 - n gradient series. i (1 = i)n – 1 G – arithmetic gradient change in periodic amounts t the end of each period. P = 1 - (1 + i)n - n P – present with of G i i (1 + i)n F – future worth of accommodated G P= G (1 + i)n -1 - n i i (1 + i)n F= G (1 + i)n – 1 - n i i Depreciation Cost d – annual depreciation Co – original cost Co - Cn n – useful life; years d = Cn – salvage value or the scrap n value Dm – accrued total depreciation Dm = m x d up to “m” years m – age of property at any time Cm = Co - Cm less than “n” Cm – book value t the end of “m” years 11  AGRICULTURAL ECONOMICS Sinking Fund Method d – annual depreciation Co – original cost d = ( Co – Cn) i n – useful life; years (1 + i)n - 1 Cn – salvage value or the scrap i value i – interest rate d – annual depreciation Co – original cost (1 + i)m - 1 n – useful life; years Cn – salvage value or the scrap i value Dm = (Co – Cn) Dm – accrued total depreciation (1 + i)n -1 up to “m” years i Declining Balance Method d – annual depreciation (Matheson Formula) Co – original cost n – useful life; years n K=1– Cn /Co Cn – salvage value or the scrap value d m = K Cm – 1 m – age of property at any time less than “n” Cm = Co (1 - K)m Cm – book value t the end of “m” years Cn = Co (1 –K)n Sum of the Years – Digits Co – original cost (SYD) Method n – useful life; years Cn – salvage value or the scrap ∑Years = n / 2 (n + 1) value Annual Depreciation = (Co – Cn) [n / ∑years] 12  AGRICULTURAL ECONOMICS Double Rate Declining Balance Co – original cost n – useful life; years Cm = Co (1 – 2 / n)m m – age of property at any time less than “n” Cm – book value t the end of “m” years Service Output Method T – total units of output produced during the life of property d1 = Co -Cn Qm – total units of output during year “m” T d1 – depreciation per unit of output Dm = Om d or Dm = (Co –Cn) Qm T Cm = Co - Dm Fixed Cost CF – fixed cost v – variable cost / unit Ct = Cp + Cv D – units produced Cv = vD CT – total cost CT = CF + vD Profit P – profit P = TR – TC TR – total revenue TC – total cost 13  ALGEBRA Laws of Exponents If m > n am. an = am+n m = n; a ≠ 0 am ÷ an = am-n = ao ( m n a ) = amn (ab)m = am bm (a/b)m = am / bm Rational Exponents a1/n = n√a am/n = n√am or (n√a)m Negative Exponents a-m = 1/ am (a-m / b) = (b /a)m 1 = am a-m Radicals A – is called the radicand m, n index (root) a1/n = n√ a am/n = n√am or (n√a)m 14  ALGEBRA Law of Radicals n √ an = a m n mn √ √ = √a m m m √a. √b = √ab m m √a = √a/b m √b Complex Number n is even i = √-1 = i2 = -1 n n √a = √a (i) Power of i (i = √-1)2 i2 = -1 Linear Equation in One Variable a≠0 ax + b = 0 15  ALGEBRA Special Products Factor Types 1. Common factor a ( x + y + z) = ax + ay + az 2. Square of binomial (a ± b)2 = a2 ± 2ab + b2 3. Sum or difference of two numbers (a + b) (a – b) = a2 – b2 4. Difference of two cubes (x – y) (x2 + xy + y2) = x3 – y3 5. Sum of two cubes (x + y) (x2 – xy + y2) = x3 + y3 6. Product of two similar numbers (x + b) (x + d) = x2 + (b + d) x + bd (ax + b) ( cx + d) = acx2 + (bc + ad)x + bd Quadratic Trinomial x2 + (b +d)x + bd = (x + b) (x +d) acx2 + (bc + ad)x + bd = (ax+b)(ax+d 16  ALGEBRA Factoring of Polynomial Functions with Rational Roots Form: anxn + an-1 xn-1 + an-2 xn-2 + …ax + a0 Possible roots: (r)=± factor of a0 factor of an Quadratic Equation in One Variable Form: Ax2 + bx + c = 0 Method of Solutions: Note: If b = 0, x = ±√ -c/a Avoid dividing an equation by variable so as not to loose roots. If factorable, use the theorem: If ab = 0, a = 0 or b = 0 17  ALGEBRA Quadratic Formula x = -b ± √ b2 – 4ac 2a The Discriminant: D = 0 Two identical and real roots D = b2 – 4ac D > 0 Two distinct and real roots D < 0 Two complex conjugates roots Sum and Products of Roots The sum (Xs) = -b/a X1 + X2 The product (Xp) = c/a X1X2 Linear Equation in Two Variables Forms: a1 x + b1y + c1 = 0 a2 x + b2y + c2 = 0 Method of Solution: 1. by elimination 2. by determinants 18  ALGEBRA Linear Equation of Three Variables a1 x + b1y + c1z + d1 = 0 a2 x + b2y + c2z + d2 = 0 a3 x + b3y + c3z + d3 = 0 Method of Solution: 1. by elimination 2. by determinants Quadratic Equations in Two Variable One Linear and One Quadratic: a1x + b1y = c1 a1x-2 + b1y2 = c2 Two Formulas Used in Solving a Problem in Arithmetic Progression: Last term (nth term) an = a1 + (n – 1) d Sum of all terms S = n/2 ( a1 + an) or S = n/2 2a1 + (n-1) d 19  ANIMAL SPACE REQUIREMENT (Minimum) Lairage SR - space requirement, m2 Na - number of animals SR = 2.23 Na : large/loose type SR = 3.30 Na : large/tie-up type SR = 0.70 Na : swine less than 100kg SR = 0.60 Na : swine more than100kg SR = 0.56 Na : small animals Goat and Sheep (Solid Floor) SR - space requirement, m2 Na - number of animals SR = 0.80 Na : 35 kg animal SR = 1.10 Na : 50 kg animal SR = 1.40 Na : 70 kg animal SR = 0.45 Na : kid/lamb SR = 3.00 Na : buck/ram Goat and Sheep (Slatted Floor) SR - space requirement, m2 Na - number of animals SR = 0.70 Na : 35 kg animal SR = 0.90 Na : 50 kg animal SR = 1.10 Na : 70 kg animal SR = 0.35 Na : kid/lamb SR = 2.60 Na : buck/ram 20  ANIMAL SPACE REQUIREMENT (Minimum) Goat and Sheep (Open Yard) SR - space requirement, m2 Na - number of animals SR = 2.00 Na : 35 kg animal SR = 2.50 Na : 50 kg animal SR = 3.00 Na : 70 kg animal Goat and Sheep (Lactating) SR - space requirement, m2 