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

In this article, we will discuss penman’s 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) = AxH_o+ γ E_a / (A+ γ)

  2. Derivation of Penmans Equation  

As we know,

H_n = G+E   ——-(i)

where,

H_n= 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) (t_s-t_a)

where,

γ= Psychrometric constant = 0.49 mmhg/ºC

f(v)= Function of wind speed

t_a = temperature of air

t_d = dew point

t_s = temperature of water surface

Then,

G = γ f(v) {(t_s-t_d)- (t_a-t_d)}

G = γ f(v) {(e_s,s -e_d)/A- (e_a-e_d)/A}

G = γ f(v) {(e_s,s -e_d)- (e_a-e_d)}/A

Where, es = saturated vapour pressure for t_s.

e_o=e_d= actual vapour pressure

e_s= Saturated vapour pressure for t_a.

A = Slope of saturation vapour pressure curve.

then, G= γ{E-E_a }/ A

Where, Ea = acrodynamic evapouration

then, from eqn i and ii, we get

Hn = G+E

Hn= γ{E-E_a }/ A + E

E = ( H A + γE_a )/ (A+γ)

Which is a required expression for penmans equation.