---
title: "Procedure of Penman's method"
subject: "Engineering Hydrology"
chapter: 3
key: "semester_5/engineering_hydrology:penman-procedure"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/penman-procedure
site: BCT Engineering
---

# Procedure of Penman's method

Engineering Hydrology · Chapter 3: Hydrological Losses

- Asked in: 2081 Baisakh, 5 marks; 2079 Baisakh, 5 marks (asked 2 times)
- Video: [Topic 3   Penman Method](https://www.youtube.com/watch?v=rMJxGG6oexA) — Sheila Cogay
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/penman-procedure
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-3

## Question

Describe the procedure of calculating evapotranspiration by Penman's method.

## Short answer

Combine energy balance and aerodynamic terms: PET = (A·Hn + Ea·γ)/(A+γ). Collect temperature, humidity, sunshine, wind; compute net radiation Hn from sunshine and radiation data, aerodynamic term Ea = 0.35(1+u2/160)(ew-ea), then PET. Multiply by days for monthly values.

## Answer

Penman's method combines the **energy balance** (net radiation) and the **aerodynamic (mass transfer)** methods to estimate evaporation or potential evapotranspiration (PET) from standard weather data. It needs no surface temperature.

$$
PET = \frac{A\,H_n + E_a\,\gamma}{A + \gamma}
$$

#### Procedure
1. **Collect data:** mean monthly air temperature $T$, relative humidity RH, observed sunshine hours $n$, wind speed $u_2$ at 2 m, latitude, and the reflection coefficient $r$ of the surface.
2. **Find from tables:** saturation vapour pressure $e_w$ at $T$ (mm Hg), the slope $A = de_w/dT$ at $T$, the extraterrestrial radiation $H_a$ (mm of evaporable water/day) for the latitude and month, and the possible sunshine hours $N$.
3. **Actual vapour pressure:** $e_a = RH \times e_w$.
4. **Net radiation (mm/day):**

$$
H_n = H_a(1-r)\left(0.29\cos\varphi + 0.52\frac{n}{N}\right) - \sigma T_a^4(0.56 - 0.092\sqrt{e_a})\left(0.1 + 0.9\frac{n}{N}\right)
$$

with $\sigma = 2.01\times10^{-9}$ mm/day/K$^4$ and $T_a$ in kelvin.

5. **Aerodynamic term:**

$$
E_a = 0.35\left(1 + \frac{u_2}{160}\right)(e_w - e_a)
$$

with $u_2$ in km/day.

6. **Compute** $PET$ using the equation above with $\gamma = 0.49$ mm Hg/$^\circ$C (psychrometric constant).
7. For the monthly value multiply by the number of days. For open-water evaporation, use $r = 0.05$; for crops use $r$ of the crop (0.15-0.25) and multiply by a crop coefficient if actual crop ET is required.

## Check yourself

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

1. Penman's method combines:
   A. Water budget and pan data
   B. Energy balance and aerodynamic (mass transfer) methods
   C. Empirical formulae and remote sensing
   D. Two pan methods
   Answer: B. It combines net radiation with the aerodynamic term and needs no surface temperature. (Key point: Principle)

2. The actual vapour pressure ea is:
   A. ea = RH x ew
   B. ea = ew / RH
   C. ea = ew - RH
   D. ea = ew x (1 - RH)
   Answer: A. RH is the ratio ea/ew, so ea = RH x ew. (Key point: Actual vapour pressure)

3. Which reflection coefficient is used for open water?
   A. 0.05
   B. 0.20
   C. 0.50
   D. 0.90
   Answer: A. For open water r = 0.05; crops use 0.15-0.25. (Key point: Water surface)

4. In Ea = 0.35(1 + u2/160)(ew - ea) the wind speed u2 is in:
   A. m/s
   B. km/h
   C. km/day
   D. knots
   Answer: C. u2 is in km/day at 2 m height. (Key point: Aerodynamic term)

## Related in Engineering Hydrology

- [PET by Penman method, Kathmandu in March](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Apenman-kathmandu-march) — Engineering Hydrology, chapter 3, asked 2×
- [PET by Penman method, Kathmandu in February](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Apenman-kathmandu-february) — Engineering Hydrology, chapter 3, asked 2×
- [PET by Penman formula, Dharan in April](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Apenman-dharan-april) — Engineering Hydrology, chapter 3
- [PET by Penman formula, Simara in April](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Apenman-simara-april) — Engineering Hydrology, chapter 3
- [Daily PET by Penman, latitude 30 N, 300 m](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Apenman-daily-lat30-elev300) — Engineering Hydrology, chapter 3
- [PET versus AET, Penman's method](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Apet-vs-aet-penman) — Engineering Hydrology, chapter 3

## Related in other subjects

- [Potential evapotranspiration by Penman method](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Apenman-pet-steps) — Irrigation and Drainage Engineering, chapter 2