---
title: "Minimum critical reservoir top elevation"
subject: "Hydropower Engineering"
chapter: 4
key: "semester_7/hydropower_engineering:spillway-min-critical-reservoir-elevation"
source: https://www.bctengineer.com/q/semester_7/hydropower_engineering/spillway-min-critical-reservoir-elevation
site: BCT Engineering
---

# Minimum critical reservoir top elevation

Hydropower Engineering · Chapter 4: Headworks of Storage Plants

- Asked in: 2081 Bhadra, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/hydropower_engineering/spillway-min-critical-reservoir-elevation
- Whole chapter: https://www.bctengineer.com/md/semester_7/hydropower_engineering/chapter-4

## Question

Determine the minimum critical elevation of the top of the reservoir, which has a spillway with a maximum discharge capacity of 5127 m³/s. The spillway has five openings, each 12.2 m wide. The crest level of the spillway is 1250 m. Assume a discharge coefficient of 0.6 for the broad crested weir.

## Short answer

Using the broad-crested weir equation with effective length 61 m and Cd=0.6, the required head is 13.10 m. The minimum critical reservoir elevation is 1263.10 m.

## Answer

**Given**: $Q_{max}=5127$ m³/s; 5 openings, each 12.2 m wide; crest level 1250 m; $C_d=0.6$ for a broad-crested weir.

The minimum critical (maximum flood) level of the reservoir is the crest level plus the head $H$ that is needed to pass the maximum discharge.

#### Effective length
$$
L=5\times12.2=61.0\ \text{m}
$$
(Pier contraction is neglected, since no pier or abutment coefficient is given.)

#### Discharge equation (broad-crested weir)
$$
Q=\frac{2}{3}C_d\sqrt{2g}\,L\,H^{3/2}
$$
$$
\begin{aligned}
5127&=\frac{2}{3}(0.6)\sqrt{2\times9.81}\,(61.0)\,H^{3/2}\\
5127&=108.08\,H^{3/2}\\
H^{3/2}&=47.44\ \Rightarrow\ H=13.10\ \text{m}
\end{aligned}
$$

#### Reservoir level
$$
\text{RL}=1250+13.10=1263.10\ \text{m}
$$

**Answer**: the top (flood) level of the reservoir must not be lower than **1263.10 m** (head over the crest $=13.10$ m).

## Check yourself

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

1. What effective length L is used?
   A. 5 x 12.2 = 61.0 m, neglecting pier contraction
   B. 12.2 m
   C. 5 + 12.2 = 17.2 m
   D. 5127/12.2 = 420 m
   Answer: A. Five openings of 12.2 m give 61 m; no pier coefficient is given so contraction is neglected. (Key point: Effective length)

2. Which equation relates Q and H for a broad-crested weir here?
   A. Q = (2/3) Cd sqrt(2g) L H^(3/2)
   B. Q = Cd L H^2
   C. Q = Cd L sqrt(H)
   D. Q = (2/3) Cd L H
   Answer: A. Broad-crested weir discharge is proportional to H^(3/2), giving H = 13.10 m. (Key point: Weir equation)

3. How is the minimum critical reservoir top level obtained?
   A. Crest level + head: 1250 + 13.10 = 1263.10 m
   B. Crest level - head = 1236.9 m
   C. Crest level only, 1250 m
   D. Crest level + 2H
   Answer: A. The reservoir must stand at the head H above the crest to pass the maximum discharge. (Key point: Reservoir level)

## Related in Hydropower Engineering

- [Gravity dam equilibrium and overtopping discharge coefficient](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-reservoir-capacity-curve-hrwl) — Hydropower Engineering, chapter 4
- [Discharge through chute spillway ogee crest](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Aspillway-chute-discharge-ogee-250m) — Hydropower Engineering, chapter 4
- [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
- [Phreatic line and discharge (crest 300 masl)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Aearthen-dam-phreatic-line-2079-baishakh) — Hydropower Engineering, chapter 4, asked 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
- [Installed capacity, energy and daily peaking reservoir (2079)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Aror-capacity-plant-factor-18cumec-peaking-79) — Hydropower Engineering, chapter 3, asked 2×

## Related in other subjects

- [Reservoir routing through spillway, 6-hr inflow](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Areservoir-routing-spillway-6hr) — Engineering Hydrology, chapter 7
- [Crest level of fall, Q 30 m3/s](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Afall-crest-level-30cumec-broad-crested) — Irrigation and Drainage Engineering, chapter 7
- [Weir waterway and crest levels, 16000 m3/s](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Aweir-waterway-crest-q16000) — Irrigation and Drainage Engineering, chapter 5
- [Discharge over overflow spillway](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Aoverflow-spillway-discharge) — Hydro Power, chapter 6