Na - number of animals SR = 1.30 Na : 50-70 kg pregnant SR = 1.60 Na : over 70 kg pregnant SR = 2.00 Na : 50-70 kg lactating SR = 2.30 Na : over 70 kg lactating Cattle Feed Lot SR - space requirement, m2 Na - number of animals SR = 4.00 Na : shed space SR = 5.00 Na : loafing area Cattle Ranch (Holding Pen) SR - space requirement, m2 Na - number of animals SR = 1.30 Na : up to 270 kg SR = 1.60 Na : 270-540 kg SR = 1.90 Na : over 540 kg 21  ANIMAL SPACE REQUIREMENT (Minimum) Cattle Shed or Barn SR - space requirement, m2 Na - number of animals SR = 1.00 Na : calves up to 3 mo SR = 2.00 Na : calves 2-3 mo SR = 3.00 Na : calves 7 mo-1 yr SR = 4.00 Na : yearling 1-2 yr SR = 5.00 Na : heifer/steer 2-3 yr SR = 6.00 Na : milking and dry cow SR = 10.00 Na : cows in maternity stall Carabao Feedlot SR - space requirement, m2 Na - number of animals SR = 4.00 Na Laying Hens (Growing 7-22 Weeks) SR - space requirement, m2 Na - number of birds SR = 0.14 Na : litter floor SR = 0.06 Na : slotted floor SR = 0.07 Na : slot-litter floor Laying Hens (Laying Beyond 22 SR - space requirement, m2 Weeks) Na - number of birds SR = 0.17 Na : litter floor SR = 0.09 Na : slotted floor SR = 0.14 Na : slot-litter floor 22  ANIMAL SPACE REQUIREMENT (Minimum) Broiler SR - space requirement, m2 Na - number of birds SR = 0.0625 Na : 4 week and below SR = 0.1250 Na : above 4 weeks Swine (Group of Growing Swine) SR - space requirement, m2 Na - number of SR = 0.11 Na : up to 10 kg animals SR = 0.20 Na : 11 to 30 kg SR = 0.35 Na : 21 to 40 kg SR = 0.50 Na : 41 to 60 kg SR = 0.70 Na : 61 to 80 kg SR = 0.85 Na : 81 to 100 kg Swine SR - space requirement, m2 Na - number of animals SR = 1.00 Na : Gilts up to mating SR = 2.50 Na : Adult pigs in group SR = 1.20 Na : Gestating sows SR = 7.50 Na : Boar in pens SR = 7.40 Na : Lactating sows and liters – individual pen SR = 5.60 Na : Lactating sows and liters - multi- suckling groups SR = 1.80 Na : Dry sows 23  BEARINGS Bearing Life L – bearing life, million revolution C – basic dynamic capacity, N F – actual radial load, N C n – 3 for ball bearing, and 3.33 for roller bearing L=[ ]n F Radial Load Acting on Shaft F – radial force on the shaft, N P – power transmitted, kW K – drive tension factor, 1 for chain drive and gears; and 1.5 for v-belt drive 19.1 x 106 P K Dp – pitch diameter of sheave, sprocket, etc, mm F= N – shaft speed, rpm Dp N Bearing Load in Belt Ft – effective force transmitted by belt or chain, kgf-mm H – power transmitted, kW N – speed, rpm 974 000 H r – effective radius of pulley or sprocket, mm Ft = N r 24  BEARINGS Actual Load Applied to Pulley shaft La – actual load applied to pulley shaft, kgf fb – belt factor, 2 to 2.5 for v-belt and 2.5 to 5 for flat belt; 1.25 to 1.5 for chain drive La = fb Ft Ft – effective force transmitted by belt or chain, kgf-mm Rating Life of Ball Bearing in Hours Lh – rating life of ball bearing, hours N - speed, rpm 106 0.33 C 3 C - basic load rating, kgf Lh = 500 P – bearing load, kgf 3 x 104 N P Rating Life of Roller Bearing in Hours Lh – rating life of roller bearing, hours N - speed, rpm 106 0.3 C 3.33 C - basic load rating, kgf Lh = 500 P – bearing load kgf 3 x 104 N P 25  BIOGAS Manure Production (Pig) Wm – weight of manure produced, kg Na - number of animals Wm = 2.20 Na Nd: 3-8 mos Nd - number of days Wm = 2.55 Na Nd: 18-36 kg Wm = 5.22 Na Nd: 36-55 kg Wm = 6.67 Na Nd: 55-73 kg Wm = 8.00 Na Nd: 73-91 kg Manure Production (Cow) Wm – weight of manure produced, kg Na - number of animals Wm = 14.0 Na Nd : Feedlot Nd - number of days Wm = 13.0 Na Nd : Breeding Wm = 7.5 Na Nd : Work Manure Production (Buffalo) Wm – weight of manure produced, kg Na - number of animals Wm = 14.00 Na Nd : Breeding Nd - number of days Wm = 8.00 Na Nd : Work Manure Production (Horse) Wm – weight of manure produced, kg Na - number of animals Wm = 13.50 Na Nd : Breeding Nd - number of days Wm = 7.75 Na Nd : Work Manure Production (Chicken) Wm – weight of manure produced, kg Na - number of birds Wm = 0.075 Na Nd : Layer Nd - number of days Wm = 0.025 Na Nd : Broiler 26  BIOGAS Volume of Mixing Tank (15% Vmt - volume of mixing tank, m3 Freeboard) wm - daily manure production, kg/day-animal Na - number of animals Vmt = wm Na Tm MR Tm – mixing time, day MR – mixing ratio, 1 for 1:1 and 2 for 1:2 Volume of Digester Tank (15% Vdt - volume of digester tank, m3 Freeboard) wm - daily manure production, kg/day-animal Na - number of animals Vdt = wm Na Tr MR Tr – retention time, day MR – mixing ratio, 1 for 1:1 and 2 for 1:2 Digester Dimension (Floating Type- Dd - inner diameter, m Cylindrical) Vd - effective digester volume, m3 r – height to diameter ratio Dd = [(4.6 x Vd) / (π x r)]1/3 Hd - digester height, m Hd = r Dd Digester Dimension (Floating Type- Sd - inner side, m Square) Vd - effective digester volume, m3 r – height to side ratio Sd = [(1.15 x Vd) / (r)]1/3 Hd - digester height, m Hd = r Sd 27  BIOGAS Digester Dimension (Floating Type- Wd - inner width, m Rectangular) Vd - effective digester volume, m3 r – height to width ratio Wd = [(1.15 Vd ) / ( r p2 )1/3 p - desired width and length proportion Hd - digester height, m Hd = r Ld Gas Chamber (Floating-Type Dg - inner diameter of gas chamber, m Cylindrical) Dd – inner diameter of digester, m Vs - effective gas chamber volume, m3 