Solution Manual For Mathematics for Plumbers and Pipefitters, 8th Edition

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’s Guide toAccompanyMathematicsforPlumbersandPipefittersSmith • Eighth Edition

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CONTENTSSECTION 1REVIEW OF BASIC FUNDAMENTALSUnit 1Some Basic Rules for Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1Unit 2Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1Unit 3Solving Formulas/Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1Unit 4Square Root . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1Unit 5Review of Angle Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2Unit 6Conversion of Length Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2SECTION 2PIPE LENGTH CALCULATIONSUnit 7Standard Weight Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Unit 8Allowance for Threaded Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Unit 9Copper Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Unit 10Allowance for Copper Fittings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Unit 11Plastic Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Unit 12Allowance for Plastic Fittings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Unit 13Welding Steel Piping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Unit 14Allowance for Weld-Type Fittings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Unit 15Equal Spacing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Unit 16Angles in Plumbing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5Unit 17Offset, Diagonal, Rise, and Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5Unit 18Solving for 45° Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6Unit 1945° Diagonal and Pipe Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7Unit 20Three-Pipe Diagrams with a 45° Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7Unit 21Right Angle with a 45° Diagonal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9Unit 2245° Offset with Wye Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9Unit 23Wye and Tee-Wye Assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10Unit 24The 0.707 Constant in 45° Pipe Assemblies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12Unit 25Solving for Other Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13Unit 26Pipe Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14Unit 27Cast Iron Pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14Unit 28Cast Iron Assemblies with Various Bends. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15Unit 291⁄5Bend Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16Unit 30Assemblies with Cast Iron Wyes and Tee-Wyes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17Unit 31Single Loop Back-Venting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17Unit 32Grade, Percent Grade, Drop and Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18Unit 33Elevation and Grade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18Unit 34Elevation in Plan View Pipe Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19Unit 35Jumper Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19Unit 3645° Offsets in Parallel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21Unit 37Special Case of 45° Offsets in Parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22Unit 38Rolling Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23Unit 39Combination Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24Unit 40Pipe Length by Layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25Unit 41Cast Iron Flanged Fittings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30Unit 42Miter Cuts, Welded Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30Instructorʼs Guideiii

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SECTION 3SHEET METAL WORKUnit 43Shower Pan or Safe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31Unit 44Rectangular Tank Liner. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32Unit 45Cylindrical Stretchouts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34Unit 46Roof Pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36SECTION 4VOLUMES, PRESSURES, AND CAPACITIESUnit 47Water Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37Unit 48Rectangular Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37Unit 49Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37Unit 50Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37Unit 51Segments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38Unit 52Partially Filled Containers of Varying Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38Unit 53Water Pressure, Head, Force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38Unit 54Ratio of Pipe Capacities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38Unit 55Pipe Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39SECTION 5PHYSICSUnit 56Mechanical Advantage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39Unit 57States of Matter and Why it Matters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40Unit 58Properties of Gases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40SECTION 6HEATINGUnit 59Heat Loss vs. Radiation Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40Unit 60Radiation Sizing for Total Heat Loss of a Room . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41Unit 61Estimating Size of Piping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42Unit 62Sizing Ventilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42Unit 63Heating Problems—Two-Floor House . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42SECTION 7THE BUILDERʼS LEVELUnit 64Word Use in Leveling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44Unit 65Math Aids in Leveling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45SECTION 8THE BUSINESS OF PLUMBINGUnit 66Starting a Business. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46Unit 67Taking Care of Business. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46ivInstructorʼs Guide

