In municipal water-supply engineering, if V is the total consumption of water in litres for a population of N individuals, what is the expression for the per capita consumption (also called the water allowance) Q?

Introduction / Context: Per capita consumption (also called water allowance) is a foundational metric in water-supply design. It expresses how much water, on average, is consumed by a single person in a service area over a specified period. This simple ratio underpins demand forecasting, sizing of treatment plants, storage, and distribution networks.

Given Data / Assumptions:

• Total water consumed over the period = V litres.
• Total number of individuals served = N.
• Uniform accounting period for V (e.g., per day, per year) is implied and consistent.
• Per capita consumption Q is required in litres per capita for the same period as V.

Concept / Approach: The concept is a straightforward average: distribute the aggregate consumption V evenly across N persons. Therefore, the per-person usage equals the total divided by the population count. Dimensional consistency confirms a result in litres per capita when V is in litres and N is dimensionless (a count).

Step-by-Step Solution: Define Q as average consumption per individual for the chosen period. Write Q = V / N. Check units: litres / person → litres per capita. Conclude the expression that satisfies dimensional and logical requirements is Q = V / N.

Verification / Alternative check: If V doubles while N doubles, Q remains unchanged, which is sensible for an average-per-person measure. If N = 1 (single user), Q = V, also consistent with intuition.

Why Other Options Are Wrong:

• N / V: Inverts the intended ratio and yields per-litre persons, not meaningful for design.
• V * N: Scales consumption incorrectly; dimensions become litres·persons.
• (V * 1000) / N: Artificial scaling inflates the value unless V was in cubic metres; the stem already states litres.
• (V / N) * 100: Arbitrary multiplication; no basis unless expressing a percentage of some benchmark.

Common Pitfalls:

• Mixing periods (e.g., V per day with N per month) which invalidates Q.
• Accidentally using service connections instead of individuals when computing per capita values.

Final Answer: Q = V / N (litres per capita).