Question

In a cultivated area, the soil has porosity of 45% and field capacity of 38%. For a particular crop, the root zone depth is 1.0 m, the permanent wilting point is 10% and the consumptive use is 15 mm/day. If the irrigation efficiency is 60%, what should be the frequency of irrigation such that the moisture content does not fall below 50% of the maximum available moisture?

• A. 5 days
• B. 6 days
• C. 9 days
• D. 11 days

Answer 1

The correct option is D 11 days

Depth of root zone,
H = 1 m
= 1000 mm
Field capacity, FC = 38%

Permanent wilting point, PWP = 10%

Moisture content can fall upto 50% of maximum available moisture, so the moisture content which plant can use is,

w = 50% of (FC - PWP)
w = 50% of (38% - 10%)
= 14%

Porosity, n = 45%

$\therefore \text{Void ratio, e}=\frac{n}{1-n}=0.818$

Assuming that at field capacity soil is fully saturated (S = 1)

$\therefore Se=w_f{G}_s$

$\Rightarrow G_s=\frac{Se}{w_f}=\frac{1\times 0.818}{0.38}=2.153$

Dry unit wt. of soil,
${\gamma }_d=\frac{G_s{\gamma }_w}{1+e}=\frac{2.153{\gamma }_w}{1.818}$

$=1.184{\gamma }_w$

Depth of water within root zone which plant can use

$h=\frac{{\gamma }_d}{{\gamma }_w}\times \text{(depth of root zone)}\times w$

$=1.184\times 1000\times 0.14=165.8mm$

Consumptive use,
$C_u=15mm/day$

Frequency of irrigation,
$=\frac{h}{C_u}=\frac{165.8}{15}=11.05$

$=11days$

Note: Irrigation efficiency has no use in calculating frequency of irrigation. However if it has been asked to calculate the depth of water required for irrigation then irrigation efficiency is useful parameter.

Depth of water to be applied,
= $\frac{165.8}{n_a}=\frac{165.8}{0.6}$
$=276.33mm$