Dg = (45 Dd – w ) / 50 : w – gas chamber wall thickness, cm inner diameter h – height of pyramidal roof, m Hs - height of gas chamber, m h = Dg Tan 9.5 / 2 : Hp - desired pressure head, m height of pyramidal roof Hs = 1.15[{4 Vs / π Ds) + Hp] : height of gas chamber Gas Chamber (Floating-Type Lg - inner length of gas chamber, m Square/Rectangular) Wg - inner width of gas chamber, m Ld – inner length of digester, m Lg = (45 Ld – w ) / 50 : Wd – inner width of digester,m inner length Vs - effective gas chamber volume, m3 w – gas chamber wall thickness, cm Wg = (45 Ld – w ) / 50 : h – height of pyramidal roof, m inner width Hg - height of gas chamber, m Hp - desired prressure head, m h = Wg Tan 9.5 / 2 : height of pyramidal roof Hg = 1.15[{Vg/LgWg) + Hp]: height of gas chamber 28  BIOMASS COOKSTOVE Design Power Pd - design power, KCal/hr Pc - chracoal power, KCal/hr Pd = 0.7 ( Pc + Pv) Pv - max volatile, KCal/hr Power Output Po - power output, KCal/hr Fc - Fuel charges, kg Po = Fc Hf / Tb Hf - heating value of fuel; KCal/kg Tb - total burning time, hr Burning Rate BR - burning rate, kg/hr Po - power output, KCal/hr BR = Po / Hf Hf - heating value of fuel; KCal/kg Fuel Consumption Rate FCR - fuel consumption rate, kg/hr Wfc - Weight of fuel consumed, kg FCR = Wfc / To To – operating time, hr Power Density PD - power density, kg/hr-m2 FCR - fuel consumption rate, kg/hr PD = FCR / Ag Ag - area of grate, m2 Height of Fuel Bed Hfb - height of the fuel bed, m Fc - fuel charges, kg Hfb = Fc / (p ρf Ab ) p - packing density, decimal ρf - density of fuel, kg/h3 Ab - area of fuel bed, m2 Area of the Fuel Bed Afb - area of the fuel bed, m2 Pd - design power, KCal/hr Afb = Pd / PD PD - power density, KCal/hr-m2 29  BIOMASS COOKSTOVE Flame Height FH – flame height, mm C – grate constant, 76 mm/KW for fire with grate, FH = C P2/5 and 110 mm/KW for fire without grate P – power output, KCal/hr Cooking Time CT - cooking time, sec Mf - mass of food, kg CT = 550 Mf 0.38 Maximum Power Pmax - maximum power, KCal/hr Mf - mass of food, kg Cp - specific heat of food, KCal/kg-C Mf Cp (Tf – Ti) Tf - final temperature of food, C Pmax = Ti - initial temperature of food, C Tc ξt Tc - cooking time, hr ξ - thermal efficiency of the stove, decimal Thermal Efficiency ξt - thermal efficiency, % Mw – mass of water, kg Cp - specific heat of water, 1 KCal/kg-C Mw Cp (Tf – Ti) + We Hv Tf - final temperature of water, C ξt = x 100 Ti - initial temperature of water, C WFC HVF We - weight of water evaporated, kg Hv – heat of vaporization of water, 540 KCal/kg WFC – weight of fuel consumed, kg HVF – heating value of fuel, KkCal/kg 30  BIOMASS FURNACE Sensible Heat Qs - sensible heat, KCal M - mass of material, kg Qs = M Cp (Tf – Ti) Cp – specific heat of material, KCal/kg-C Tf – final temperature of material, C Ti - initial temperature of material, C Latent Heat of Vaporization Ql - latent heat of vaporization, KCal/hr m - mass of material, kg Ql = m Hfg Hfg - heat of vaporization of material, KCal/kg Design Fuel Consumption Rate FCRd - design fuel consumption rate, kg/hr Qr - heat required for the system, KCal/hr FCRd = Qr / ( HVF ξt ) HVF – heating value of fuel, KCal/kg ξt - thermal efficiency of the furnace, decimal Actual Fuel Consumption Rate FCRa - fuel consumption rate, kg/hr Wfc - Weight of fuel consumed, kg FCRa = Wfc / To To – operating time, hr Fuel Consumption Rate for Rice Husk FCR – fuel consumption rate, kg/hr Fueled Inclined Grate Furnace with BR – burning rate, 40-50 kg/hr-m2 Heat Exchanger Ag – grate area, m2 ξf – furnace efficiency, 50 to 70% FCR = (1000 BR x Ag) / (ξf x ξhe) ξhe – heat exchanger efficiency, 70-80% Fuel Consumption Rate for Rice Husk FCR – fuel consumption rate, kg/hr Fueled Inclined Grate Furnace BR – burning rate, 40-50 kg/hr-m2 without Heat Exchanger Ag – grate area, m2 ξf – furnace efficiency, 50 to 70% FCR = (100 BR x Ag) / ξf 31  BIOMASS FURNACE Burning Rate BR - burning rate, kg/hr-m2 FCR – fuel consumption rate, kg/hr BR = FCR / Ag Ag - area of grate; m2 Power Density PD - power density, kg/hr-m2 FCR - fuel consumption rate, kg/hr PD = FCR / Ag Ag - area of grate, m2 Area of the Fuel Bed Afb - area of the fuel bed, m2 Pd - design power, KCal/hr Afb = Pd / BR BR - burning rate, KCal/hr-m2 Air Flow Rate Requirement AFR - airflow rate, kg/hr FCR - fuel consumption rate, kg/hr AFR = FCR Sa Sa - stoichiometric air requirement, kg air per kg fuel Thermal Efficiency ξt - thermal efficiency, % Qs – heat supplied, KCal/hr Qs FCR – fuel consumption rate, kg/hr ξt = x 100 HVF – heating value of fuel, KCal/kg FCR HVF Burning Efficiency ξb - burning efficiency, % Hv - heating value of fuel, KCal/kg Hv - Hr Hr - heating value of ash residue, KCal/kg ξb = x 100 Hv 32  BOARDER IRRIGATION Maximum Stream Size per Foot Q max - maximum stream size per foot of width of Width of Boarder Strip the boarder strip, cfs S - slope, % Q max = 0.06 S 0.75 Minimum Stream size per Foot Qmin - minimum stream size per foot of width of Width of Boarder Strip the boarder strip, cfs S - slope, % Qmin = 0.004 S 0.5 333333333 33  CHAIN TRANSMISSION Speed and Number of Teeth Nr – speed of driver sprocket, rpm Nn – speed of driven sprocket, rpm Nr Tr = Nn Tn Tr – no. of teeth of driver sprocket Tn – no. of teeth of driven sprocket Length of Chain L – chain