By-pass factor (sensible cooling): Select the correct expression in terms of dry-bulb temperatures td1 (entering air), td2 (leaving air), and td3 (coil surface/apparatus dew-point).

Introduction / Context:
The by-pass factor (BPF) quantifies how closely the leaving air approaches the coil surface temperature during sensible cooling. A low BPF indicates effective contact and good approach to the apparatus dew-point, important for comfort cooling and dehumidification.

Given Data / Assumptions:

• Steady air flow across a cooling coil.
• td1 = entering dry-bulb, td2 = leaving dry-bulb, td3 = coil surface (apparatus dew-point).
• Negligible reheat between coil and measurement point.

Concept / Approach:
For sensible cooling, the fraction of air that effectively “bypasses” the coil behaves as if it were mixed with air cooled to the coil surface temperature. From the standard mixing relation, BPF is the ratio of the leaving-to-entering temperature differences measured relative to the coil surface temperature.

Step-by-Step Solution:

Verification / Alternative check:
The equation satisfies dimensional consistency and limiting cases; it is the standard textbook form used in coil selection and performance rating.

Why Other Options Are Wrong:

Other forms invert or misplace temperature differences, leading to values outside the 0–1 range or violating limits at perfect contact.

Common Pitfalls:
Using mixed air temperature after a reheat coil as td2, which inflates BPF; always use the air temperature immediately leaving the cooling coil.

Final Answer:

BPF = (td2 − td3) / (td1 − td3)