Practical Implications of the Relationship
The Fixed Relationship: If You Know Two, You Know the Third
Given the equation H = Q × R × C, these relationships are mathematically locked:
| If This Changes… | And This Is Held Constant… | Then This Must… |
| Heat Load (H) ↑ | Flow Rate (Q) | Range (R) ↑ |
| Heat Load (H) ↑ | Range (R) | Flow Rate (Q) ↑ |
| Flow Rate (Q) ↑ | Heat Load (H) | Range (R) ↓ |
| Flow Rate (Q) ↑ | Range (R) | Heat Load (H) ↑ |
| Range (R) ↑ | Heat Load (H) | Flow Rate (Q) ↓ |
| Range (R) ↑ | Flow Rate (Q) | Heat Load (H) ↑ |
Real-World Example:
A cooling tower designed for: H = 1,000 TR (12,000,000 BTU/h
If the actual flow drops to 2,400 GPM but the heat load remains 1,000 TR, then:
- New Range = 12,000,000 ÷ (2,400 × 500) = 10°F
- The tower must provide a 10°F range instead of 8°F, which it may not be able to do!
4. Design Perspective
The Design Triangle
Engineers typically fix two parameters and calculate the third:
Common Design Scenarios:
- Known Process: “My process rejects X BTU/hr, and I have Y GPM available”
→ Calculate required Range: R = H ÷ (Q × 500) - Known Temperature Requirements: “I need to cool from 95°F to 85°F (R=10°F) with Z BTU/hr”
→ Calculate required Flow: Q = H ÷ (R × 500) - Existing Tower Evaluation: “I have a 1,500 GPM tower with 10°F range”
→ Calculate capacity: H = 1,500 × 10 × 500 = 7,500,000 BTU/hr (625 TR)
Typical Design Values by Application:
| Application | Typical Range | Typical Flow/TR | Notes |
| HVAC Chiller Condenser | 8-12°F | 2.5-3.0 GPM/TR | 24 ÷ Range = GPM/TR |
| Power Plant Condenser | 20-30°F | 1.5-2.0 GPM/TR | Large ΔT, lower flow |
| Process Cooling | 10-25°F | Varies widely | Depends on process |
| Plastics Cooling | 5-15°F | 2.0-4.0 GPM/TR | Sensitive temperature control |