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SECTION 1REVIEW OF BASIC FUNDAMENTALSUNIT 1SOME BASIC RULES FOR MATHEMATICSAnswer these questions.1) What kind of measure is used to describe the size of a car’s fuel tank? Cubic, volume, three dimensional.2) What kind of measure is used to order fabric? Square, area, two dimensional.3) The distance between cities is expressed with what kind of measure? Lineal or linear.1. 15.74. 17007.310. 1913. 0.333 or1/32. 9.425. 85408. 911. 03. 38.277 or 38.27666.69.212. 4UNIT 2FORMULASDo the following problems.1) 334155) 3(54)2849) 364392) (33)4246) (35)422410) (364)333) 3(34)157) 3(542)2411) 3(643) 154) 3342518) 3436912) 3[(64)3] 2713) 11624432A.1. P50-0B.1. A210.25 sq. in.C.1. V1,728 cu. in.2. 942 m2. A1,225 cm22. V1,000 cm33. P67-63. A15.75 sq. ft.3. V180 cu. yd.4. P19.5 m4. A15.75 m24. V154 m35. C40.0355. A117 sq. ft.5.V3,264 cu. ft.6. C101.422 cm6. A216 sq. in.6. V302.76 cm37. P35.98 ft.7. A864 cm27. V699.435 cu. ft.8. A254.34 sq. in.8. V11,627.42 cm39. A2,122.64 cm29. V5,699.10 cu. in.10. A196.25 cm210.ALW11.VSShUNIT 3SOLVING FORMULAS/EQUATIONSPractice problems:Formula: ALW: this is the formula for the area of a rectangle. Area is equal to length multiplied times width.1. 603. 205. 172. 94. 126. 4.51. 15 ft.5. 7.019. 4radius2. 4 m6. 17.83 cm8diameter3. 16-67. 4.810. 6 cm radius4. 21 m8. 4 cm12 cm diameterUNIT 4SQUARE ROOT1. 103. 32.025. 47.932. 174. 41.876. 16.97Instructorʼs Guide1

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7. 1.41410. 29.10 cm13. 12.458. 15.05 cm11. 914. 7 cm9. 18.61 cm12. 2.2415. 39.55 cmUNIT 5REVIEW OF ANGLE MEASURE1. a.b. Student readings should compare closely with computed measurements.c. Angle C48° Alternate angles are equal.Angle A90°48°42° Right angle90°orAngle B180°(48°90°)42° Sum of 3 angles180°Angle A42° Alternate angles are equal.Angle DAngle C48° Opposite angles are equal.2. A30°D102°G48°B45°E9°H67°C66°F22°I78°3.∠A25°∠C58°∠E160°∠B10°∠D122°∠F311/2° or 31°30UNIT 6CONVERSION OF LENGTH MEASURES11. 85 cm12. 8.72 mInches and FractionalInches and DecimalFeet, Inches andFeet and DecimalParts of InchParts of InchFractional Parts ofParts of FootInch1.1911/1619.6871-711/161.642.423/842.3753- 63/83.533.263/826.352-23/82.204.6915/1669.945-915/165.835.1001/2100.58- 41/28.386.333/1633.192-93/162.777.6613/1666.845-613/165.578.1811/16181.0815-11/1615.099.1033/4103.758-73/48.6510.793/479.756-73/46.652Instructorʼs Guide

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SECTION 2 PIPE LENGTH CALCULATIONSUNIT 7STANDARD WEIGHT PIPE1.1/162.1/8,1/8,1/43. A hole drilled, into which a tap is turned to cut internal threads. There must be metal left into which to cut thethreads.4.1/85. About3/32UNIT 8ALLOWANCE FOR THREADED PIPE1. e-e18 [(13/8 13/8)2(1/2)]161/4, or 1- 41/42. e-e251/2 [(11/8 11/8)2(1/2)]241/4, or 2-1/43. e-e40 [(11/2 11/8)2(1/2)]383/8, or 3-23/84. e-e40 [(15/16 15/16)2(1/2)]383/8, or 3-23/85. e-e63 [13/4 13/4)2(1/2)]601/2, or 5-1/2UNIT 9COPPER TUBING1. 0.0452. 0.0903. K and L4. The long length would not need joints. It is easier to get in place.5. Yes. It is a heavier wall than DWV.6. No. It is not recommended for this service.UNIT 10ALLOWANCE FOR COPPER FITTINGS1. e-e18 (1/2 1/2)18117, or 1-52. e-e87 (27/8 27/8)87 53/4 811/4or 6-91/43. e-e311/2 (11/8 7/16)311/2 19/16 2915/16or 2-515/164. e-e43 (17/8 5/16)43 23/16 4013/16or 3413/145. e-e81 (15/16 13/16)81 21/8 787/8or 6-67/8UNIT 11PLASTIC PIPE1. C2. B3. A4. A5. D6. C7. CUNIT 12ALLOWANCE FOR PLASTIC FITTINGS1. e-e71/2 (9/16 9/16)63/82. e-e74 (31/16 31/16)677/8or 5-77/83. e-e37 (19/16 1)347/16or 2-107/164. e-e421/4 (25/16 11/16)391/4or 3-31/45. e-e92 (13/4 1)891/4or 7-51/4UNIT 13WELDED STEEL PIPING1. a3. b5. d7. a9. d2. c4. d6. b8. c10. cInstructorʼs Guide3c-ce-e1.18172.87811/43.311/22915/164.434013/165.81787/8

