---
title: "Potential evapotranspiration by Penman method"
subject: "Irrigation and Drainage Engineering"
chapter: 2
key: "semester_6/irrigation_and_drainage_engineering:penman-pet-steps"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/penman-pet-steps
site: BCT Engineering
---

# Potential evapotranspiration by Penman method

Irrigation and Drainage Engineering · Chapter 2: Irrigation Water Requirements

- Asked in: 2065 Shrawan (old course), 8 marks
- Video: [Potential evapotranspiration using Penman's equation | Hydrology](https://www.youtube.com/watch?v=ifZ2sOisH34) — The Study Sphere
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/penman-pet-steps
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-2

## Question

Write the definition of potential evapotranspiration and write down the steps for calculation of potential evapotranspiration by Penman's method with all associated formula.

## Short answer

Potential evapotranspiration is ET from a well-watered short grass cover. Penman's method combines energy and aerodynamics: PET = (Δ Hn + γ Ea)/(Δ + γ). Steps: compute Δ, ea, ed; net radiation Hn = Ha(1-r)(a+b n/N) - σTa4(0.56-0.092√ed)(0.1+0.9 n/N); wind term Ea = 0.35(1+u2/160)(ea - ed); substitute.

## Answer

**Potential evapotranspiration (PET):** the amount of water evaporated and transpired per unit area per unit time from a short green grass cover (0.12 m height, well-watered, actively growing, completely shading the ground) with unlimited water supply.

#### Penman's combination method (steps)
Penman combines the energy-balance (radiation) and aerodynamic (wind) terms:

$$
PET = \frac{\Delta H_n + \gamma E_a}{\Delta + \gamma}
$$

where $PET$ in mm/day, $\Delta$ = slope of the saturation vapour pressure curve at air temperature (mm Hg/$^\circ$C), $\gamma$ = psychrometric constant (0.49 mm Hg/$^\circ$C), $H_n$ = net radiation (mm of evaporable water/day), $E_a$ = aerodynamic term (mm/day).

1. **Mean air temperature $T$** and saturation vapour pressure $e_a$ (mm Hg) at $T$; get $\Delta$ from tables.
2. **Actual vapour pressure** $e_d = e_a \times RH/100$.
3. **Net radiation:**
$$
H_n = H_a(1-r)\left(a+b\frac{n}{N}\right) - \sigma T_a^4(0.56-0.092\sqrt{e_d})\left(0.1+0.9\frac{n}{N}\right)
$$
 where $H_a$ = extraterrestrial radiation (table by latitude and month), $r$ = albedo (0.25 for grass), $n/N$ = ratio of actual to possible sunshine hours, $a = 0.18$, $b = 0.55$ (typical), $\sigma$ = Stefan-Boltzmann constant.
4. **Aerodynamic term:**
$$
E_a = 0.35\left(1+\frac{u_2}{160}\right)(e_a - e_d)
$$
 with $u_2$ = wind speed at 2 m height (km/day).
5. **Substitute** into the Penman equation to get PET (mm/day).
6. **Crop evapotranspiration:** $ET_c = K_c\times PET$.
7. Multiply by the number of days of the month for monthly values.

## Check yourself

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

1. Potential evapotranspiration refers to evaporation and transpiration from
   A. bare soil
   B. short green grass, well watered, completely shading the ground
   C. an open water surface only
   D. a crop under water stress
   Answer: B. The reference cover is 0.12 m grass with unlimited water. (Key point: PET definition)

2. Penman's method combines
   A. temperature and rainfall
   B. pan evaporation and Kc
   C. energy balance (radiation) and aerodynamic (wind) terms
   D. sunshine and soil moisture
   Answer: C. PET = (Delta Hn + gamma Ea)/(Delta + gamma). (Key point: Penman equation)

3. The actual vapour pressure e_d is found as
   A. e_a / RH
   B. e_a + RH
   C. e_a x u2
   D. e_a x RH/100
   Answer: D. Saturation vapour pressure scaled by relative humidity. (Key point: Actual vapour pressure)

4. The aerodynamic term Ea depends on
   A. wind speed at 2 m and the vapour pressure deficit (e_a - e_d)
   B. net radiation and albedo
   C. sunshine ratio n/N only
   D. latitude only
   Answer: A. Ea = 0.35(1+u2/160)(e_a - e_d). (Key point: Aerodynamic term)

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