length, pitches C – center distance between sprockets, T2 + T1 T2 - T1 pitches L=2C + + T2 – no. of teeth on larger sprocket 2 4π2C T1 – no. of teeth on smaller sprocket Length of Driving Chain L – length of chain in pitches Cp - center to center distances in pitches T t T- t 1 T - no. of teeth on larger sprocket L = 2Cp + + + t - no. of teeth on smaller sprocket 2 2 2π Cp 34  CHAIN TRANSMISSION Pitch Diameter of Sprocket PD – pitch diameter of sprocket, inches P – pitch, inch P Nt – number of teeth of sprockets PD = sin (180/Nt) Chain Pull CP – chain pull, kg P – chain power, watts CP = 1000 (P / V ) V – chain velocity, m/s Chain Speed V – chain speed, m/s p – chain pitch, in V = p T N / 376 T – number of teeth of sprocket N – sprocket speed, rpm Speed Ratio Rs – speed ratio Tn – driven sprocket, inches Rs = Tn / Tr Tr – driver sprocket, inches Design Power DP - design power, Watts Pt - power to be transmitted, Watts S - service factor, 1.0 to 1.7 DP = Pt S / MSF MSF – multiple strand factor, 1.7 to 3.3 @ 2 to 4 strands 35  CHAIN TRANSMISSION Power Rating Required PR - Power rating required, Watts DP - design power, Watts DP DL DL - design life, hours PR = 15,000 Horsepower Capacity (At Lower Speed) HP – horsepower capacity, hp Tl – number of teeth of smaller sprocket HP = 0.004 T1 1.08 N1 0.9 P 3 - 0.007 P N1- speed of smaller sprocket, rpm P – chain pitch, inches Horsepower Capacity (At Higher Speed) HP – horsepower capacity, hp Tl – number of teeth of smaller sprocket 1.5 0.8 1700 T1 P N1- speed of smaller sprocket, rpm HP = P – chain pitch, inches N1 1.5 Center Distance C - center distance in mm P - pitch of chain in mm P Lp - length of chain in pitches C= [ 2Lp – T – t T - number of teeth in large sprocket 8 t - number of teeth in small sprocket + (2Lp - T- t )2 – 0.810 (T-t)2 ] 36 CONSERVATION STRUCTURES, DAMS AND RESREVIOR Capacity of drop spillway q – discharge, cubic meter per second C – weir coefficient q = 0.55 C L h3/2 L – weir length, meter h – depth of flow over the crest, meter Total width of the dam W – top width, meters H – maximum height of embankment, meters W = 0.4 H + 1 Wave height h – height of the wave from through to crest under ,maximum wind velocity, meters H = 0.014 (Df)1/2 Df – fetch or exposure, meters Compaction and settlement V = total in-place volume, m3 Vs = volume of solid particles, m3 V = Vs + Vo Vo = volume of voids, either air or water, m3 37  CONVEYANCE CHANNEL Continuity Equation Q - discharge, m3/sec A – cross-sectional area of the channel, m2 Q = AV V – velocity of water, m/sec Manning Equation V – velocity, m/sec n – Manning’s coefficient, 0.010 to 0.035 R – hydraulic radius, m V = (1.00 / n ) R 2/3 S 1/2 S – slope of water surface Chezy Equation V – flow velocity C - coefficient of roughness, 50 to 180 V = C ( R S )½ R – hydraulic radius, m S – slope of water surface, decimal Hydraulic Radius R – hydraulic radius, m A – cross-sectional area of flow, m2 R=A/P P – wetted perimeter, m Best Hydraulic Cross-Section b - bottom width of channel, m d – depth of water in the canal, m b = 2 d tan (θ / 2) θ - angle between the side slope and the horizontal 38  CONVEYANCE CHANNEL Cross-Sectional Area of Channel A - cross sectional area, m2 b – base width of the channel, m A = b d + z d2 : Trapezoidal d – depth of water, m A = z d2 : Triangular z - canal slope h/d, decimal A = 2/3 + t d : Parabolic t - top width, m Wetted Perimeter of Channel WP - wetted perimeter, m b – base width of the channel, m WP = b + 2d ( z2 + 1 ) ½ : d – depth of water, m Trapezoidal z - canal slope h/d, decimal t - top width, m WP = 2d ( z2 + 1 ) ½ : Triangular WP = t + ( 8 d2 / 3t ) : Parabolic Top Width t - top width, m b – base width of the channel, m t = b + 2 d z : Trapezoidal d – depth of water, m t = 2dz : Triangular z - canal slope h/d, decimal t = A /(0.67 d) : Parabolic A - cross sectional area, m2 Discharge ( Float Method) Q - discharge, m3/s C – coefficient, 2/3 Q = C A Vmax A - cross-sectional area of the stream, m2 Vmax - average maximum velocity of stream, m/s 39  CORN SHELLER Kernel-Ear Corn Ratio R – grain ratio, decimal Wk – weight of kernel, grams R = (Wk / Wec) Wec – weight of ear corn, grams Actual Capacity Ca – actual capacity, kg/hr Ws -weight of shelled kernel, kg Ca = Ws / To To – operating time, hr Corrected Capacity Cc – corrected capacity, kg/hr MCo – observed moisture content, % 100 - MCo MCr – reference MC, 20% Cc = -------------- x P Ca P – kernel purity, % 100 - MCr Ca – actual capacity, kg/hr Purity P – purity, % Wu – weight of uncleaned kernel, grams P = ( Wc / Wu ) 100 Wc – weight of cleaned kernel, grams Total Losses Lt – total losses, kg Lb – blower loss, kg Lt = Lb + Ls + Lu + Lsc Ls – separation loss, kg Lsc – scattering loss, kg Lu – unthreshed loss, kg 40  CORN SHELLER Shelling Efficiency ξ s – shelling efficiency,% Wc – weight of clean shelled kernel, kg Wc + Lb + Ls + Lsc Lb – blower loss, kg ξs = x 100 Ls – separation loss, kg Wc + Lb + Ls + Lu + Ls Lsc – scattering loss, kg Lu – unthreshed loss, kg Fuel Consumption Fc – fuel consumption, Lph Fu - amount of fuel used, liters Fc = Fu / to To – operating time, hrs Shelling Recovery Sr – threshing recovery, % Wc – weight of clean shelled kernels, kg Wc Lb – blower loss, kg Sr = x 100 Ls – separation loss, kg Wc + Lb + Ls + Lu + Ls Lsc – scattering loss, kg Lu – unthreshed loss, kg Cracked Kernels Ck – percentage cracked kernel, % Nck – number of cracked kernels Ck = Nck 100 / 100 kernel sample Mechnically Damaged Kernel Dk – percentage damage kernel, % Ndk – number of damaged kernels Dk = Ndk 100 / 100 kernel sample 41  COST-RETURN ANALYSIS Investment Cost IC - investment cost, P EC - equipment cost, P IC = MC + PMC PMC – prime mover cost, P Total Fixed Cost FC – total fixed cost, P/day D - depreciation, P/day FCt = D + I + RM + i I - interest on investment, P/day RM - repair and maintenance, P/day i - insurance, P/day Total Variable Cost VCt - total variable cost, P/day L - labor cost, P/day VCt = L + F + E F – fuel cost, P/day E – electricity, P/day Total Cost TC – total cost, P/day FCt – total fixed cost, P/day TC = FCt + VCt VCt - total variable cost, P/day Operating Cost OC - operating cost, P/ha or P/kg TC - total cost, P/day OC = TC / C C - capacity, Ha/day or Kg/day 42  COST-RETURN ANALYSIS Depreciation (Staight Line) D - depreciation, P/day IC - investment cost, P IC - 0.1 IC LS – life span, years D= 365 LS Interest on Investment I - interest on investment, P/day Ri - interest rate, 0.24/year I = Ri IC / 365 IC – investment cost, P Repair and Maintenance RM – repair and maintenance, P/day Rrm - repair and maintenance rate, 0.1/year RM = Rrm IC / 365 IC - investment cost, P Insurance i - insurance, P/day Ri - insurance rate, 0.03/year i = Ri IC / 365 IC - investment cost, P Labor Cost L - labor cost, P/day NL – number of laborers L = NL Sa Sa – salary, P/day Fuel Cost F - fuel cost, P/day Wf - weight of fuel used, kg F = Wf Cf Cf - cost of fuel, P/kg 43  COST-RETURN ANALYSIS Electricity E – cost of electricity, P/day Ec - electrical consumption, KW-hr E = Ec Ce Ce – cost of electricity, P/KW-hr Net Income NI - net income, P/yr CR – custom rate, P/ha or P/kg NI = (CR - OC) C OP OC – operating cost, P/ha or P/kg C - capacity, Ha/day or Kg/day OP – operating period, days/year Payback Period PBP – payback period, years IC - investment cost, P PBP = IC / NI NI - net income, P/yr Benefit Cost Ratio BCR - benefit cost ratio, decimal NI - net income, P/year BCR = NI / (TC OP) TC – total cost, P/day OP – operating period, days per year Return on Investment ROI - return on investment, % TC - total cost, P/year ROI = ( TC / NI ) 100 NI - net income, P/year 44  CYCLONE SEPARATOR Diameter of Cyclone Separator Dc - diameter of cyclone separator, m Q – airflow, m3/hr Vt – velocity of air entering the cyclone, m/s Dc = ( Q / 0.1 Vt ) 0.5 Pressure Draft of the Cyclone Pd - pressure drop, mm Da – air density, 1.25 kg/m3 Vt – velocity of air entering the cyclone, m/s 6.5 Da Vt 2 Ad Ad – inlet area of the duct, m2 Pd = Ds - diameter of separator, m Ds Cyclone Cylinder Height (High Hcy – cylinder height, m Efficiency) Dc - cyclone diameter, m Hcy = 1.5 Dc Inverted Cone Height (High Efficiency) Hco - cone height, m Dc - cyclone diameter, m Hco = 2.5 Dc Air Duct Outlet Diameter (High Do - air duct outlet diameter, m Efficiency) Dc - cyclone diameter, m Do = 0.5 Dc 45  CYCLONE SEPARATOR Air Duct Outlet Lower Height (High HDOl - lower height of air duct outlet, m Efficiency) Dc - cyclone diameter, m HDOl = 1.5 Dc Air Duct Outlet Upper Height (High HDOu - upper height of air duct outlet, m Efficiency) Dc - cyclone diameter, m HDOu = 0.5 Dc Width of the Inlet Rectangular Square Duct WD – width of the inlet duct, m (High Efficiency) Dc – cyclone diameter, m WD = 0.2 Dc Height of the Inlet Rectangular Square Duct HD – height of the inlet duct, m (High Efficiency) Dc – cyclone diameter, m HD = 0.5 Dc Cylinder Height (Medium Efficiency) Hcy – cylinder height, m Dc - cyclone diameter, m Hcy = 1.5 Dc Inverted Cone Height (Medium Efficiency) Hco - cone height, m Dc - cyclone diameter, m Hco = 2.5 Dc 46  CYCLONE SEPARATOR Air Duct Outlet Diameter (Medium Do - air duct outlet diameter, m Efficiency) Dc - cyclone diameter, m Do = 0.75 Dc Air Duct Outlet Lower Height (Medium HDOl - lower height of air duct outlet, m Efficiency) Dc - cyclone diameter, m HDOl = 0.875 Dc Air Duct Outlet Upper Height (Medium HDOu - upper height of air duct outlet, m Efficiency) Dc - cyclone diameter, m HDOu = 0.5 Dc Width of the Inlet Rectangular Square WD – width of the inlet duct, m Duct (Medium Efficiency) Dc – cyclone diameter, m WD = 0.375 Dc Height of the Inlet Rectangular Square HD – height of the inlet duct, m Duct and Upper Cyclone Cylinder Dc – cyclone diameter, m (Medium Efficiency) HD = 0.75 Dc 47  DIFFERENTIAL CALCULUS d (u + v) = du + dv d (log 10u) = 0.4343. du/dx dx dx dx dx u = du/dx. log 10e d u/v = vdu - udv u dx dx dx d (√u) = du/dx 2 v dx 2√u d (xn) = nxn-1 dx d (sin u) = cos u.du/dx dx d u.v = vdu + udv dx dx dx d (cos u) = -sin u.du/dx dx d (un) = nun-1 du dx dx d (tan u) = sec2 u.du/dx dx d (ln u) = du/dx dx u d (csc u) = -cscu.cot u.du/dx dx d (au) = au. ln a. du/dx dx d (sec u) = secu.tan u.du/dx dx d (eu) = eu. du/dx dx d (cot u) = csc2 u.du/dx dx eln u = u d (arcsin u) = du/dx e0 = 1 dx √1-u2 48  DIFFERENTIAL CALCULUS d (arctan u) = du/dx d (arccos u) = - du/dx dx 1 + u2 dx √1-u2 d (arcsec u) = du/dx xm/n = (n√ x )m dx u √u2-1 d (sin h u) = cos h u.du/dx d (arccsc u) = - du/dx dx dx u √u2-1 d (cos h u) = sin h u.du/dx d (arccot u) = - du/dx dx dx 1 + u2 d (tan h u) = sec h2 u.du/dx d (log au) = du/dx. log ae dx dx du d (csc h u) = -csc h u cot h u.du/dx dx d (sec h u) = -sec h u tn h u.du/dx dx d (cot h u) = -csc h2 u.du/dx dx 49  DRIP IRRIGATION Maximum Depth of Irrigation Idn - maximum net depth of each irrigation application, mm Idn = Ds [ (Fc - Wp) / 100 ] Dd P Ds - depth of soil, m Fc - field capacity, % Wp - wilting point, % Dd - portion of the available moisture allowed to deplete, mm P - area wetted, % of total area Irrigation Interval Ii - irrigation interval, days Id - gross depth of irrigation, mm Ii = [Id TR EU ] / 100T TR - ratio of transpiration to application, 0.9 EU - emission uniformity, % T = ET (min of PS/85) ET - conventionally accepted consumptive use rate of crop, mm/day PS - area of the crop as percentage of the area, % Gross Depth of Irrigation Id - gross depth of irrigation, mm Idn - maximum net depth of each irrigation application, Id = 100 Idn / [TR EU] mm TR - ratio of transpiration to application, 0.9 EU - emission uniformity, % 50  DRIP IRRIGATION Average Emitter Discharge Qa - emitter discharge, m3/hr k - constant, 1 for metric unit Qa = k [Id Se Sl] / It Id - gross depth irrigation, m Se - emitter spacing on line, m Sl - average spacing between lines, m It - operational unit during each of irrigation cycle, hrs Lateral Flow Rate Ql - lateral flow rate, lps Ne - number of emitters on laterals Ql = 3600 Ne Qa Qa - emitter discharge, m3/hr 51  ELECTRICITY Power (DC) P – power, Watts V – voltage, volt P = VI I – current, Ampere Power (AC) P – power, volt-ampere V – voltage, volt P = VI I – current, Ampere Power (AC) P – power, Watts V – voltage, volt P = V I pf I – current, Ampere pf – power factor Ohms Law (DC) I – current, Ampere V– voltage, volt I = V/R R – resistance, ohms Ohms Law (AC) I – current, Ampere V – voltage I= V/Z Z – impedance Power P – power, Watts I – current, Ampere P= I2 R R – resistance, ohms Power P – power, Watts V – voltage, volts P = V2 / R R – resistance, ohms 52  ELECTRICITY Resistance P – power, Watts I – current, Ampere R = P / I2 R – resistance, ohms Resistance P – power, Watts V – voltage, volts R = V2 / P R – resistance, ohms Voltage V – voltage, volt P – power, Watts V=P/ I I – current, Ampere Voltage (Series) Vt – total voltage, volt V1 – voltage 1, volt Vt = V1 + V2 + V3 … V2 – voltage 2, volt V3 – voltage 3, volt Resistance (Series) Rt – total resistance, ohms R1 – resistance 1, ohms Rt = R1 + R2 + R3 … R2 – resistance 2, ohms R3 – resistance 3, ohms Current (Series) It – total current, ampere I1 – current 1, Ampere It = I1 = I2 = I3 I2 – current 2, Ampere I3 – current 3, Ampere 53  ELECTRICITY Voltage (Parallel) Vt – total voltage, volt V1 – voltage 1, volt Vt = V1 = V2 = V3 V2 – voltage 2, volt V3 – voltage 3, volt Resistance (Parallel) Rt – total resistance, ohms 1 R1 – resistance 1, ohms Rt = R2 – resistance 2, ohms 1/R1 + 1/R2 + 1/R3 R3 – resistance 3, ohms Current (Parallel) It – total current, Ampere I1 – current 1, Ampere It = I1 + I2 + I3 I2 – current 2, Ampere I3 – current 3, Ampere Energy E – energy, Watt-hour P – power, Watts E=PT T – time, hour 54  ELECTRICITY Current (Parallel) It – total current, Ampere I1 – current 1, Ampere It = I1 + I2 + I3 I2 – current 2, Ampere I3 – current 3, Ampere Energy E – energy, Watt-hour P – power, Watts E=PT T – time, hour Power Factor pf – power factor E – voltage, volt Pr E I cos θ I – current, ampere pf = ------------ = ------------- Pr – real power, watts Pa EI Pa – apparent power, watts R – resistance, ohms = cos R/Z Z – impedance, ohms KVA (Single Phase Circuit) KVA – kilovolt ampere E – voltage, volt E I I – current, ampere KVA = 1000 KVA (Three-Phase Circuit) KVA – kilovolt ampere E – voltage, volt 1.732 E I I – current, ampere KVA = 1000 Horsepower Output (Single-Phase) HP – power output, hp E – voltage, volt η I E pf I – current, amperes HP = η - efficiency, decimal 746 pf – power factor, decimal 55  ELECTRIC MOTOR Horsepower Output (Three-Phase) HP – power output, hp E – voltage, volt η I E pf I – current, amperes HP = √3 η - efficiency, decimal 746 pf – power factor, decimal Power in Circuit (Single-Phase) P – power, watts E – voltage, volts P=EI I – current, ampere Power in Circuit (Three Phase) P – power, watts E – voltage, volts P = √3 E I I – current, ampere KVA (Single-Phase Circuit) KVA – kilovolt ampere E – voltage, volt E I I – current, ampere KVA = 1000 KVA (Three-Phase Circuit) KVA – kilovolt ampere E – voltage, volt 1.732 E I I – current, Ampere KVA = 1000 Horsepower Output (Single-phase) HP – power output, hp E – voltage, volt η I E pf I – current, amperes HP = η - efficiency, decimal 746 pf – power factor, decimal 56  ELECTRIC MOTOR Horsepower Output (Three-phase) HP – power output, hp E – voltage, volt η I E pf I – current, amperes HP = √3 η - efficiency, decimal 746 pf – power factor, decimal Slip (Three-Phase Motor) S - slip, decimal Ns – motor synchronus speed, rpm S = [Ns – N ] / Ns N – actual motor speed, rpm Power in Circuit (Single-Phase) P – power, Watts E – voltage, volts P=EI I – current, Ampere Power in Circuit (Three-Phase) P – power, Watts E – voltage, volts P = √3 E I I – current, Ampere Rotr Speed (Synchronous Motor) Ns – rotor speed, rpm F - frequency of stator volatge, hertz Ns = 120 [ f / P ] P–n umber of pole Motor