Complete First Year Field Reference — SKILLED TRADES

📐

AREAS & PERIMETERS

CIRCLE

Area = π × r²
Area = 0.7854 × d²
Circumference = π × d
π=3.1416 · r=radius · d=diameter

Pipe bore area for flow calcs, flange face area for pressure/force, insulation takeoffs, tank end caps.

RECTANGLE / SQUARE

Area = L × W
Perimeter = 2 × (L + W)
Square: all sides = S → A = S²

Equipment pads, boiler room floors, duct openings, trench sizing, concrete pads for supports.

TRIANGLE

Area = ½ × base × height
Perimeter = a + b + c
Height must be perpendicular to base

Gusset plates, roof slopes, triangular support brackets, cut-off material estimates.

CYLINDER

Lateral SA = 2π × r × h
Total SA = 2π × r × (r + h)
Volume = π × r² × h
r=radius · h=height/length

Tank insulation takeoffs, pipe insulation quantity, paint coverage on vessels and storage tanks.

BOX / RECTANGULAR PRISM

Surface Area = 2(LW + LH + WH)
Volume = L × W × H
L=length · W=width · H=height

Equipment housings, duct volumes, trenches, concrete pours, insulated box enclosures.

TRAPEZOID

Area = ½ × (a + b) × h
a,b = parallel sides · h = height

Sloped trenches, tapered insulation sections, eccentric reducer face areas.

△

TRIANGLE & SLOPE FORMULAS

📐

Pythagorean Theorem

c² = a² + b²
c = √(a² + b²)

Find the hypotenuse (diagonal) of any right triangle. Foundation of ALL pipe offset calculations — rise, run, and travel.

📉

Rise, Run & Slope

Slope = Rise ÷ Run
Rise = Run × Slope
Run = Rise ÷ Slope

Drain lines, condensate returns — any gravity-flow pipe needs minimum slope. Know two values, find the third.

📏

Grade & Drop

Drop = Length × Grade per foot
Grade (%) = (Drop ÷ Run) × 100
1% grade = ⅛" per foot

Drain and condensate lines. Minimum ¼"/ft (2% grade) typical. Calculate total drop before routing through structure.

📐

SOH · CAH · TOA

sin θ = Opposite ÷ Hypotenuse
cos θ = Adjacent ÷ Hypotenuse
tan θ = Opposite ÷ Adjacent

Find any angle or side in a right triangle. Used in advanced rolling offsets and precise fitting angle calculations.

🔢

Common Pipe Slopes

⅛"/ft = 1.04% grade
¼"/ft = 2.08% ← most common
½"/ft = 4.17% grade
1"/ft = 8.33% grade

Drain lines minimum ¼"/ft. Condensate returns often ⅛"/ft. Verify with local plumbing/mechanical code.

🔺

Pipe Drop Over Length

Drop (in) = Length (ft) × Drop per ft
40 ft × ¼"/ft = 10" total drop

How low the far end of a drain line will be — critical for fitting through floor joists and structural members.

🧊

VOLUME CALCULATIONS

🔵

Cylinder (Tank / Pipe)

V = π × r² × h
V = 0.7854 × d² × h

Volume of any cylindrical tank, vessel, or pipe section. Use consistent units throughout (all feet or all inches).

📦

Rectangular Tank

V (ft³) = L × W × H
V (gal) = L × W × H × 7.481

Expansion tanks, day tanks, equipment pits. Multiply ft³ × 7.481 to get US gallons.

🧮

Pipe System Volume

Gal = 0.0408 × ID² (in) × Length (ft)

Total water content of piping — chemical dosing, glycol fill ratio, drain-down planning.

🔺

Cone / Hopper

V = ⅓ × π × r² × h

Conical reducer sections, hopper bottoms on vessels, sump designs, cone-bottom tanks.

💧

Volume → Weight (Water)

Weight (lb) = Volume (gal) × 8.34
Weight (lb) = Volume (ft³) × 62.4

Structural loading of water-filled systems — floor loading, hanger design, lifting calculations.

🔄

ft³ ↔ Gallons

US gal = ft³ × 7.481
ft³ = US gal ÷ 7.481

Tank manufacturers give ft³, systems are filled in gallons. Convert freely between both.

