Engineering Analysis: Hydraulic Calculations

Static Pressure Fundamentals

The static pressure difference between two points in the pipework is calculated using the fundamental fluid statics equation:

Where:
p = Pressure (Pa)
h = Height difference (m)
ρ = Density of water (1000 kg/m³)
g = Gravitational acceleration (9.81 m/s²)

This simplifies to a practical engineering formula:

Design Assumptions:

• Elevation of distribution pipes relative to FFL: 3.35m
• Elevation of alarm valve relative to FFL of LL3: 1.20m

Critical Calculation: The highest static head occurs at the 6th floor:

Static Head Gain Engineering Principle

A key engineering concept applied in this design is the static head gain for secondary design points at lower elevations.

This gain represents available pressure that can be "consumed" as additional frictional losses in pipe sizing calculations for lower floors.

Example: Static head gain for LL3:

This approach allows for smaller pipe diameters on lower floors while maintaining adequate pressure throughout the system.

Hazen-Williams Formula Application

Frictional pressure losses are calculated using the Hazen-Williams formula:

Where:
p = Pipe frictional loss (bar)
C = Pipe roughness coefficient (120 for galvanized steel)
d = Mean internal diameter of pipe (mm)
L = Equivalent length of pipe and fittings (m)
Q = Flow rate (L/min)

This is simplified to:

Where k is a constant for pipe size, type, and condition.

Fitting Loss Calculations

Pressure losses through fittings are calculated using equivalent lengths of straight pipe.

Fundamental Design Criterion

The fundamental design criterion for pipes upstream of the most remote design point:

Standard: BS EN 12845, Clauses 13.3.4.2 and 13.3.4.3

This ensures adequate pressure is available at all design points while optimizing pipe sizes.

Iterative Calculation Process

The design follows an iterative process:

1. Start with smallest permissible pipe size (DN65mm)
2. Calculate total frictional loss at 1000 L/min
3. If (Frictional Loss - Static Head Gain) > 0.5 bar, increase pipe size
4. Repeat process until criterion is met

Example from 6th Floor Calculation:

Strategic Pipe Sizing Approach

The design employs a strategic approach to pipe sizing:

• Upper floors: Larger diameters (DN150mm, DN100mm)
• Lower floors: Smaller diameters (DN65mm, DN80mm)

This approach efficiently utilizes the available static head gain on lower floors to reduce pipe sizes while maintaining system performance.

Calculation Implementation

The complex iterative calculations were implemented using MS Excel with:

• Named variables for all parameters
• Predefined k-values and equivalent lengths
• Formulae replicating the Hazen-Williams equation
• Automated calculation of static head gains

This approach provided flexibility to accommodate design changes and ensured accuracy in calculations.

Design Verification

The final design was verified against the criterion for all design points:

All design points show compliance with the requirement that the difference does not exceed 0.5 bar.

Key Engineering Achievements

The hydraulic design successfully achieves:

• Optimal pipe sizing across all floors
• Compliance with BS EN 12845 requirements
• Efficient use of static head gain principle
• Verification of pressure adequacy at all design points
• Cost-effective solution through strategic pipe sizing