---
title: "Hydrologic cycle and water balance equation"
subject: "Engineering Hydrology"
chapter: 1
key: "semester_5/engineering_hydrology:hydrologic-cycle-water-balance"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/hydrologic-cycle-water-balance
site: BCT Engineering
---

# Hydrologic cycle and water balance equation

Engineering Hydrology · Chapter 1: Introduction

- Asked in: 2078 Bhadra, 1+3 marks; 2072 Kartik, 2+2 marks; 2071 Shrawan, 4 marks (asked 3 times)
- Video: [What is water budget or hydrologic budget or water balance?](https://www.youtube.com/watch?v=h34ZlI3HrcE) — HydroMohsen
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/hydrologic-cycle-water-balance
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-1

## Question

Explain the hydrologic cycle and the water balance equation.

## Short answer

The hydrologic cycle is the endless movement of water from oceans to atmosphere to land and back, via evaporation, condensation, precipitation, runoff, and groundwater flow. The water balance equation (P − R − G − ET = ΔS) applies mass conservation; long-term, P ≈ R + G + ET, used for yield assessment and reservoir sizing.

## Answer

#### Hydrologic cycle
The hydrologic cycle is the endless movement of water from the oceans to the atmosphere, to the land and back to the oceans by evaporation, condensation, precipitation, runoff, infiltration and groundwater flow. The sun supplies the energy and gravity moves the water.

```text
   Sun's energy
      |
  Evaporation          Condensation -> Clouds
  + Transpiration  ^        |
      ^            |        v
 [Ocean]---------->|   Precipitation
      ^                     |
      |    Surface runoff   v
      +----- Rivers <--- [Land/Catchment]
      |                     |
      +--- Groundwater <----+  (infiltration,
           flow to sea          percolation)
```

- **Evaporation/transpiration** puts vapour in the air.
- **Condensation** forms clouds, and **precipitation** brings water to earth.
- Part of the precipitation is intercepted, part **infiltrates**, and the rest becomes **surface runoff** that reaches streams and the sea.
- Infiltrated water feeds **groundwater**, which flows slowly to rivers and oceans.

#### Water balance equation
By the law of conservation of mass, for any basin and time interval:

$$
\text{Inflow} - \text{Outflow} = \Delta S
$$

$$
P - R - G - E - T = \Delta S
$$

Here $P$ is precipitation, $R$ surface runoff, $G$ net groundwater outflow, $E$ evaporation, $T$ transpiration and $\Delta S$ the change in storage. Over a long term $\Delta S \approx 0$, so $P = R + G + ET$.

For the global balance, the land receives more precipitation than it evaporates, and the extra flows to the oceans as runoff. The equation is used to find unknown components, to size reservoirs and to assess the water yield of a basin.

## Check yourself

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

1. Which equation is the basin water balance?
   A. P - R - G - E - T = ΔS
   B. P + R + G + E + T = ΔS
   C. P - R = E + T + 2ΔS
   D. ΔS = P x R
   Answer: A. Precipitation minus all outputs equals change in storage. (Key point: Water balance form)

2. Why does P = R + G + ET hold over a long term?
   A. Because precipitation is zero
   B. Because ΔS is about zero
   C. Because evaporation is zero
   D. Because runoff equals rain
   Answer: B. Storage does not keep increasing or decreasing over many years. (Key point: Long-term)

3. For the global balance, what happens on land?
   A. Evaporation exceeds precipitation
   B. Land receives no water from the sea cycle
   C. Precipitation exceeds evaporation and the extra flows to oceans as runoff
   D. Runoff flows from sea to land
   Answer: C. The excess on land returns to oceans as runoff. (Key point: Global land balance)

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