%

PERCENTAGE & RATIO

🔢

Part–Whole–Percent

Part = Whole × (% ÷ 100)
Whole = Part ÷ (% ÷ 100)
Percent = (Part ÷ Whole) × 100

Cover any % problem — inhibitor concentration, glycol mix, efficiency ratings, material waste allowances.

🧪

Glycol Mix Calculation

Glycol (gal) = Total Vol × (% ÷ 100)
Water (gal) = Total Vol − Glycol

30% in 500-gal system: 500 × 0.30 = 150 gal glycol, 350 gal water. Standard freeze protection mixing.

📊

% Increase / Decrease

% Change = ((New − Old) ÷ Old) × 100
New Value = Old × (1 + % ÷ 100)

Pressure loss through components, pump efficiency degradation, material cost estimates and budget changes.

⚖️

Ratio & Proportion

a/b = c/d → cross multiply: a×d = b×c
Solve x: x = (b × c) ÷ d

Scaling drawings, adjusting chemical doses, proportional flow splitting in parallel circuits.

⚙️

Efficiency & Derating

Output = Input × (Eff% ÷ 100)
Input = Output ÷ (Eff% ÷ 100)

Boiler efficiency, pump efficiency, heat exchanger effectiveness — useful output vs rated input.

🏗

Material Waste Allowance

Order Qty = Net Qty × (1 + Waste%/100)
Pipe: 5–10% · Insulation: 15%

Material takeoffs — always add waste factor to net quantities. Running short on site costs more than over-ordering.

⬆

PRESSURE

⬡ PRESSURE · FORCE · AREA — THE MAGIC TRIANGLE

PRESSURE

P = F ÷ A

PSI = lb ÷ in²

FORCE

F = P × A

lb = PSI × in²

AREA

A = F ÷ P

in² = lb ÷ PSI

Cover the value you want to find — the remaining two values show the formula. Bolt loads, flange ratings, anchor sizing, cap end forces.

🌍

Atmospheric Pressure

14.696 PSI (use 14.7)
= 101.325 kPa = 1.01325 bar
= 29.92 in Hg = 33.9 ft H₂O

The baseline "zero" for gauge pressure readings. At sea level. Decreases with altitude — affects boiling points and steam table accuracy at elevation.

📊

Gauge · Absolute · Vacuum

PSIA = PSIG + 14.7
PSIG = PSIA − 14.7
PSIG = 0 → PSIA = 14.7 (atm)
Below 0 PSIG = vacuum

Gauges read PSIG. Steam tables, gas laws, and absolute calcs require PSIA. Always check which unit a formula needs.

💧

Head Pressure

PSI = Height (ft) ÷ 2.31
Height (ft) = PSI × 2.31
2.31 ft water = 1 PSI

Static pressure at bottom of water column — pump sizing, gravity feed, elevated tank systems. Every floor (≈10 ft) = +4.33 PSI.

⚗️

Pressure–Height–Density

P (PSI) = Density (lb/ft³) × h (ft) ÷ 144
Water ρ=62.4 · Oil ρ≈55 · Glycol ρ≈66

For fluids other than water, adjust density. Oil, glycol, and brine all have different densities — pressure at depth changes accordingly.

🔄

PSI ↔ kPa ↔ Bar

kPa = PSI × 6.895
PSI = kPa × 0.1450
Bar = PSI × 0.06895
PSI = Bar × 14.504

Canadian specs in kPa, European in bar, US in PSI. Convert before comparing ratings or performing any calculation.

💥

Thrust Force at Caps & Bends

Force (lb) = PSI × Area (in²)

100 PSI × 4" pipe (12.57 in²) = 1,257 lb on a capped end. Every plugged end, elbow, and reducer needs to be restrained or anchored for this load.

💧

WATER PROPERTIES & WEIGHT

🏋️

Water Weight — Key Values

1 US gallon   = 8.34 lb
1 ft³         = 62.4 lb
1 Imperial gal = 10.0 lb
1 litre       = 1 kg = 2.205 lb

Structural loads on floors, hangers, supports. A 500-gal tank full of water = 4,170 lb — always check floor load ratings.