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UNIT 14ALLOWANCE FOR WELD-TYPE FITTINGSSize-fitting-fittingInchC to ConeAllowancetwoAllowanceE to E2A197/16flange1/4tee21/8171/16B91/2tee21/8flange1/471/8C33flange1/4LR Ell31/8255/8D22LR Ell31/8SR Ell21/8163/4E10SR Ell21/845° Ell13/861/23A197/16flange5/16tee31/816B91/2tee31/8flange5/1661/16C33flange5/16LR Ell45/8281/16D22LR Ell45/8SR Ell31/8143/8E10SR Ell31/845° Ell247/84A197/16flange5/16tee41/815B91/2tee41/8flange5/1651/16C33flange5/15LR Ell61/8269/16D22LR Ell61/8SR Ell41/8113/4E10SR Ell41/845° Ell25/831/45A197/16flange5/16tee51/814B91/2tee51/8flange5/1641/15C33flange5/16LR Ell75/8251/16D22LR Ell75/8SR Ell51/891/4E10SR Ell51/845° Ell31/411/4UNIT 15EQUAL SPACING1. 171/2 17.5; 17.5 28.75or 83/4J: c-c83/4e-e83/4 [(11/8 11/8)2(1/2)]71/2(threaded)e-e83/4 (3/8 3/8)8(copper)e-e83/4 (1/2 1/2)73/4(PVC)K: c-c83/4e-e83/4 [(11/8 11/8)2(1/2)]71/2(threaded)e-e83/4 (3/8 3/8)8(copper)e-e83/4 (1/2 1/2)73/4(PVC)2. 41 313.666 or 1311/16L: c-c1311/16e-e1311/16 [(11/2 11/2)2(1/2)]1111/16(threaded)e-e1311/16 (3/4 3/4)123/16(copper)e-e1311/16 (11/16 11/16)125/16(PVC)M: c-c1311/16e-e1311/16 [(11/2 11/2)2(1/2)]1111/16(threaded)e-e1311/16 (3/4 3/4)123/16(copper)e-e1311/16 (11/16 11/16)125/16(PVC)N: c-c1311/16e-e1311/16 [(11/2 11/2)2(1/2)]1111/16(threaded)e-e1311/16 (3/4 3/4)123/16(copper)e-e1311/16 (11/16 11/16)125/16(PVC)3. 671/2 67.5; 67.5416.875or 167/8P: c-c167/8e-e167/8 [(1 13/8)2(1/2)]151/2, or 1-31/2(threaded)e-e167/8 (1/4 1/2)161/8or 1-41/8(copper)e-e167/8 (5/16 9/16) or 1-4(PVC)4Instructorʼs Guide