Size to Replace Engine MHP - motor power, hp EHP - engine power, hp MHP = EHP 2/3 Motor Size to Replace Human MHP - motor power, hp NH - number of human MHP = NH 1/4 57  ELECTRIFICATION Energy Loss in Lines Le – energy loss, KW-hr Vl - voltage loss in line, volt Vl I To I - current flowing, Amp Le = To - operating time, hr 1000 Area Circular Mill Acm - area, circular mill D - diameter, mill or 1/1000 of an inch Acm = D 2 Energy Consumption (Disk Meter) EC = electrical consumption, KW-hr Kh - meter disk factor, 2.5 60 Kh Drev Drev – number of revolutions, rev EC = Tc - counting period, min 1000 tc Minimum Number of Convenience Nco - minimum number of convenience outlet, Outlet pieces of duplex receptacle Pf - floor perimeter, ft Nco = Pf / 20 No. of Branch Circuit (15-amp) Nbc - number of branch circuit Af - floor area, ft2 Nbc = Af / 500 NOgp - number of general outlet Nbc = NOgp / 10 58  ELECTRIFICATION No. of Branch Circuit (20 Nbc - number of branch circuit Amp) NOsa - number of small appliance outlet Nbc = NOsa / 8 Resistance of Copper Wire R - resistance in wire, ohms L – length of wire, ft 10.8 L A - cross sectional area of wire, cir mil R = A Wire Size Selection A - area of wire, circular mill Nw - number of wires L - length of wire, ft 10.8 Nw L I I - current flowing, amp A = ------------------ Vd - allowable voltage drop, decimal equal to 0.02 adequate Vd E for all conditions E – voltage, volt Lamp Lumen Required Ll - lamp lumen required, lumen Li - light intensity, foot candle Li Af Af - floor area, ft2 Ll = CU - coefficient of utilization, 0.04 to 0.72 CU SF SF - service factor, 0.7 Maximum Lamp Spacing MS - maximum lamp spacing, ft (Florescent Lamp) Ci - lamp coefficient, 0.9 for RLM standard-dome frosted lamp and 1.0 for RLM standard silvered-bowl lamp MS = Ci MH MH – Lamp height, ft Maximum Lamp Spacing MS - maximum lamp spacing, ft (Incandescent Lamp) Cf - lamp coefficient, 0.9 for Direct RLM with louvers, 1.0 for direct RLM 2-40 watts, and 1.2 for indirect-glass, MS = Cf MH plastic, metal MH - lamp height, ft 59  ENGINE Indicated Horsepower IHP – indicated horsepower, hp P – mean effective pressure, psi PLANn L – length of stroke, ft IHP = A – area of bore, in2 33000 c N – crankshaft speed, rpm n – number of cylinder c - 2 for four stroke engine and 1 for two stroke engine Piston Displacement PD – piston displacement, cm3 Dp – piston diameter, cm π D2 L – length of stroke, cm PD = L n n – number of cylinders 4 Piston Displacement Rate PDR – piston displacement rate, cm3/min PD – piston displacement, cm3 PDR = 2 π PD N N – crankshaft speed, rpm Compression Ratio CR – compression ratio PD – piston displacement, cm3 PD + CV CV – clearance volume, cm3 CR = CV Brake Horsepower BHP – brake horsepower, hp IHP – indicated horsepower, hp BHP = IHP ξm or ξm – engine mechanical efficiency, decimal FHP – friction horsepower, hp = IHP - FHP 60  ENGINE Mechanical Efficiency BHP – brake horsepower, hp IHP – indicated horsepower, hp BHP ξm – engine mechanical efficiency, decimal ξm = x 100 IHP Rate of Explosion ER – explosion rate, explosion per minute N – crankshaft speed, rpm N C – 2 for four stroke engine ER = c Thermal Efficiency, Theoritical ξtheo –theoretical thermal efficiency, % Wt – theoretical work, kg-m C Wt Qt – supplied heat quantity, Kcal/hr ξtheo = x 100 C – conversion constant Qt Thermal Efficiency, Effective ξeff – effective thermal efficiency, % Ne – Effective output, watt C Ne Hu – calorific value of fuel, kCal/kg ξeff = x 100 B - indicated work, kg/hr Hu B C – conversion constant 61  ENGINE Specific Fuel Consumption SFC – specific fuel consumption, kg/W-sec V – fuel consumption, m3 V Ne – Brake output SFC = S T – time, sec Ne t S – specific gravity of fuel, kg/m3 Break Mean Effective Pressure BMEP – brake mean effective pressure, kg/cm2 BHP – brake horsepower, hp (75) 50 BHP L – piston stroke, m BMEP = A – piston area, cm2 LANn N – number of power stroke per minute N – number of cylinders Number of Times Intake Valve TO – number of time intake valve open Open N – crankshaft speed, rpm C – 2 for four stroke engine - 0 for two stroke engine N TO = c Piston Area Ap - piston area, cm2 D – piston diameter, cm π D2 Ap = 4 62  ENGINE Stroke to Bore Ratio R – stroke to bore ratio S – piston stroke, cm S B – piston diameter, cm R= B BHP Correction Factor (Gasoline Engine- Kg – BHP correction factor. Dmls Carburator or Injection) T – ambient air temperature, C Pb – total atmospheric pressure, mb 0.5 1013 T + 273 Kg = -------- x ----------- Pb 293 BHP Correction Factor (Diesel Engine-4 Kd – BHP correction factor. Dmls Stroke Naturally Aspirated) T – ambient air temperature, C Pb – total atmospheric pressure, mb 0.65 0.5 1013 T + 273 Kd = ------- x ---------- Pb 293 Output Power Po – power output, KW T – shaft torque, kg-m T N N – shaft speed, rpm Po = 974 63  ENGINE Fuel Consumption Fc – fuel consumption, lph Fu – fuel used, liters Fc = Fu / To To – total operating time, hrs Specific Fuel Consumption SFC – specific fuel consumption, g/KW-hr Fc – fuel consumption, lph SFC = Fc ρf / Ps ρf - fuel density, kg/liter Ps – shaft power, KW Fuel Equivalent Power Pfe - fuel equivalent power, kW Hf - heating value of fuel, kJ/kg Pfe = [Hf mf ] / 3600 mf - rate of fuel consumption, kg/hr Air Fuel Ratio A/F - mass of air