$0.65, 0.83, 0.79, 0.87,$
$0.67, 0.85, 0.86, 0.68,$
$0.88, 0.77, 0.73, 0.59,$
$0.89, 0.63, 0.72, 0.70$
The distribution uniformity low-quarter (DULQ) (in fraction) is ________
(Rounded off to two decimal places)
To determine the Distribution Uniformity Low-Quarter (DULQ) for irrigation, we need to analyze the water penetration depths measured at different stations along a border strip.
Distribution Uniformity Low-Quarter (DULQ) Irrigation Calculation
Water Penetration Depths Data
The measured water penetration depths (in mm) are:
| 0.65 | 0.83 | 0.79 | 0.87 |
| 0.67 | 0.85 | 0.86 | 0.68 |
| 0.88 | 0.77 | 0.73 | 0.59 |
| 0.89 | 0.63 | 0.72 | 0.70 |
Step-by-Step Calculation of DULQ
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Sort the Data: Arrange the penetration depths in ascending order.
Sorted Depths: $0.59, 0.63, 0.65, 0.67, 0.68, 0.70, 0.72, 0.73, 0.77, 0.79, 0.83, 0.85, 0.86, 0.87, 0.88, 0.89$
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Identify the Lowest Quarter: With 16 measurements, the lowest quarter consists of the smallest $16 / 4 = 4$ values.
Lowest Quarter Depths: $0.59, 0.63, 0.65, 0.67$
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Calculate Average of Lowest Quarter: Sum the depths in the lowest quarter and divide by the number of measurements in that quarter (4).
Average of Lowest Quarter ($L$) = $ \frac{0.59 + 0.63 + 0.65 + 0.67}{4} $
$L = \frac{2.54}{4} = 0.635 $ mm
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Calculate Average of All Measurements: Sum all 16 depths and divide by 16.
Sum of All Depths = $ 12.06 $ mm
Average of All Measurements ($A$) = $ \frac{12.06}{16} $
$A = 0.75375 $ mm
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Calculate Distribution Uniformity Low-Quarter (DULQ): DULQ is the ratio of the average depth of the lowest quarter to the average depth of all measurements.
DULQ = $ \frac{L}{A} $
DULQ = $ \frac{0.635}{0.75375} $
DULQ $ \approx 0.84249 $
- Round to Two Decimal Places: The calculated DULQ value rounded to two decimal places is 0.84.
Important Questions from Surface Irrigation Methods
The difference between a given surface and the actual time of advance of water in a surface irrigation event is known as ____________.
- Furrows of 120 m length with 0.5% slope are made at 90 cm spacing. The maximum non-erosive stream flow rate is applied in a furrow that takes 1.0 hour to reach the lower end. Then this flow rate is reduced to half of its size and, subsequently, continued for another 1.0 hour. The average depth of applied water is ________ cm.
Graded furrows of 80 m length and 0.75 m spacing are used for irrigating a field with an initial furrow stream of 100 L $min^{-1}$. The initial furrow stream flow reaches the lower end of the field in 40 min. Thereafter, the furrow stream flow is reduced to 30 L $min^{-1}$ and the cutback stream flow is continued for 1 hour. The average depth of irrigation over the field in cm will be ______________.
- A border strip of $8 \times 250 \text{ m}$ is being irrigated by a border stream of $50 \text{ lps}$. The infiltration capacity of the soil is $25 \text{ mm h}^{-1}$ (assumed to be constant throughout the period of irrigation). The average depth of the advancing sheet of water over the land is $70 \text{ mm}$. The time required to irrigate the border strip, in minutes, will be