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Q: c-c167/8e-e167/8 [(13/8 13/8)2(1/2)]151/8, or 1-31/8(threaded)e-e167/8 (1/2 1/2)157/8or 1-37/8(copper)e-e167/8 (9/16 9/16)153/4or 1-33/4(PVC)R: c-c167/8e-e167/8 [(13/8 13/8)2(1/2)]151/8, or 1-31/8(threaded)e-e167/8 (1/2 1/2)157/8or 1-37/8(copper)e-e167/8 (9/16 9/16)153/4or 1-33/4(PVC)4. 325/8 32.625; 32.625 216.312 5 165/16T: c-c165/16e-e165/16 [(3/4 1)2(3/8)]155/16or 1-35/16(threaded)e-e165/16 (3/165/16)1513/16or 1-313/16(copper)e-e165/16 (1/4 3/8)1511/16or 1-311/16(PVC)U: c-c165/16e-e165/16 [(1 3/4)2(3/8)]155/16or 1-35/16(threaded)e-e165/16 (5/163/16)1513/16or 1-313/16(copper)e-e165/16 (3/8 1/4)1511/16or 1-311/16(PVC)UNIT 16ANGLES IN PLUMBING1.ComplementaryFitting AngleAngleBend90°0°1/472°18°1/560°30°1/645°45°1/8221/2°671/2°1/16111/4°783/4°1/322.50/3605/36bend3.1/936040°, fitting angle90°40°50°, complementary angle4. A—fitting angleB—right angleC—complementary angleD—fitting angleE—complementary angleF—right angleUNIT 17OFFSET, DIAGONAL, AND RISE OR RUN1. 45° fitting angleInstructorʼs Guide5

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Solution Manual For Mathematics for Plumbers and Pipefitters, 8th Edition - Page 10 preview image

2. 221/2° fitting angle3. 111/4° fitting angle4. 72° fitting angleUNIT 18SOLVING FOR 45° ANGLES1. Run9;9292162Diagonal16212.727Diagonal12.72891.414offsetOffset912.7270.707diagonal2.OffsetRunDiagonala.101014.14141/8b.1-41-422.624225/8c.21.21213/1621.21213/162-6d.3-53-557.97458e.28.9872928.987293-5f.1-21-219.7961913/16g.20 cm20 cm28.28 cmh.106.05 cm106.05 cm150 cm6Instructorʼs Guide

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Solution Manual For Mathematics for Plumbers and Pipefitters, 8th Edition - Page 11 preview image