required per unit mass of fuel x, y, z – number of carbon, hydrogen, and oxygen atoms 137.3 [ x + y/4 – z/2 ] in the fuel molecule A/F = φ - equivalence ratio φ [ 12 x + y + 16 z ] Air Handling Capacity ma – air handling capacity, kg/hr Ve – engine displacement, liters ma = 0.03 Ve Ne ρa ηv Ne – engine speed, rpm ρa - density of air, 1.19 kg/m3 ηv - air delviery ratio0.85 for CI, 2.0 turbocharge engine Engine Air Density ρa - density of inlet air, kg/m3 ρex - density of engine exhaust, kg/m3 ρa = p / 0.287 Θ : inlet p – gas pressure, kPa Θ - gas temperature, K ρex = p / 0.277 Θ : exhaust 64  ENGINE FOUNDATION Weight of Foundation Wf - weight of foundation, kg ε - empirical coefficient, 0.11 Wf = ε We [ N ] 0.5 We - weight of engine and base frame, kg N - maximum engine speed, rpm Volume of Foundation Vf - volume of foundation, m3 Wf - weight of foundation, kg Vf = Wf / ρc ρc - density of concrete, 2,4006 kg/m3 Depth of Foundation Df - depth of foundation, m Vf - volume of foundation, m3 Df = Vf / [ we + Le ] we - width of engine plus allowance, m Le - length of engine plus allowance, m Exerted Soil Pressure at the Ps - soil pressure exerted at the based of foundation, kg/m2 Foundation We - weight of engine, kg Wf - weight of foundation, kg Ps = [We + Wf ] / Af Af - area of foundation , kg Factor of Safety FS - factor of safety, dmls BCs - safe soil bearing capacity, 12,225 kg/m2 Ps - soil pressure exerted at the based of foundation, kg/m2 FS = BCs / Ps 65  FLAT AND V-BELT TRANSMISSION Width of Flat belt W – width of flat belt, in. R – nameplate horsepower rating of motor, hp R M K – theoretical belt capacity factor, 1.1 to 19.3 W= P – pulley correction factor, 0.5 to 0.1 K P Width of Belt W - width of belt, mm H - power transmitted, Watts H S S - service factor, 1.0 to 2.0 W = K - power rating of belt, watts/mm K C C - arc correction factor, 0.69 at 90 deg and 1.00 at 180 deg Horespower Rating of Belt H – horsepower rating of belt, hp W – width of belt, in W K P M – motor correction factor, 1.5 to 2.5 H= P – pulley correction factor, 0.5 to 1.0 M K – theoretical belt capacity factor, 1.1 to 19.3 66  FLAT AND V-BELT TRANSMISSION Speed and Diameter Nr – speed of driver pulley, rpm Nn – speed of driven pulley, rpm Nr Dr = Nn Dn Dr – diameter of driver pulley, inches Dn – diameter of driven pulley, inches Length of Belt (Open drive) L – length of belt, inches C – center distance between pulleys, inches (Dr – Dn) 2 Dr – diameter of driver pulley, inches L = 2 C + 1.57 (Dr + Dn) + Dn – diameter of driven pulley, inches 4C Length of Belt (Cross drive) L – length of belt, inches C – center distance between pulleys, inches (Dr + Dn) 2 Dr – diameter of driver pulley, inches L = 2 C + 1.57 (Dr + Dn) + Dn – diameter of driven pulley, inches 4C 67  FLAT AND V-BELT TRANSMISSION Length of Belt (Quarter-Turn drive) L – length of belt, inches C – center distance between pulleys, inches Dr – diameter of driver pulley, inches L = 1.57(Dr+Dn) + √ C2+Dr2 + √ C2+Dn2 Dn – diameter of driven pulley, inches Belt Speed V – belt speed, fpm Np – pulley speed, rpm V = 0.262 Np Dp Dp – pulley diameter, inches Speed Ratio Rs – speed ratio Nn – driven pulley, inches Rs = Nn / Nr Nd – driver pulley, inches Arc of Contact Arc – arc of contact, degrees Dl – diameter of larger pulley, inches (Dl – Ds) Ds – diameter of smaller pulley, inches Arc = 180° - 57.3 C – center distance between pulleys, inches C 68  FLAT AND V-BELT TRANSMISSION Effective Pull (T1-T2) - effective pull, N P – power, KW 1000 P V – belt speed, m/s (T1 – T2) = V Center Distance C – distance between centers of pulley, mm Ls – available belts standard length, mm Dl – diameter of larger pulley, mm b + b2 - 32 (Dl – Ds) 2 Ds – diameter of small pulley, mm C = 16 b = 4Ls – 6.28 (Dl + Ds) Length of Arc La – length of arc, mm D – diameter of pulley, mm D A A – angle in degrees subtended by the arc of belt La = contact on pulley, deg 115 69  FLUID MECHANICS Density, ρ m – mass, kg, slug ρ = m/v v – volume, m3, ft3 Specific volume, υ v – volume, m3, ft3 υ = v/m m – mss, kg, slug Specific weight, γ, ω ρ – density, kg/m3, slug/ft3 γ = ω = ρg g – gravitational acceleration, ft/sec2, m/sec2 Specific gravity, s subs – substance ssubs = ρsubs std subs – standard substance ρstd subs = γsubs γstd subs Vapor Pressure, Pv Pv – vapor pressure Pv α Ts Ts – saturation or boiling Temperature Viscosity v – kinematic viscosity, m2/sec v = μ/ρ μ – absolute viscosity, Pasec ρ – density, kg/m3 Ideal Gas P – absolute pressure, kPaa Equation of State: v – total or absolute volume, m3 Pv = mRT R – gas constant, 8.3143 kJ/M kg K, 1545.32 ft lb/M lb °R M – molecular weight of gas T – absolute temperature, K Gas constant and specific heat Cp – specific heat at constant pressure R = Cp – Cv Cv – specific heat at constant k = Cp/Cv > 1.0 volume R – gas constant k – specific heat ratio Gay – Lussac’s Law P1 – initial absolute pressure, kPaa,psia P2 – final absolute pressure, kPaa, psia Pv = Pv T1 - initial absolute temperature, K, °R mT mT T2 – final absolute temperature, K, °R 1 2 v1 – absolute initial volume, m3, ft3 m1 ≠ m2 v2 - absolute final volume, m3, ft3 P1v1 = P2v2 m1 – initial mass, kg, lb m1T1 m2T2 m2 – final mass, kg, lb m1 = m2 P1v1 = P2v2 T1 T2 70  FLUID MECHANICS Boyle’s Law υ1 – initial specific volume,