---
title: "Balancing reservoir, 3 million city, 10 hours pumping"
subject: "Water Supply Engineering"
chapter: 7
key: "semester_5/water_supply_engineering:res-b78"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/res-b78
site: BCT Engineering
---

# Balancing reservoir, 3 million city, 10 hours pumping

Water Supply Engineering · Chapter 7: Reservoirs and Distribution System

- Asked in: 2078 Bhadra, 8 marks
- 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-b78
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-7

## Question

Determine the storage capacity of balancing reservoir by analytical method for 10 hours pumping (5 am to 10 am and 2 pm to 7 pm) and continuous water supply. The population of a city is 3 million has a water demand of 110 lpcd. The consumption pattern as follows:

| Time | 5-10 | 10-14 | 14-19 | 19-22 | 22-5 |
|---|---|---|---|---|---|
| Consumption | 35 | 15 | 25 | 15 | 10 |

## Short answer

Using the analytical mass-curve method with pumping 10 h/day and daily demand 330,000 m³, cumulative surplus peaks at 82,500 m³ and no deficit occurs. Balancing reservoir capacity = 82,500 m³, or 25% of daily demand.

## Answer

#### Given data
- Population 3,000,000 × 110 lpcd = 330,000 m³/day
- Pumping 10 h/day (5–10 h and 14–19 h), at a constant rate of 330,000/10 = 33,000 m³/h
- Supply from the tank to the city is continuous, with the % consumption given

#### Mass-curve table (analytical method)
Inflow: 33,000 m³/h during 5–10 h and 14–19 h only (pumped). 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 | 115500.00 | 165000.00 | +49500.00 | +49500.00 |
| 10:00–14:00 | 49500.00 | 0.00 | -49500.00 | 0.00 |
| 14:00–19:00 | 82500.00 | 165000.00 | +82500.00 | +82500.00 |
| 19:00–22:00 | 49500.00 | 0.00 | -49500.00 | +33000.00 |
| 22:00–05:00 | 33000.00 | 0.00 | -33000.00 | 0.00 |

Total demand = 330000.00 m³; total inflow = 330000.00 m³.

#### Capacity
- Maximum cumulative surplus = 82500.00 m³
- Maximum cumulative deficit = 0.00 m³
- Balancing capacity = max. surplus + max. deficit = 82500.00 + 0.00 = **82500.00 m³**

**Answer: Balancing reservoir capacity = 82,500 m³ (25% of the daily demand).**

## Check yourself

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

1. What is the daily demand of 3 million people at 110 lpcd?
   A. 33,000 m3
   B. 330,000 m3
   C. 3,300 m3
   D. 110,000 m3
   Answer: B. 3,000,000 x 110 L = 330,000,000 L = 330,000 m3. (Key point: Daily demand)

2. What is the constant pumping rate for 10 hours per day?
   A. 33,000 m3/h
   B. 3,300 m3/h
   C. 330,000 m3/h
   D. 16,500 m3/h
   Answer: A. 330,000/10 = 33,000 m3/h. (Key point: Pumping rate)

3. What is the demand during 5-10 h (35%)?
   A. 115,500 m3
   B. 49,500 m3
   C. 82,500 m3
   D. 165,000 m3
   Answer: A. 0.35 x 330,000 = 115,500 m3. (Key point: Demand 5-10 h)

4. What is the balancing capacity?
   A. 49,500 m3
   B. 82,500 m3
   C. 33,000 m3
   D. 165,000 m3
   Answer: B. Max surplus 82,500 + max deficit 0 = 82,500 m3, which is 25% of daily demand. (Key point: Capacity)

## Related in Water Supply Engineering

- [Balancing reservoir: village 600 population, 65 lpcd](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ares-as70) — Water Supply Engineering, chapter 7
- [Balancing reservoir, town of 1.3 million](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ares-c70o) — Water Supply Engineering, chapter 7, asked 2×
- [Balancing reservoir: 500 population, spring 0.28 lps](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ares-a75) — Water Supply Engineering, chapter 7
- [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×
- [Service reservoir capacity, 10,000 m3/day city](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ares-s73) — Water Supply Engineering, chapter 7
- [Storage tank capacity and water level, 20000 L/day](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Areservoir-level-river-20000) — Water Supply Engineering, chapter 7, asked 2×

## Related in other subjects

- [Minimum reservoir capacity and wasted water](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Areservoir-minimum-capacity-wasted-water-1000hp) — Hydropower Engineering, chapter 3
- [Peak demand of load center from load pattern](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Apeak-demand-load-center-load-pattern) — Transmission and Distribution System Design, chapter 6, asked 2×
- [Reservoir storage for wheat, rice, maize](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Areservoir-supply-40000ha-wheat-rice-maize) — Irrigation and Drainage Engineering, chapter 2
- [Uniform draw-off and reservoir capacity](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Auniform-drawoff-driest-year-reservoir) — Hydropower Engineering, chapter 3