Chapter 9 — The Numbers: A Complete Sizing Calculation Reference and Design Worksheets

This chapter consolidates all sizing calculations from the preceding chapters into structured, step-by-step worksheets. Work through them in order for a new design, or jump to a specific worksheet when reviewing a single component.

Worksheet 1: Household Demand Assessment

Purpose: Calculate total daily and annual demand, and the potable/non-potable split.

Step	Input	Formula	Result
1	Number of occupants (N)	—	N = ___
2	Toilet demand	N × flushes/day × L/flush	___ L/day
3	Shower demand	N × duration (min) × flow (L/min)	___ L/day
4	Bath demand	N × freq/week × volume (L) / 7	___ L/day
5	Washing machine	Cycles/week × L/cycle / 7	___ L/day
6	Dishwasher	Cycles/day × L/cycle	___ L/day
7	Kitchen sink	estimate from Table 2.2	___ L/day
8	Bathroom sinks	N × L/person/day	___ L/day
9	Garden irrigation	m² × L/m²/week / 7	___ L/day
10	Total daily demand	Sum rows 2–9	___ L/day
11	Annual demand	Row 10 × 365 / 1000	___ m³/year
12	Non-potable demand	Rows 2 + 5 + 9 (+ showers if Tier 2)	___ L/day
13	Non-potable fraction	Row 12 / Row 10	___%

Reference values: Use Table 2.1 and 2.2 (Chapter 2) for fixture consumption data.

Worksheet 2: Rainwater Collection Yield

Purpose: Calculate monthly collection potential.

Inputs:

Roof plan area (A): ___ m²
Runoff coefficient (C): ___ (from Table 3.1)
Monthly rainfall data (from local meteorological source)

Month	Rainfall R (mm)	Yield V = A × R × C (L)
Jan	___	___
Feb	___	___
Mar	___	___
Apr	___	___
May	___	___
Jun	___	___
Jul	___	___
Aug	___	___
Sep	___	___
Oct	___	___
Nov	___	___
Dec	___	___
Annual	___ mm	__ L / __ m³

First-flush diverter volume: A × 0.75 L/m² = ___ L

Annual supply / demand ratio: Annual yield / Annual non-potable demand = ___

If ratio >1.0: Proceed to Rippl method (Worksheet 3A)
If ratio <1.0: Proceed to simulation method (Worksheet 3B); mains backup required

Worksheet 3A: Tank Sizing — Rippl Method

Use when: Annual supply ≥ Annual demand (ratio ≥ 1.0 from Worksheet 2)

Month	Supply (L)	Demand (L)	Cumulative Supply	Cumulative Demand	Gap (Cum.D − Cum.S)
Jan
Feb
…
Dec

Minimum tank size = Maximum positive value in the “Gap” column

With safety factor (×1.25): Tank size = ___ L

Round up to nearest standard available size.

Worksheet 3B: Tank Sizing — Simulation Method

Use when: Annual supply < Annual demand (ratio <1.0); requires mains backup.

# Run this script with your monthly data
monthly_supply = [...]   # Fill from Worksheet 2, in liters
monthly_demand = [...]   # Fill from Worksheet 1 (non-potable monthly demand)
tank_sizes = [1000, 2000, 3000, 5000, 8000, 10000, 15000, 20000]

for tank_cap in tank_sizes:
    level = tank_cap / 2
    mains_total = 0
    for s, d in zip(monthly_supply, monthly_demand):
        level = min(level + s, tank_cap)
        drawn = min(level, d)
        mains_total += (d - drawn)
        level -= drawn
    autonomy = 100 * (1 - mains_total / sum(monthly_demand))
    print(f"Tank {tank_cap:6d} L → Autonomy: {autonomy:.1f}%")

Select tank size at the “knee” of the autonomy curve — beyond this, additional storage yields diminishing returns.

Worksheet 4: Pipe Sizing

Purpose: Size the distribution pipe for a given design flow and acceptable friction loss.