📏

Water Weight in Pipe per Foot

lb/ft = 0.3405 × ID² (inches)

2" pipe (ID 2.067) → 1.45 lb/ft
4" pipe (ID 4.026) → 5.52 lb/ft
6" pipe (ID 6.065) → 12.5 lb/ft

Add pipe metal weight + insulation weight for total hanger load. Critical for support spacing design.

🌡

Pressure per Foot of Head

0.433 PSI per foot of water
PSI = ft ÷ 2.31
1 PSI = 2.31 ft of water head

Every 1 ft rise = 0.433 PSI of static pressure added at the base. Used for pump sizing and elevated system designs.

🌡

Water Density vs Temperature

40°F → 62.43 lb/ft³ (max density)
60°F → 62.37 lb/ft³ (standard)
100°F → 61.99 lb/ft³
200°F → 60.13 lb/ft³
300°F → 57.31 lb/ft³

Hot water is less dense and lighter. High-temp hydronic systems: use temperature-corrected density for accurate hanger loads and pump sizing.

❄️

Glycol Freeze Protection

20% EG → −10°F freeze point
30% EG → −15°F freeze point
40% EG → −25°F freeze point
50% EG → −35°F freeze point

EG = Ethylene Glycol. Propylene glycol (food-grade) has slightly higher freeze points. Design 10°F below lowest expected ambient temperature.

💥

Water Hammer — What It Is

Fast valve close = pressure spike
2" pipe at 5 ft/s → can spike 100+ PSI
Use slow-close valves to prevent

Sudden valve closures create destructive pressure surges. Remedies: slow-close valves, air chambers, expansion tanks, reduced velocity.

🌡

TEMPERATURE

🇺🇸

°F → °C

°C = (°F − 32) × 5/9

Converting spec sheets, boiler manuals, thermometers. Freeze=32°F=0°C · Boiling=212°F=100°C.

🌍

°C → °F

°F = (°C × 9/5) + 32

Converting metric temperatures to field gauge readings or imperial spec sheets.

🔬

°C → Kelvin

K = °C + 273.15

Required for ALL gas law calculations. Every "T" in a formula = Kelvin. Never negative — absolute zero = −273.15°C.

⚗️

°F → Kelvin (Direct)

K = (°F − 32) × 5/9 + 273.15

Direct conversion for gas law problems when starting from a Fahrenheit gauge reading.

〰

FLOW & VELOCITY

🔄

GPM → L/min

L/min = GPM × 3.785

US pump specs in GPM, Canadian/metric in L/min. 1 US gallon = 3.785 litres.

💨

Pipe Velocity

V (ft/s) = GPM × 0.408 ÷ ID²

Target: 2–4 ft/s cold water · ≤8 ft/s hot water · ≤15 ft/s steam. High velocity = noise, erosion, water hammer.

↔️

Continuity Equation

A₁ × V₁ = A₂ × V₂

At reducers: smaller pipe = faster flow. Area halved = velocity doubled. Critical check at all size changes.

🧮

Pipe Volume

Gal = 0.0408 × ID² × Length (ft)

System fluid volume for chemical dosing, glycol fill ratio, drain-down time planning.

♨

STEAM SYSTEMS

📖

Saturation Temperature

Steam Tables: PSIA → °F saturation

Every steam job — saturation temp tells you if steam is wet, dry, or superheated. Always convert PSIG to PSIA (+14.7) before table lookup.

💦

Condensate Load

lb/hr = BTU/hr ÷ Latent Heat

Size steam traps to handle condensate rate. Trap too small = backup = water hammer. Latent heat ≈ 970 BTU/lb at 15 PSIG.

🔥

BTU to Heat Water

BTU = Weight (lb) × 1.0 × ΔT (°F)

Sizing boilers, heat exchangers, and storage tanks. 1 gallon water = 8.34 lb. Specific heat of water = 1.0 BTU/lb/°F.

⚡

Steam Velocity Guide

Distribution mains: 4,000–8,000 ft/min
Branch lines: 2,000–4,000 ft/min
Condensate return: 100–200 ft/min

Too slow = condensate backup. Too fast = erosion, noise, pressure drop. Always check velocity when sizing steam mains.

