HVAC Psychrometric Chart Practice Questions Engineering Analysis: Pressure & Flow Requirements

Engineering Analysis: Pressure & Flow Requirements

Comprehensive analysis of fire sprinkler system pressure and flow requirements

Technical Document

August 2023

This analysis details the pressure and flow requirements for the fire sprinkler system, following BS EN 12845 standards.

1Pressure & Flow Determination Methods

Method 1: Pre-calculated Tables

Using pre-calculated tables for preliminary design stages

  • Sufficient for initial design phases
  • Based on BS EN 12845:2004, Clause 7.3
  • Provides conservative estimates
BS EN 12845:2004, Clause 7.3
Method 2: Hydraulic Calculations

Detailed hydraulic calculations for accurate requirements

  • Required for final design and pump selection
  • Based on actual system configuration
  • Provides precise pressure and flow data
BS EN 12845:2004, Clause 13

2Characteristic Points Analysis

Characteristic Point 1 - Minimum Flow Rate

Refers to the instance when sprinklers at the hydraulically most unfavorable location activate.

Flow rate (minimum): 1,100 litres/min
Pressure at downstream side of alarm valve: 1.7 + Ps bar
Where Ps = Static head at 6th floor = 4.571 bar
Pressure required: 1.7 + 4.571 = 6.271 bar

Assumption: Pressure required for sprinkler discharge and pipe frictional losses downstream of alarm valve does not exceed 1.7 bar at minimum flow rate.

BS EN 12845:2004, Table 6
Characteristic Point 2 - Maximum Flow Rate

Refers to the instance when sprinklers at the hydraulically most favorable location activate.

Maximum demand flow: 1,350 litres/min
Pressure required: 1.4 + Ps bar
Where Ps = Static head at 6th floor = 4.571 bar
Pressure required: 1.4 + 4.571 = 5.971 bar

Assumption: Pressure required for sprinkler discharge and pipe frictional losses downstream of alarm valve does not exceed 1.4 bar at maximum flow rate.

BS EN 12845:2004, Table 6
Pressure & Flow Requirements Summary
Characteristic Point Flow Rate (litres/min) Pressure at Alarm Valve (bar) Remarks
Point 1 (Most Unfavorable) 1,100 6.271 Design requirement (minimum flow rate)
Point 2 (Most Favorable) 1,350 5.971 Requirement at maximum demand

The pump must be capable of providing these flow rates and pressures at the alarm valve ('C' gauge location).

3Hydraulic Calculations Methodology

Assumed Maximum Area of Operation (AMAO)

Hydraulic calculations consider the AMAO - the maximum area where sprinklers are assumed to operate during a fire.

For OH3 wet systems: AMAO = 216 m²
Design density: 5 mm/min (5 litres/min/m²)

Standard: BS EN 12845:2004, Table 3

Locating Hydraulically Most Unfavorable AMAO

Determining the most unfavorable AMAO involves considering:

  • Sprinkler spacing and layout variations
  • Elevation differences
  • Range centers and sprinkler orifice sizes
  • Pipe sizes and configurations

For this design, the most unfavorable AMAO includes sprinklers downstream of Design Point E at the 6th floor.

BS EN 12845:2004, Clause 13.4.2.1
AMAO Shape and Configuration

The AMAO should be as near as possible to rectangular shape, symmetrical with respect to sprinkler layout.

Far side length: 21.6 m
Total area: 216 m² (minimum)
Approximate length: 216 m² / 21.6 m = 10 m

Actual AMAO shape determined by sprinkler coverage boundaries, resulting in a total area of 221.52 m² (>216 m² requirement).

BS EN 12845:2004, Clause 13.4.3.1

4Hydraulic Calculation Criteria

Key Design Parameters
Parameter Value Standard Reference
Minimum Design Density 5.0 mm/min (5.0 l/min/m²) BS EN 12845:2004, Table 3
Minimum Sprinkler Discharge Pressure 0.35 bar BS EN 12845:2004, Clause 13.4.4
Maximum Flow Velocity (Pipes) 10 m/s BS EN 12845:2004, Clause 13.2.3
Maximum Flow Velocity (Valves) 6 m/s
Calculation Method Hazen-Williams formula (C=120) BS EN 12845:2004, Clause 13.2.1
Sprinkler Flow-Pressure Relationship

The relationship between pressure and flow rate for sprinklers is defined by:

Q = k√P
Where:
Q = Flow through sprinkler orifice (litres/min)
P = Pressure at entry to sprinkler shank (bar)
k = K-factor (80 for this installation)

Minimum flow rate calculation:

Q_min = 80√0.35 = 47.33 litres/min
BS EN 12845:2004, Clause 14.3

5Computational Approach

Newton-Raphson Iteration Method

Complex hydraulic calculations were solved using the Newton-Raphson iterative method:

qₙ₊₁ = qₙ - f(qₙ)/f'(qₙ)
Where:
qₙ = nth solution for flow rate
f(q) = Function representing pressure-flow relationship
f'(q) = First derivative of f(q)

This method was implemented using custom functions in MS Excel for accurate and efficient calculations.

MS Excel Implementation

Custom functions were developed in Excel for:

  • Sprinkler flow rate calculations
  • Pipe friction loss computations
  • Node pressure balancing
  • Velocity pressure calculations

The spreadsheet automated complex iterative calculations while allowing manual adjustment of key parameters.

Hydraulic Calculation Results

Final results from hydraulic calculations:

Total flow rate to AMAO: 1,438.534 litres/min
Pressure at entry point to AMAO: 1.027 bar
Pressure at alarm valve: 6.528 bar
Minimum design density achieved: 5.574 mm/min

These values exceed the minimum requirements specified in BS EN 12845:2004.

6Water Storage Requirements

Water Storage Capacity Methods
Method 1: Pre-calculated Tables

Minimum water volume: 185 m³

BS EN 12845:2004, Table 9
Method 2: Characteristic Points

81 m³ (1,350 l/min × 60 min)

BS EN 12845:2004, Table 6
Method 3: Hydraulic Calculations

87 m³ (1,439 l/min × 60 min)

Based on actual calculations
Reduced Capacity Tank Option

A reduced capacity tank can be used with sufficient inflow rate:

Reduced tank capacity + Inflow = Full capacity
20,000 litres + (x litres/min × 60 minutes) = 86,340 litres
x = 1,106 litres/min = 18.2 litres/s

Requirement: City water supply must provide this inflow rate during peak demand periods.

BS EN 12845:2004, Table 11

7Engineering Summary

Key Design Outcomes
Parameter Table Method Hydraulic Calculation Status
Flow Rate (l/min) 1,350 1,439 Adequate
Pressure at Alarm Valve (bar) 5.971-6.271 6.528 Adequate
Design Density (mm/min) 5.0 5.574 Exceeds Requirement
Water Storage (m³) 81-185 87 Adequate
The hydraulic design meets and exceeds all BS EN 12845:2004 requirements, ensuring system reliability and performance.