Inputs:

Design flow rate (Q): ___ L/min (from Worksheet 1 peak demand × 1.5 safety factor)
Pipe material (Hazen-Williams C): ___ (PVC/PEX: 150; Copper: 130)
Pipe run length (L): ___ m
Allowable friction head loss: ___ m (target ≤ 5 m per 100 m of pipe)

Step 1 — Select pipe diameter from velocity criterion:

Q (m³/s) = Q (L/min) / 60,000
A_required = Q / v_max     (v_max = 1.5 m/s for supply)
D_min = 2 × sqrt(A_required / π)     → round up to standard size

Trial D (mm)	Velocity v (m/s)	Friction loss h_f (m)	Acceptable?
15
20
25
32

Hazen-Williams friction loss formula: h_f = 10.67 × L × Q^1.852 / (C^1.852 × D^4.87) (Q in m³/s, D in m, h_f in m)

Add 40% to h_f for fittings: Total friction loss = h_f × 1.40

Selected pipe diameter: ___ mm

Worksheet 5: Pump Selection

Purpose: Calculate Total Dynamic Head and required pump power.

Component	Value	Notes
Static head (ΔZ)	___ m	Height difference: tank surface to highest delivery point
Suction lift (if applicable)	___ m	Add if pump is above tank water level
Friction losses (from Worksheet 4)	___ m	Include fittings
Minimum delivery pressure	___ m	Typically 10–15 m (1.0–1.5 bar)
Total Dynamic Head (TDH)	___ m	Sum all above

Design flow rate: ___ L/min (from Worksheet 4)

Select a pump from manufacturer curves with Q ≥ design flow rate at H = TDH.

Pump electrical power:

P_hydraulic = ρ × g × Q(m³/s) × H(m)   [Watts]
P_electrical = P_hydraulic / η_pump      (η ≈ 0.50–0.65 for small centrifugal pumps)

P_electrical = ___ W

Pressure vessel: Select a pressure vessel with drawdown volume ≥ 10 L; typical choice: 24 L or 50 L vessel.

Worksheet 6: Greywater System Sizing

Purpose: Size a greywater surge tank and assess toilet flushing offset.

Item	Calculation	Result
Greywater available (showers)	N × shower_duration × flow_rate	___ L/day
Greywater available (sinks)	N × 15 L/person	___ L/day
Greywater available (washing machine)	cycles/week × 50 / 7	___ L/day
Total greywater	Sum	___ L/day
Toilet demand (target use)	N × 21 L/person/day	___ L/day
Offset ratio	Total greywater / Toilet demand	___ (>1 = surplus)
Morning peak generation	N × shower_min × flow + sinks (6–9 AM)	___ L in 3 hrs
Surge tank size	Peak generation × 2 hr buffer / peak_rate	___ L

Minimum surge tank: 200 L for 2-person household; 300–500 L for 4-person.

Worksheet 7: Full System Autonomy

Purpose: Estimate total mains water offset from combined rainwater + greywater systems.

Demand category	Annual demand (m³)	Source	Annual saved (m³)
Toilet flushing	___	Greywater / Rainwater	___
Laundry	___	Rainwater	___
Garden irrigation	___	Rainwater / Greywater	___
Showering (if Tier 2 system)	___	Treated rainwater	___
Potable uses	___	Mains only	0
Total	___ m³		___ m³

Overall system autonomy: Autonomy = Total saved / Total demand = ___% of mains replaced

Annual mains volume remaining: Total demand − Total saved = ___ m³/year

Sensitivity Analysis

Key uncertainties affect all calculations. Test these:

Variable	Base case	−20% scenario	+20% scenario
Rainfall	792 mm	634 mm	950 mm
Tank size	5,000 L	—	10,000 L
Occupants	4	3	5
Autonomy (%)	___	___	___

Recommendation: Design for the −20% rainfall scenario if the system will be relied upon during dry periods.

Unit Conversion Reference

From	To	Multiply by
mm of rainfall on 1 m²	Liters	1
m³	Liters	1,000
L/day	m³/year	0.365
m of water head	kPa	9.81
bar	kPa	100
bar	m head	10.2
L/min	m³/s	1.667 × 10⁻⁵
US gallons	Liters	3.785

Previous: Chapter 8 — System Integration and Design

Next: Chapter 10 — Water Quality Testing and Monitoring

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