INTRODUCTION
Surface irrigation is the most extensively used way of
applying irrigation water in the world and furrow irrigation one of its
main variants (Elliot and Walker, 1982).
There are a number of methods of applying water to croplands.
As the oldest and most common method of watering croplands, surface irrigation
has evolved into an extensive array of configurations. The distinction
between types of surface irrigation systems is based on physical features
of the irrigated fields. An alternative to flooding the entire field surface
is to construct small channels along the primary direction of water movement.
Water introduced in these furrows, creases, or corrugations infiltrates
through the wetted perimeter and moves vertically and laterally thereafter
to refill the soil (Walker and Skogerboe, 1987).
Generally, however, furrow irrigation is favored for
less then 23% slope and by moderate to slow intake soils. Furrow length
depends on water inflow rate and field slope. Usually long furrow length
is preferred by the user because of short furrows need more time and labor,
but long furrows need high inflow rate.
The inflow rate, which is affected by the slope, the
length of the furrow and the intake rate, can be adjusted by the designer
to achieve good uniformity and to irrigate to the required depth in reasonable
time. The effectiveness of an irrigation water supply can be increased
by improving the efficiency of water application. In surface irrigation,
water application efficiency is influenced principally by the amount of
water applied, the intake characteristics of the soil and the rate of
advance of water over the soil surface. Optimal furrow length and irrigation
cutoff can be determined according to soil infiltration characteristics
and by the time ratio, to achieve maximum application efficiency.
Uniform flow in furrows depends on soil infiltration
properties. For this reason, A quarter time rule is very often used in
furrow irrigation application. The quarter time rule is the time that
water reaches to end of furrow has to be equal ¼ of time the water
would give to furrow for depletion. If the time over than ¼ of
applying depletion time, it imposes serious problems on fields that allow
water high deep percolation from soil surface to deeper soil profiles
and this is meaning of low application efficiency.
Generally, field experiments need a high level of labor,
considerable installation time and management also needs high attention
levels to get good results. Scientists investigate relationships between
surface irrigation flow length and water application time. Results of
the research produce new theories and methods (Elliot and Walker, 1982;
Walker and Busman, 1990; Katopodes and Strelkoff, 1977; Strelkoff and
Katopodes, 1977; Walker and Humpherys, 1983; Jaynes and Clemmens, 1986;
Childs et al., 1993; Oyonarte et al., 2002).
The evaluation of surface irrigation at the field level
an important aspect of both management and design Field measurements are
necessary to characterize the irrigation system in terms of its most important
parameters, to identify problems in its function and to develop alternative
means for improving systems (Walker, 1989).
Estimation of soil infiltration is a major problem in
irrigation studies due to proper selection of the technique used to determine
the parameters of the infiltration models, the use of empirical models
and its dependence on soil moisture, soil characteristics and surface
roughness. The techniques used to determine soil infiltration characteristics
(Walker and Busman, 1990).
For furrow irrigation, the shape and size of the furrow
affect the volume of water infiltrated because of the size increases the
water perimeter and the area of contact between soil and water in the
furrow (Trout, 1992). The objectives of this research were to measure
from field and also determine infiltration characteristics in furrows
and classify soils into intake families by USDASCS and Volume Balance
Equations. Compare results of Empirical and field furrow characteristics
and results. Determine optimum furrow length by using equations for experimental
area.
MATERIALS AND METHODS
This experiment was conducted at Altinova village at
the Bafra Plain in Samsun Province, Turkey. Some physical properties of
the experimental soils are given in Table 1. The soil is a clay soil,
approximately 090 cm depth.
Furrows were installed with 1.20 m centres and 100 m
in length. The slope of furrows was 0.0036 mm^{1}. Irrigation
water was diverted from an irrigation canal on the south side of the experiment
area. Inlet and outlet flow measurement equipment was installed in furrows.
To determine the infiltration characteristics five furrows
had installed, two side furrows were conducted for blind furrow, middle
three furrows were conducted for measure data. Three orifices were installed
100 m from furrow head. Water depth in the furrow was adjusted to not
exceed 75% of furrow depth. Furrow width was measured at three points.
Furrow crosssection is shown in Fig. 1.

