---
title: "Water budget equation and its role"
subject: "Engineering Hydrology"
chapter: 1
key: "semester_5/engineering_hydrology:water-balance-equation-processes"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/water-balance-equation-processes
site: BCT Engineering
---

# Water budget equation and its role

Engineering Hydrology · Chapter 1: Introduction

- Asked in: 2080 Bhadra, 4 marks; 2079 Bhadra, 4 marks; 2074 Asoj, 2+2 marks; 2073 Shrawan, 4 marks; 2068 Chaitra, 4 marks (asked 5 times)
- Video: [Water Budget Equation - Hydrology](https://www.youtube.com/watch?v=bM1Dlyy_jWY) — Engr. Clidez
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/water-balance-equation-processes
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-1

## Question

Explain water budget equation. What is the role of water budget equation in hydrology?

## Short answer

The water budget equation, I − O = ΔS, applies mass conservation. For a basin it becomes P + Q_in + G_in − E − T − Q_out − G_out = ΔS; over long term ΔS ≈ 0 yields P = R + G + ET. It helps estimate unknown fluxes, plan reservoirs, and check data.

## Answer

The **water budget (water balance) equation** is an application of the law of conservation of mass to a hydrologic system: inflow minus outflow equals the change in storage over a time period.

$$
I - O = \frac{dS}{dt} \quad\text{or}\quad I - O = \Delta S
$$

For a catchment over a period $\Delta t$:

$$
P + Q_{in} + G_{in} - E - T - Q_{out} - G_{out} = \Delta S
$$

where $P$ = precipitation, $Q_{in}, Q_{out}$ = surface inflow and outflow, $G_{in}, G_{out}$ = groundwater inflow and outflow, $E$ = evaporation, $T$ = transpiration, and $\Delta S$ = change in storage (soil moisture, groundwater, surface water, snow). For a closed natural basin with no inflow, it reduces to

$$
P - R - G - E_T = \Delta S
$$

with $R$ = surface runoff, $G$ = net groundwater outflow and $E_T$ = evapotranspiration. Over a long period (many years) $\Delta S \approx 0$, so $P = R + G + E_T$.

#### Role of the water budget equation
- **Estimating an unknown component:** If P, R and ET are measured, the groundwater recharge or storage change can be found. Evaporation from lakes and reservoirs can be found in the same way.
- **Water resources assessment:** It gives the available yield of a basin for water supply, irrigation and hydropower.
- **Reservoir planning:** Inflow, outflow and storage are balanced to find the reservoir capacity and change in level.
- **Checking data:** A large non-closure of the budget shows errors in measured data.
- **Impact studies:** It helps to study the effect of land-use change, dams or climate change on a basin.

## Check yourself

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

1. On what law is the water budget equation based?
   A. Conservation of mass: inflow - outflow = change in storage
   B. Conservation of energy: inflow + outflow = storage
   C. Darcy's law
   D. Bernoulli's principle
   Answer: A. The water budget applies mass conservation to a hydrologic system. (Key point: Principle)

2. Over many years, what does the budget of a basin reduce to?
   A. P = R only
   B. P = R + G + ET since change in storage is about zero
   C. P = ET only, since runoff is lost
   D. P - R = storage always rising
   Answer: B. Over a long period storage change is negligible, so precipitation equals runoff, groundwater outflow and evapotranspiration. (Key point: Long-term form)

3. Which is a use of the water budget equation?
   A. Measuring rainfall intensity
   B. Drawing isohyets
   C. Finding an unknown component such as groundwater recharge from measured P, R and ET
   D. Finding the silt factor
   Answer: C. If other terms are measured, the remaining one follows from the balance. (Key point: Role)

4. What does a large non-closure of the budget indicate?
   A. The catchment is perfectly balanced
   B. Storage is zero
   C. Evaporation is absent
   D. Errors in the measured data
   Answer: D. A budget that does not close points to measurement errors. (Key point: Data checking)

## Related in Engineering Hydrology

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- [Importance of hydrology in Nepal, global water balance](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ahydrology-importance-global-balance) — Engineering Hydrology, chapter 1
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