---
title: "Balancing reservoir, town of 1.3 million"
subject: "Water Supply Engineering"
chapter: 7
key: "semester_5/water_supply_engineering:res-c70o"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/res-c70o
site: BCT Engineering
---

# Balancing reservoir, town of 1.3 million

Water Supply Engineering · Chapter 7: Reservoirs and Distribution System

- Asked in: 2070 Chaitra (old course)
- Video: [Problem On Distribution Reservoir(Module-V) Water supply and treatment Engineering](https://www.youtube.com/watch?v=-7mIGJa120U) — satish hooli
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/water_supply_engineering/res-c70o
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-7

## Question

A newly established town with a population of 1.3 million is to be supplied with water daily at 110 liters per head. The variation in demand is as follows.

| Time | Consumption % |
|---|---|
| 05.00-10.00 | 55 |
| 10.00-14.00 | 10 |
| 14.00-18.00 | 20 |
| 18.00-22.00 | 10 |
| 22.00-05.00 | 5 |

Determine analytically the balancing reservoir capacity assuming pumping to be done at a uniform rate and the period of pumping is 5 A.M to 6 P.M. Neglect fire demand.

## Short answer

The balancing reservoir capacity is 45,100 m³, obtained as the sum of maximum cumulative surplus (21,450 m³) and maximum cumulative deficit (23,650 m³) from the mass curve of uniform 13-h pumping at 11,000 m³/h against the hourly demand pattern.

## Answer

#### Given data
- Population 1,300,000 × 110 lpcd = 143,000 m³/day
- Pumping at a uniform rate from 5 AM to 6 PM (13 h): rate = 143,000/13 = 11,000 m³/h
- Fire demand neglected

#### Mass-curve table (analytical method)
Inflow: 11,000 m³/h during 5–18 h. Time is counted from the start of the first demand period; a positive cumulative value means surplus in the tank.

| Time | Demand (m³) | Inflow (m³) | Inflow − demand | Cumulative |
|---|---|---|---|---|
| 05:00–10:00 | 78650.00 | 55000.00 | -23650.00 | -23650.00 |
| 10:00–14:00 | 14300.00 | 44000.00 | +29700.00 | +6050.00 |
| 14:00–18:00 | 28600.00 | 44000.00 | +15400.00 | +21450.00 |
| 18:00–22:00 | 14300.00 | 0.00 | -14300.00 | +7150.00 |
| 22:00–05:00 | 7150.00 | 0.00 | -7150.00 | +0.00 |

Total demand = 143000.00 m³; total inflow = 143000.00 m³.

#### Capacity
- Maximum cumulative surplus = 21450.00 m³
- Maximum cumulative deficit = 23650.00 m³
- Balancing capacity = max. surplus + max. deficit = 21450.00 + 23650.00 = **45100.00 m³**

**Answer: Balancing reservoir capacity = 45,100 m³ (31.5% of the daily demand).**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Demand is 143,000 m3/day and pumping runs 5 am to 6 pm (13 h). What is the rate?
   A. 5,958 m3/h
   B. 11,000 m3/h
   C. 143,000 m3/h
   D. 6,500 m3/h
   Answer: B. 143,000/13 = 11,000 m3/h. (Key point: Pumping rate)

2. In 5-10 h demand is 55% and pumping is on. What is inflow minus demand?
   A. +23,650 m3
   B. -23,650 m3
   C. +55,000 m3
   D. -78,650 m3
   Answer: B. Inflow 5 x 11,000 = 55,000; demand 0.55 x 143,000 = 78,650; difference -23,650 m3. (Key point: First period)

3. Max surplus 21,450 m3 and max deficit 23,650 m3. What is the capacity?
   A. 23,650 m3
   B. 21,450 m3
   C. 2,200 m3
   D. 45,100 m3
   Answer: D. Add them: 21,450 + 23,650 = 45,100 m3. (Key point: Capacity)

## Close variants set in other exams

- [Balancing reservoir: town 1.2 million, 45 L/head](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ares-bk68) — Water Supply Engineering, chapter 7, asked 2×

## Related in Water Supply Engineering

- [Balancing reservoir, 3 million city, 10 hours pumping](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ares-b78) — Water Supply Engineering, chapter 7
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