↗

PIPE OFFSETS

↗

45° Offset Travel

Travel = Offset × 1.414

Most common offset in commercial work. √2 = 1.414. Offset = perpendicular distance between parallel pipes.

↗

22.5° Offset Travel

Travel = Offset × 2.613

When 45° elbows won't clear an obstacle. Gentler angle = longer travel piece needed.

↗

60° Offset Travel

Travel = Offset × 1.155

Tight space, steep angle. Steeper angle = shorter travel piece.

🎲

Rolling Offset (45°)

Travel = √(Offset² + Rise²) × 1.414

Multi-plane obstacle avoidance. Find the diagonal with Pythagoras first, then multiply by 1.414.

⭕

Circumference

C = π × D (π = 3.1416)

Wrap-around marking, insulation cutting, branch layout. Always use actual OD, not nominal size.

🔵

Pipe Cross-Section Area

A = 0.7854 × d²

Flow calcs, velocity checks, thrust force at fittings. Use ID (inside) for flow area, OD for external area/pressure calcs.

⚡ OFFSET MULTIPLIERS AT A GLANCE

22.5°

× 2.613

30°

× 2.000

45°

× 1.414

60°

× 1.155

Rolling Offset: Step 1 → Diagonal = √(Offset² + Rise²)
Step 2 → Travel = Diagonal × angle multiplier
Most common: 45° rolling → multiply diagonal × 1.414

↕

THERMAL EXPANSION

📏

Pipe Growth Formula

ΔL = α × L × ΔTemp

Hot pipe WILL move — anchors, loops, and flex joints must absorb it.
Carbon steel α = 6.5×10⁻⁶/°F ≈ 0.78"/100ft per 100°F
Stainless α = 9.9×10⁻⁶/°F · Copper α = 9.3×10⁻⁶/°F

🔁

Expansion Loop Size

L (ft) = 0.0275 × √(D × ΔL)

D = pipe OD in inches, ΔL = expected expansion in inches. Gives minimum leg length. Undersized loops crack welds and stress anchors.

🌡

Quick Field Estimate

C-steel ≈ 0.78" per 100 ft per 100°F

200 ft steam main, 70°F → 370°F (300°F rise): 200 × 0.78 × 3 = 4.68" total growth. Plan expansion provisions before fabrication.

⚗

GAS LAWS

⚠ Gas laws ALWAYS require: Pressure in PSIA · Temperature in KELVIN · Volume in consistent units

BOYLE'S LAW

Constant Temperature

P₁ × V₁ = P₂ × V₂

Pressure changes, temperature stays the same. Compressed air systems, nitrogen purging, gas cylinder volumes.
100 PSIA × 10 ft³ → compressed to 200 PSIA: V₂ = 5 ft³

CHARLES' LAW

Constant Pressure

V₁ ÷ T₁ = V₂ ÷ T₂

Temperature changes, pressure stays same. Expansion tanks, accumulators, seasonal gas volume changes.
10 ft³ at 300K → 600K: V₂ = 20 ft³

COMBINED LAW

P, V, and T all change

P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂

Most real-world gas problems. Solve for the unknown by rearranging.
V₂ = (P₁ × V₁ × T₂) ÷ (T₁ × P₂)

⚖

FORCE, TESTING & HANGERS

🏗

Water Weight in Pipe

lb/ft = 0.3405 × ID² (inches)

Hanger and support spacing. Water-filled pipe is much heavier than empty. Add pipe metal + insulation for total hanger load.

🧪

Hydrostatic Test Pressure

Test = Design Pressure × 1.5

After completing any piping system. Verify with code (B31.1, B31.9). ALWAYS bleed all air before testing — trapped air is dangerous.

💥

Thrust Force on Fittings

Force (lb) = PSI × Area (in²)

100 PSI in 4" pipe = 1,257 lb on a capped end. Size thrust blocks, anchors, and pipe restraints from this value.

🔩

Flange Bolt Torque Sequence

Star pattern: 30% → 70% → 100%

Three passes in a star (cross) pattern. NEVER fully torque one bolt at a time — uneven load crushes and blows gaskets.