UNIT 1945° DIAGONAL AND PIPE LENGTHNote: Diagonal K = offsetconstant.1. K: c-c81/4 1.41411.665 5 1111/16e-e1111/16 [(1 1)2(1/2)]1011/16(threaded)e-e1111/16 (1/4 1/4)113/16(copper)e-e1111/16 (5/16 5/16)111/16(PVC)2. K: c-c9 1.41412.726 123/4or 1-3/4e-e123/4 [(11/8 11/8)2(1/2)]111/2(threaded)e-e123/4 (5/16 5/16)121/8or 1-1/8(copper)e-e123/4 (5/16 5/16)121/8or 1-1/8(PVC)3. K: c-c111/2 1.41416.261 161/4or 1-41/4e-e161/4 [(3/4 3/4)2(1/2)]153/4or 1-33/4(threaded)e-e161/4 (3/16 3/16)157/8or 1-37/8(copper)e-e161/4 (1/4 1/4)153/4or 1-33/4(PVC)4. K: c-c18 1.41425.452 257/16or 2-17/16e-e257/16 [(15/16 15/16)2(1/2)]2313/16or 1-1113/16(threaded)e-e257/16 (7/16 7/16)249/16or 2-9/16(copper)e-e257/16 (11)237/16or 1-117/16(PVC)5. K: c-c223/4 1.41432.168 5 323/16or 2-83/16e-e323/16 [(15/16 15/16)2(1/2)]309/16or 2-69/16(threaded)e-e323/16 (7/16 7/16)315/16or 2-75/16(copper)e-e323/16 (1 1)303/16or 2-63/16(PVC)6. c-c24 1.41433.936 3315/16or 2-915/16e-e3315/16 [(17/16 17/16)2(1/2)]321/16or 2-81/16(threaded)e-e3315/16 (9/16 9/16)3213/16or 2-813/16(copper)e-e3315/16 (11/8 11/8)3111/16or 2-711/16(PVC)7. c-c271/2 1.41438.885 387/8or 3-27/8e-e387/8[(17/16 17/16)2(1/2)]37or 3-1(threaded)e-e387/8(9/16 9/16)373/4or 3-13/4(copper)e-e387/8(11/8 11/8)365/8or 3-5/8(PVC)8. c-c45 1.41463.63 635/8or 5-35/8e-e635/8[(111/16 111/16)2(1/2)]611/4or 5-11/4(threaded)e-e635/8(3/4 3/4)621/8or 5-21/8(copper)e-e635/8(11/2 11/2)605/8or 5-5/8(PVC)9. c-c661/21.41494.031 94or 7-10e-e94 [(111/16 111/16)2(1/2)]915/8or 7-75/8(threaded)e-e94 (3/4 3/4)921/2or 7-81/2(copper)e-e94 (11/2 11/2)91or 7-7(PVC)UNIT 20THREE-PIPE DIAGRAMS WITH A 45° OFFSET1. J: c-c9e-e9 [(11/2 11/8)2(1/2)]73/8K: c-c11 1.41415.554 159/16or 1-39/16e-e159/16[(11/8 11/8)2(1/2)]145/16or 1-25/16L: c-c30 (9 11)30 20 10e-e10 [(11/8 11/2)2(1/2)]83/82. J: c-c12or 1e-e12 (3/8 3/16)117/16K: c-c131/2 1.41419.089 191/16or 1-71/16e-e191/16 (3/163/16)1811/16or 1-611/16L: c-c421/2 (12 131/2)17or 1-5e-e17 (3/16 3/8)167/16or 1-47/16Instructorʼs Guide7

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Solution Manual For Mathematics for Plumbers and Pipefitters, 8th Edition - Page 12 preview image

3. J: c-c15or 1-3e-e15 [(13/8 1)2(1/2)]135/8or 1-15/8K: c-c16 1.41422.624 225/8or 1-105/8e-e225/8 [(1 1)2(1/2)]215/8or 1-95/8L: c-c533/4 (15 16)223/4or 1-103/4e-e223/4 [(1 13/8)2(1/2)]213/8or 1-93/84. J: c-c14e-e14 (19/16 1)117/16K: c-c32 1.41445.248 451/4or 3-91/4e-e451/4 (1 1)431/4or 3-71/4L: c-c60 (14 32)14or 1-2e-e14 (1 19/16)117/165. J: c-c70 34 36; 36 218or 1-6e-e18 (13/4 11/8)151/8or 1-31/8K: c-c34 1.41448.076 481/16or 4-1/16e-e481/16 (11/8 11/8)4513/16or 3-913/16L: c-c18or 1-6e-e18 (11/8 13/4)151/8or 1-31/86. J: c-c72 163/4 55.25; 55.25227.625 275/8or 2-35/8e-e275/8 [(115/16 17/16)2(1/2)]251/4or 2-11/4K: c-c163/4 1.41423.684 5 2311/16or 1-1111/16e-e2311/16 [(17/16 17/16)2(1/2)]2113/16or 1-913/16L: c-c275/8e-e275/8 [(17/16 115/16)2(1/2)]251/4or 2-11/47. M: c-c5e-e5 [(1 3/4)2(3/8)]4N: c-c51/2 1.4147.777 73/4e-e73/4 [(3/4 3/4)2(3/8)]7O: c-c17 (5 51/2)61/2e-e61/2 [(3/4 1)2(3/8)]51/28. M: c-c73/4e-e73/4 (1/2 1/4)7N: c-c8 1.41411.312 115/16e-e115/16 (1/4 1/4)1013/16O: c-c33 (73/4 8)171/4or 1-51/4e-e171/4 (1/4 1/2)161/2or 1-41/29. M: c-c91/2e-e91/2 [(13/8 1)2(1/2)]81/8N: c-c91/2 1.41413.433 137/16or 1-17/16e-e137/16 [(1 1)2(1/2)]127/16O: c-c39 (91/2 91/2)20or 1-8e-e20 [(1 13/8)2(1/2)185/8or 1-65/810. M: c-c121/2e-e121/2 [(11/2 11/8)2(1/2)]107/8N: c-c151/2 1.41421.917 2115/16or 1-915/16e-e2115/16 [(11/8 11/8)2(1/2)]2011/16or 1-811/16O: c-c453/4 (121/2 151/2)173/4or 1-53/4e-e173/4 [(11/8 11/2)2(1/2)]161/8or 1-41/811. M: c-c48 12 36; 36 218or 1-6e-e18 (3/4 5/16)1615/16or 1-415/16N: c-c12 1.41416.698 1615/16or 1-415/16e-e1615/16 (5/16 5/16)165/16or 1-45/16O: c-c18or 1-6e-e18 (5/16 3/4)1615/16or 1-415/1612. M: c-c55 21 34; 34 217or 1-5e-e17 [(13/4 15/16)2(1/2)]1415/16or 1-215/16N: c-c21 1.41429.694 2911/16or 2-511/168Instructorʼs Guide

