Cooling-water fouling factors: For cooling-water services in heat exchanger design, the fouling factor typically lies in the range 0.001 to 0.003 in which set of units?

Introduction / Context:
The fouling factor accounts for additional thermal resistance caused by deposits, scaling, and biofouling on heat-transfer surfaces. Appropriate selection of fouling factors is critical to ensure realistic exchanger sizing and reliable operation in cooling-water duties.

Given Data / Assumptions:

• Cooling water of typical industrial quality.
• Fouling factor range specified: 0.001 to 0.003 (English units).
• We are identifying the correct dimensional form corresponding to that numerical range.

Concept / Approach:
Fouling resistance R_f adds to the overall thermal resistance and has the same units as 1/U (the inverse of overall heat-transfer coefficient). In English units, U is BTU/(hr·ft²·°F), hence R_f has units of (hr·ft²·°F)/BTU, which is equivalently written as (BTU/hr·ft²·°F)^-1.

Step-by-Step Solution:

Verification / Alternative check:
Design manuals commonly cite cooling-water fouling factors around 0.001–0.002 (hr·ft²·°F)/BTU. Writing these as the reciprocal of U’s units is standard shorthand, which corresponds to option (a).

Why Other Options Are Wrong:

• (b) and (c) are SI-based inverses; the stated numerical range is not directly transferable without conversion.
• (d) has incorrect dimensional length in the denominator (m instead of m²).
• (e) shows the correct dimension but not the exact notation offered in the options; the question’s intended match is the reciprocal-unit form in (a).

Common Pitfalls:
Mixing SI and English units or forgetting that fouling resistance is an added inverse-U term leading to incorrect sizing margins.

Final Answer:
(BTU/hr·ft²·°F)^-1