Evaporation fundamentals – Relating capacity and economy to steam consumption In a single- or multiple-effect evaporator, the steam consumption in kg per hour is expressed in terms of the evaporator capacity C (kg of water evaporated per hour) and the economy E (kg of water evaporated per kg of steam). Choose the correct formula.

Introduction / Context:
Evaporator performance is often summarized by capacity and economy. Capacity tells how much water is evaporated per hour, whereas economy captures how effectively steam is used (how many kilograms of water removed per kilogram of steam supplied). Converting between these defines the steam consumption, critical for utility sizing and cost analysis.

Given Data / Assumptions:

• C = capacity = kg water evaporated per hour.
• E = economy = kg water evaporated per kg steam.
• Steady operation; negligible heat leaks for the relation.

Concept / Approach:
By definition, economy E = (water evaporated) / (steam used). Rearranging yields steam used = (water evaporated) / E. In rate form, steam consumption (kg/h) = C / E. This relation is independent of the number of effects and directly ties utility usage to throughput and economy.

Step-by-Step Solution:

Verification / Alternative check:
If E = 1 (single effect ideal), steam consumption equals capacity, as expected. If E increases, required steam per hour decreases proportionally.

Why Other Options Are Wrong:

• E/C: Inverts the relationship and has incorrect units.
• C E: Multiplies rather than divides, grossly overpredicting steam usage.
• E - C: Nonsensical dimensionally.

Common Pitfalls:
Confusing economy with efficiency; economy is a ratio tied to mass balance, not a percentage.

Final Answer:
C/E