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Solution Manual For Mathematics for Plumbers and Pipefitters, 8th Edition - Page 13 preview image

e-e2911/16 [(15/16 15/16)2(1/2)]281/16or 2-41/16O: c-c17or 1-5e-e17 [(15/16 13/4)2(1/2)]1415/16or 1-215/16UNIT 21RIGHT ANGLE WITH A 45° DIAGONAL1. J: c-c16e-e16 (3/8 1/4)153/8or 1-33/8K: c-c30 16 14; 14 1.41419.796 1913/16or 1-713/16e-e1913/16 (1/4 1/4)195/16or 1-75/16L: c-c36 14 22or 1-10e-e22 (1/4 3/8)213/8or 193/82. J: c-c21or 1-9e-e21 [(211/16 21/16)2(3/4)]171/4or 1-51/4K: c-c43 21 22; 22 1.41431.108 311/8or 2-71/8e-e311/8 [(21/16 21/16)2(3/4)]281/2or 2-41/2L: c-c38 22 16or 1-4e-e16 [(21/16 211/16)2(3/4)]123/4or 1-3/43. J: c-c191/2or 1-71/2e-e191/2 [(21/4 111/16)2(1/2)]169/16or 1-49/16K: c-c48 191/2 281/2; 28.51.41440.299 405/16or 3-45/16e-e405/16 [(111/16 111/16)2(1/2)]3715/16or 3-115/16L: c-c60 281/2 311/2or 2-71/2e-e311/2 [(111/16 21/4)2(1/2)]289/16or 2-49/164. J: c-c261/2or 2-21/2e-e261/2 (11/8 7/16)2415/16or 2-15/16K: c-c63 261/2 361/2; 36.51.41451.611 515/8or 4-35/8e-e515/8 (7/16 7/16)503/4or 4-23/4L: c-c58 361/2 211/2or 1-91/2e-e211/2 (7/16 11/8)1915/16or 1-715/165. J: c-c76 401/4 353/4or 2-113/4e-e353/4 (1/2 1/4)35or 2-11K: c-c401/4 1.41456.9135or 5615/16or 4-815/16e-e5615/16 (1/4 1/4)567/16or 4-87/16L: c-c71 401/4 303/4or 2-63/4e-e303/4 (1/4 1/2)30or 2-6UNIT 2245° OFFSET WITH WYE FITTING1. J: c-c8e-e8 [(115/16 115/16)2(1/2)]51/8K: c-c451/2 8371/2or 3-11/2e-e371/2 [(39/16 115/16)2(1/2)]33or 2-9L: c-c23 1.41432.522 321/2or 2-81/2e-e321/2 [(39/16 17/16)2(1/2)]281/2or 2-41/2M: c-c451/2 (8 23)141/2or 1-21/2e-e141/2 [(17/16 115/16)2(1/2)]121/8or 1-1/82. J: c-c15or 1-3e-e15 (13/4 11/8)121/8or 1-1/8K: c-c67 15 52or 4-4e-e52 (27/8 13/4)473/8or 3-113/8L: c-c30 1.41442.42427/16or 3-27/16e-e427/16 (27/8 11/8)387/16or 3-27/16M: c-c67 (15 30)22or 1-10e-e22 (11/8 13/4)191/8or 1-71/8Instructorʼs Guide9