⚡

OHM'S LAW & WATT'S LAW

⚡ V = Voltage (volts) · I = Current (amps) · R = Resistance (ohms Ω) · P = Power (watts W)

OHM'S LAW

Voltage · Current · Resistance

V

V = I × R

I

I = V ÷ R

R

R = V ÷ I

Cover what you want → remaining values show the formula

Checking motor voltage, troubleshooting control circuits, sizing fuses, understanding electrical drawings on steam and HVAC equipment.

WATT'S LAW

Power · Voltage · Current

P

P = V × I

V

V = P ÷ I

I

I = P ÷ V

Cover what you want → remaining values show the formula

Converting kW boiler rating to amps, sizing breakers for heat trace, understanding power consumption of pumps and motors.

⚡ ALL 12 COMBINATIONS — OHM + WATT

FIND VOLTAGE (V)

V = I × R
V = P ÷ I
V = √(P × R)

FIND CURRENT (I)

I = V ÷ R
I = P ÷ V
I = √(P ÷ R)

FIND RESISTANCE (R)

R = V ÷ I
R = V² ÷ P
R = P ÷ I²

FIND POWER (P)

P = V × I
P = I² × R
P = V² ÷ R

Pipefitters encounter electrical on: pump motors, control panels, electric heat trace, immersion heaters, solenoid valves, and actuators. These 12 formulas cover every combination.

★

KEY CONSTANTS

VALUE

NUMBER

NOTES

π (pi)

3.1416

C = π×D · Area = π×r² = 0.7854×d²

√2

1.4142

45° offset multiplier

1 US gallon (water)

8.34 lb

Weight of water

1 ft³ of water

62.4 lb

Weight of water per cubic foot

Water pressure per ft

0.433 PSI

1 PSI = 2.31 ft head

Atmospheric pressure

14.7 PSI

= 101.3 kPa = 1.013 bar = 29.92 in Hg

C-steel expansion

0.78"/100ft

Per 100°F temperature rise

Steam latent heat

~970 BTU/lb

At 15 PSIG — decreases at higher pressure

Specific heat of water

1.0 BTU/lb/°F

Used in all heat-up calculations

Boiler horsepower

33,475 BTU/hr

Old unit still on equipment nameplates

1 kilowatt

3,412 BTU/hr

Power → heat conversion

1 ton refrigeration

12,000 BTU/hr

Chiller and cooling system sizing

1% grade

⅛" per foot

Pipe slope: 1% = ⅛"/ft

Min drain slope

¼" per foot

2% grade — typical code minimum

1 ft³

7.481 US gal

Volume conversion

⇄

UNIT CONVERSIONS

📏

Length

1 ft = 12 in = 0.3048 m
1 m = 3.281 ft · 1 in = 25.4 mm

Metric drawings, international equipment. DN50 ≈ 2" nominal pipe.

🪣

Volume

1 US gal = 3.785 L
1 ft³ = 7.481 US gal
1 Imp gal = 1.2 US gal

Chemical treatment, tank sizing. US ≠ Imperial gallons — concentrations can be dangerously wrong if mixed up.

⚖️

Mass / Weight

1 lb = 0.4536 kg
1 kg = 2.205 lb
1 short ton = 2,000 lb

Equipment rigging, boiler capacity. Short ton (US) = 2,000 lb. Metric tonne = 2,205 lb.

⚡

Power & Heat

1 kW = 3,412 BTU/hr
1 Ton = 12,000 BTU/hr
Boiler HP = 33,475 BTU/hr

Comparing boiler ratings, HX capacity, chiller sizing. 100 kW boiler = 341,200 BTU/hr.

🔧

Nominal Pipe Size vs Actual OD — CRITICAL

½" NPS → 0.840" OD    1" NPS → 1.315" OD    1½" NPS → 1.900" OD
2" NPS → 2.375" OD    3" NPS → 3.500" OD    4" NPS → 4.500" OD
6" NPS → 6.625" OD    8" NPS → 8.625" OD    10" NPS → 10.750" OD

ALWAYS — nominal size ≠ actual OD. Critical for fitting selection, welding preps, threading, and insulation takeoffs. Pipe ID depends on Schedule. Schedule 40 is most common.