Fig 1: 
Measured furrow
crosssectional area and irrigation water in furrow 
Determination of furrow length under field conditions:
Furrow length and application time are the most important
factors affecting efficiency in furrow irrigation. Under given soil conditions,
when the furrow length is short, surface runoff increase; if furrows are
long, then deep percolation losses increase. The objective of an optimum
design is to maximise water application efficiency by minimizing the losses.
The ratio between the times required for infiltration of the net amount
of water needed for root zone and the time when the water front reaches
the end of the run (time ratio) plays an important role in determining
optimum furrow length and providing maximum irrigation efficiency. The
ratio has given most of the literatures and is called Quarter time rule
(Hart et al., 1980). Optimal furrow length and irrigation cutoff
are related to soil infiltration characteristics (Walker, 1989). As above,
furrow length and inflow rate can be determined by the quarter time rule.
For the field experiment, the flow rate has to be as
much as the maximum point of soil erosion for particular soil. One of
the equations to calculate the maximum rate was given by Hamad and Stringham
(1978) below,
Q 
= 
Maximum flow rate (L sec^{1}) 
S 
= 
Furrow slope 
α and β 
= 
Coefficient parameters depends of soil properties (Table
2) 
Table 2: 
Coefficient parameters
used for maximum flow rate for furrow 

Table 3: 
Furrow intake family
and advance coefficients (Hard et al., 1980) 

Determining furrow infiltration parameters in field
by inflowoutflow methods:
Water moves horizontally and vertically in soil. The
ring infiltration test measures vertical water movement in soil. In general,
a relatively large number of field measurements of infiltration are required
to represent the average field condition. Methods that employ a static
water condition (such as ring infiltration) often fail to indicate the
typically dynamic field condition. There are other approaches for obtaining
field representative infiltration function, based on the response of the
field to an actual watering (Walker and Skogerboe, 1987).
USDASCS Method:
Hart et al. (1980) gave the definition of the
USDASCS method. The basis of the SCS design is to classify soils into
intake families. According to the SCS equation, families are as determined
follows. Cumulative intake (mm), the time water is in contact with soil
(min) and a, b and c are constants unique to each intake family. Values
of constants are given in Table 3.
The opportunity time required for intake of selected
net application depth, d_{n}, the net opportunity time can be
estimated by using Eq. 2.
The time for water to advance to successive points along the furrow calculated
by regression analysis of trial measurements, is a semilogarithmic relation
of length, inflow rate and slope (Hart et al., 1980). The advance
time can be estimated by using Eq. 3.
Tn 
= 
The net opportunity time (min) 
dn 
= 
The desired net application depth (mm) 
W 
= 
Furrow width (m) 
P 
= 
(m) 
Q 
= 
Inflow rate (L sec^{1}) 
S 
= 
Furrow slope (m m^{1}) 
Ti 
= 
Advance time (min) 
a,b,c,f,g 
= 
Empirical coefficients 
Volume balance method:
The volume balance model has been the basis for most
design and field evaluation procedures and has been proven with field
and laboratory data (Fok and Bishop, 1965; Walker and Skogerboe, 1987).
It allows quick and reliable definition of infiltration rates over the
length of the field and it is easily extended to indications of uniformity
and efficiency parameters (Fok and Bishop, 1965; Levien and Souza, 1987;
Walker and Skogerboe, 1987).
The volume balance model is applied primarily to the
advance phase and can be written for the furrow condition. At a time (t)
water entering the field will progress a distance (x) toward the lower
end as illustrated in Fig. 2.
It is implicit that the discharge at the field inlet
(Q_{0}) is steady, so that at time (t) the product of Q_{0}
and t equals the volume of water on the soil surface (V_{y}(t))
plus the volume infiltrated (V_{z}(t)) which are both time dependent.
This can be presented as equation (4) (Fok and Bishop,
1965; Levien and Souza, 1987; Walker and Skogerboe, 1987).
Q_{0}.t = Vy(t) + Vz(t) 
(4) 
The length (x) covered by water at the time (t) can be
estimated by Eq. 5.
x 
= 
The distance covered by the water in time (t) in meters 
t 
= 
Total water application time in minutes and A and b empirical constants
of advance function (De Tar, 1989) 

