---
title: "Lake loss from monthly pan evaporation"
subject: "Engineering Hydrology"
chapter: 3
key: "semester_5/engineering_hydrology:pan-evap-kathmandu-lake"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/pan-evap-kathmandu-lake
site: BCT Engineering
---

# Lake loss from monthly pan evaporation

Engineering Hydrology · Chapter 3: Hydrological Losses

- Asked in: 2078 Kartik, 5 marks
- Video: [Lake evaporation of each month using Meyer's formula | Hydrology](https://www.youtube.com/watch?v=Mi-ACOJEmf0) — The Study Sphere
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/pan-evap-kathmandu-lake
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-3

## Question

Following are the monthly pan evaporation data (Jan-Dec) near Kathmandu in a certain year in cm: 16.7, 14.3, 17.8, 25.0, 28.6, 21.4, 16.7, 16.7, 16.7, 16.7, 21.4, 16.7. The water spread area in a lake nearby in the beginning of January in that year was 2.80 km$^2$ and at the end of December it was measured as 2.55 km$^2$. Calculate the loss of water due to evaporation in that year. Assume a pan coefficient of 0.7.

## Short answer

Annual pan evaporation sum is 228.7 cm. Lake evaporation depth = 0.7 ×228.7 =160.1 cm. Mean area 2.675 km² gives loss volume 4.28×10⁶ m³.

## Answer

Lake evaporation $= C_p \times$ pan evaporation, and the volume lost $=$ depth $\times$ mean water-spread area.

#### Step 1: Annual pan evaporation
$16.7+14.3+17.8+25.0+28.6+21.4+16.7+16.7+16.7+16.7+21.4+16.7 = 228.7$ cm

#### Step 2: Lake evaporation depth
$$
E_L = 0.7\times228.7 = 160.09\ \text{cm} = 1.6009\ \text{m}
$$

#### Step 3: Mean water-spread area
$$
A_{avg} = \frac{2.80 + 2.55}{2} = 2.675\ \text{km}^2 = 2.675\times10^6\ \text{m}^2
$$

#### Step 4: Volume of evaporation loss
$$
V = 1.6009\times 2.675\times10^6 = 4,282,407\ \text{m}^3
$$

**Answer: Evaporation depth = 160.1 cm; volume lost = 4.28 × 10⁶ m³ (about 4.28 million m³) in the year.**

## Check yourself

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

1. The lake evaporation depth is:
   A. 228.7 cm
   B. 160.09 cm
   C. 326.7 cm
   D. 114.4 cm
   Answer: B. 0.7 x 228.7 = 160.09 cm. (Key point: Lake evaporation)

2. Which area multiplies the depth?
   A. Initial area 2.80
   B. Final area 2.55
   C. Mean area 2.675 km2
   D. Sum 5.35 km2
   Answer: C. The area changes during the year, so the mean is used. (Key point: Area)

3. The volume lost is:
   A. 4.28 x 10^6 m3
   B. 1.6 x 10^6 m3
   C. 4.28 x 10^3 m3
   D. 2.675 x 10^6 m3
   Answer: A. 1.6009 m x 2.675 x 10^6 m2 = 4.28 x 10^6 m3. (Key point: Volume)

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