# Penmans Equation | Engineering Hydrology | Calculation of Potential Evapotranspiration by Penmans Equation

### 1. Introduction

Penman’s equation is the semi-empirical equation used for the calculation of potential Evapotranspiration using various meteorological data. The daily potential evapotranspiration.

Potential Evapotranspiration (PET) = AxHo+ γ Ea / (A+ γ)

### 2. Derivation of Penmans Equation

As we know,

Hn = G+E   ——-(i)

where,

Hn= net solar radiation with a unit of mm of evaporable water per day.

G= energy used for heating for air

E= energy used for evapotranspiration

Now, from Dalton’s law

G = γ f(v) (ts-ta)

where,

γ= Psychrometric constant = 0.49 mmhg/ºC

f(v)= Function of wind speed

ta = temperature of air

t= dew point

ts = temperature of water surface

Then,

G = γ f(v) {(ts-td)- (ta-td)}

G = γ f(v) {(es,s -ed)/A- (ea-ed)/A}

G = γ f(v) {(es,s -ed)- (ea-ed)}/A

Where, es = saturated vapour pressure for ts.

eo=ed= actual vapour pressure

es= Saturated vapour pressure for ta.

A = Slope of saturation vapour pressure curve.

then, G= γ{E-Ea }/ A

Where, Ea = acrodynamic evapouration

then, from eqn i and ii, we get

Hn = G+E

Hn= γ{E-Ea }/ A + E

E = ( H A + γE)/ (A+γ)

Which is a required expression for penmans equation.

 Read Also: Derivation of Unit Hydrograph

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