Fig 2: 
Definition sketch of an advancing
flow down a furrow (Walker and Skogerboe, 1987) 
A commonly used expression for the infiltration function
(z) which is dependent on infiltration opportunity time (t) is given Eq.
6.
z 
= 
The cumulative infiltration depth; 
t 
= 
The infiltration opportunity time and k and a are constants for
a given soil at a particular moisture level (Christiansen et al.,
1966). 
The volume of water above the soil surface can be found
by integrating the flow area over the advance distance Eq.
7.
in which s is the integrand of x and A is the crosssectional
area. In the absence of a momentum or energy relationship to describe
the temporal and spatial distribution of A, the volume balance model assumes
that the average area, Ā, is constant. The usual practice to define
Â is shown in Eq. 8
Where
σ_{y} = The surface water profile shape factor (i.e., the
ratio of the average area to the inlet area, A_{0}). σ_{y}
values can be between 0.60.8 (Delibas, 1984). The inlet area (A_{0})
is assumed to be a function of the normal depth associated with the discharge,
slope, roughness and hydraulic radius at the field inlet (Alazba, 1999).
Eq. 7 reduces to Eq. 9.
The volume of infiltrated water is found by integrating
the infiltrated volume per unit length, Z(s, t), over the advance length:
For practical uses Eq. 10 can be written
as Eq. 11.
Z_{0} 
= 
The infiltrated depth at the field inlet 
σ_{z} 
= 
A subsurface shape factor can be calculated by 1/(1+a), where, a
is an infiltration parameter. (Alazba, 1999). 
The LewisMilne equation can be written in terms of both
shape factors as:
Q_{0}.t = σ_{y}.A_{0}.X
+ σ_{z}.Z_{0}.X 
(12) 
Lewis and Milne (1938) described a recursive method of
solving the border advance problem.
The change in surface inflow, Q_{0}Δ_{t},
equals the change in surface storage, A Δx_{4}, plus the
change in subsurface storage. Thus, using the trapezoidal rule, the subsurface
volume can be estimated by;
In which the equation can be written as 
These results can be written in general form as Eq.
15 
RESULTS AND DISCUSSION
Equation 2 was used to determine maximum
inflow that would not cause erosion in furrow. The result was 2.32 L sec^{1},
with the chosen constant being 2.00 L sec^{1} inflow for furrow
experiments.
The derived infiltration equation was based on inflow
and outflow measurements. Measured inflow and outflow data was plotted
with cumulative depth to get the infiltration equation for the research
field soil with the result given in Eq. 16
D = 0.9446 T ^{0.4624} 
(16) 
According to the experimental area soil physical properties,
the calculated irrigation water amount was 96 mm. After using Eq.
16, D was 9.6 cm and Tn was 151 min.
The results from the experiment and the USDASCS and
Volume Balance Methods are plotted on the same graph in Fig.
3.
Experimental results were compared with the empirical
methods the USDASCS and Volume Balance individually. Statistical analysis
found that the relationships between the experiment result and USDASCS
were y=0.4143x+1.6792 and R^{2} is 0.998. The statistical result
shows that relationships between field experiment and USDASCS are significant
at the 1% probability level. As the result shows, the USDASCS method
can be used to determine furrow length but there is a coefficient between
methods (Fig. 4).
The Results of statistical comparison found that the
relationships between the experimental result and Volume Balance Method
were y = 0.7313x+12.307 and R^{2} is 1.0. Results show that the
Volume Balance method can be used to determine furrow length directly
(Fig. 5).
According to the results, USDASCS and Volume Balance
Equations can be used to determine furrow length on the Bafra Plain. Results
of maximum furrow length are 71 m from the field experiment, 79 m from
Volume Balance Equation and 172 m from USDASCS equation.
The field experiment and Volume Balance results are very
close to each other, can be use to predict furrow length by using this
empirical equation. Experiment results are different from USDASCS equation
results, but there is a relationship between them. As it was mentioned

Fig 3: 
Observed and predicted advance for furrow 

Fig 4: 
Relationships between
predicted USDASCS and observed furrow length 

Fig 5: 
Relationships between
predicted volume balance and observed furrow length 
earlier, there is a coefficient between both the values
of USDASCS furrow length multiplied by the coefficient of 0.41, can be
get close value. The result is 73 m, which is very close to the field
experimental results of 71 m.
CONCLUSIONS
The furrow irrigation data used in this study was collected
from the field measurements. In general, the furrow length for furrows
does not differ significantly for each method. However, a calculated USDASCS
furrow length value slightly different than field measurements. The study
has shown the Volume Balance method predicts significant furrow length.
However USDASCS method can be used to predict but need a calibration
with a constant value.
ACKNOWLEDGMENT
The authors thank Gregory T. Sullivan of Ondokuz Mayis
University for his comments on this manuscript.