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Solution Manual For Mathematics for Plumbers and Pipefitters, 8th Edition - Page 14 preview image

3. J: c-c12or 1e-e12 (25/16 13/8)85/16K: c-c53 12 41or 3-5e-e41 (35/8 25/16)351/16or 2-111/16L: c-c24 1.41433.936 3315/16or 2-915/16e-e3315/16 (35/8 11/2)2813/16or 2-413/16M: c-c53 (12 24)17or 1-5e-e17 ( 11/2 25/16)133/16or 1-13/164. J: c-c22or 1-10e-e22 [(21/4 21/8)2(1/2)185/8or 1-65/8K: c-c56 2234or 2-10e-e34 [(43/8 21/4)2(1/2)]283/8or 2-43/8L: c-c93/4 1.41413.7865 1313/16or 1-113/16e-e1313/16 [(43/8 111/16)2(1/2)]83/4M: c-c56 (22 93/4)241/4or 2-1/4e-e241/4 [(111/1621/4)2(1/2)]215/16or 1-95/165. J: c-c113/4e-e113/4 (17/8 1/2)93/8K: e-e26 113/4 141/4or 1-21/4c-c141/4 (27/8 17/8)91/2L: c-c81/2 1.41412.019 12or 1-0e-e12 (27/8 3/4)83/8M: c-c26 (113/4 81/2)53/4e-e53/4 (3/4 17/8)31/86. J: c-c19or 1-7e-e19 [(21/4 113/16)2(1/2)]1515/16or 1-315/16K: c-c70 19 51or 4-3e-e51 [(41/16 21/4)2(1/2)]4511/16or 3-911/16L: c-c29 1.41441.006 41or 3-5e-e41 [(41/8 17/16)2(1/2)]367/16or 3-7/16M: c-c70 (19 29)22or 1-10e-e22 [(17/16 115/16)2(1/2)]195/8or 1-75/8UNIT 23WYE AND TEE-WYE ASSEMBLIES1.c-ce-eJ.14111/2K.48427/8L.383/16341/2M.21173/162.c-ce-eJ.191/2175/8K.501/24613/16L.4313/164015/16M.191/2179/163.c-ce-eJ.213/4173/16K.553/4501/2L.473/8425/8M.221/4183/1610Instructorʼs Guide

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Solution Manual For Mathematics for Plumbers and Pipefitters, 8th Edition - Page 15 preview image

4.c-ce-eJ.27235/16K.61551/16L.5211/16479/16M.233/41915/165.c-ce-eJ.341/2327/16K.75709/16L.6013/16579/16M.32301/166.c-ce-eN.50471/4O.20171/8P.281/4241/4Q.30271/87.c-ce-eN.322811/16O.331/2309/16P.1711/16131/4Q.191/2169/168.c-ce-eN.6360O.153/4133/8P.399/163515/16Q.35323/89.c-ce-eN.581/4531/2O.321/2283/16P.41361/4Q.291/4257/1610.c-ce-eN.491/2473/16O.1077/8P.399/163611/16Q.211/2199/1611.c-ce-eR.302711/16S.115/1673/8T.32291/16U.25203/8V.115/1673/8W.32291/16Instructorʼs Guide11

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