12.5.3: Operational Characteristics
- Page ID
- 44655
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The depth of water applied with a traveler can be computed by:
\(d_g=\dfrac{96.3 q_s T_o}{W_p L_l}=\dfrac{96.3 q_s}{W_p v_t}\) (12.11)
where: dg = average depth of application (in),
qs = discharge from the gun (gpm),
To = time of operation for one lane (hr),
Wp = width of the travel lanes = set width (ft),
Ll = length of the travel lane (ft), and
vt = speed of travel of the traveler (ft/hr).
The speed of travel is vt = Ll / To which is represented in equation 12.11. Most travelers are designed to allow several specific speeds of travel or a variable range of speeds which allows a range of application depths. The average rate of water application is given by:
\(A_r=\left(\dfrac{11035}{\beta}\right)\dfrac{q_s}{{W_p}^2}\) (12.12)
where: Ar = average application rate (in/hr),
qs = discharge from the traveler gun, (gpm),
Wr = wetted radius of gun, (ft), and
β = central angle of gun operation (degrees).
Consider the following example.
You represent a company that sells traveler irrigation systems. A client recently bought a field and needs to know how much water will be applied per irrigation for an existing traveler system. They also want to know the application rate of the system.
Given: The traveler is depicted in Figure 12.20. The system uses a gun that discharges 585 gpm on a set that is 264 ft wide and 1,300 ft long. The traveler starts 88 ft from the field edge as a setback to balance uniformity against overspray at the end of the path.
The travel speed is adjusted to irrigate the set in 11 hrs of operation and to be moved every 12 hrs.The central angle of rotation for the lateral is 270 degrees and the wetted radius of the gun is 220 ft.
Solution
- The velocity of travel is:
\(v_t=\dfrac{L_l}{T_o}=\dfrac{1300-88\text{ ft}}{11\text{ hr}}=110\text{ ft/hr}\)
The depth of application is computed using Eq. 12.11:
\(d_g=\dfrac{96.3 q_s}{W_p v_t}=\dfrac{96.3\times 585}{264\times 110}=1.94\text{ in}\) - The application rate is given by Eq. 12.12:
\(A_r =\left(\dfrac{11035}{\beta}\right)\dfrac{q_s}{{W_p}^2}=\left(\dfrac{11035}{270} \right) \times \left(\dfrac{585}{220^2} \right)=0.49\text{ in/hr}\)
The flow rate needed for the traveler (qs) is determined by revising Equation 11.14 to:
\(q_s=\left(\dfrac{C_n W_p L_l}{E_a \times 43560}\right) \left(\dfrac{N_s}{N_t}\right) \left(\dfrac{T_s}{T_o}\right) \left(\dfrac{I_i}{I_i-T_d}\right) \) (12.13)
where: Cn = net system capacity requirement (gpm/ac),
Ea = application efficiency (decimal fraction),
Wp = width of the travel path (ft),
Ll = Length of the travel length (ft),
Ns = number of sets in the field,
Nt = number of travelers used,
Ts = set time between moving traveler to next travel lane (hr),
To = time of operation, i.e., time water is applied for the travel lane (hr),
Ii = irrigation interval (time between irrigations of the field) (days), and
Td = down time between irrigations (days).
Equation 12.13 is applied to the system in Figure 12.20 in the following example.
A field and traveler similar to the system shown in Figure 12.20 has a net system capacity is 4.5 gpm/acre. The irrigation interval is 5.5 days with half a day to reposition. Find: The area irrigated in one set (i.e., one traveler path) and the flow rate needed for a traveler to service the field.
Solution
- The area per set = \(\dfrac{W_p \times L_l}{43560}=\dfrac{264 \times 1300}{43560}=7.88 \text{ acres/set} \)
- The system flow is determined from Eq. 12.13:
\(q_s=\left(\dfrac{4.5\times 264\times 1300}{0.75 \times 43560}\right) \left(\dfrac{10}{1}\right) \left(\dfrac{12}{11}\right) \left(\dfrac{5.5}{5.5-0.5}\right)=567\text{ gpm} \)
The pressure loss in the hoses used to supply travelers can be quite high due to the use of hoses that are relatively small for the required flow rates. Small hoses are used because large diameter hoses are harder to pull and much more expensive. The friction loss for a range of diameters of hose and flow rates is given in Table 12.9 and 12.10. Friction loss for the lay-flat used with a cable-tow traveler is shown in Table 12.9. The diameter of lay-flat hose varies depending on the pressure. Values in Table 12.9 are for a tube pressure of about 100 psi. Comparison of losses for hard hoses is slightly higher than for lay-flat hoses. However, hard hose systems are by far the most common system today.
| Flow (gpm) | Nominal Inside Diameter: 2.5 in | Nominal Inside Diameter: 3 in | Nominal Inside Diameter: 4 in | Nominal Inside Diameter: 4.5 in | Nominal Inside Diameter: 5 in |
|---|---|---|---|---|---|
| 100 | 1.6 | - | - | - | - |
| 150 | 3.4 | 1.4 | - | - | - |
| 200 | 5.6 | 2.4 | - | - | - |
| 250 | - | 3.6 | 0.9 | - | - |
| 300 | - | 5.1 | 1.3 | 0.6 | - |
| 400 | - | 2.3 | 1.3 | - | |
| 500 | - | - | 3.5 | 2.1 | 1.1 |
| 600 | - | - | 4.9 | 2.7 | 1.6 |
| 700 | - | - | - | 3.6 | 2.1 |
| 800 | - | - | - | 4.6 | 2.7 |
| 900 | - | - | - | - | 3.4 |
| 1000 | - | - | - | - | 4.2 |
| Flow (gpm) | House Inside Diameter: 2.5 in | House Inside Diameter: 2.7 in | House Inside Diameter: 3.0 in | House Inside Diameter: 3.3 in | House Inside Diameter: 3.7 in | House Inside Diameter: 4.0 in | House Inside Diameter: 4.5 in | House Inside Diameter: 5.0 in |
|---|---|---|---|---|---|---|---|---|
| 75 | 1.45 | 1.00 | 0.60 | - | - | - | - | - |
| 100 | 2.48 | 1.70 | 1.02 | 0.64 | - | - | - | - |
| 125 | 3.74 | 2.57 | 1.54 | 0.97 | 0.56 | - | ||
| 150 | 5.24 | 3.61 | 2.16 | 1.36 | 0.78 | 0.53 | - | |
| 175 | 6.98 | 4.80 | 2.87 | 1.81 | 1.04 | 0.71 | 0.40 | - |
| 200 | 8.94 | 6.14 | 3.68 | 2.31 | 1.33 | 0.91 | 0.51 | 0.31 |
| 250 | - | 9.29 | 5.56 | 3.50 | 2.00 | 1.37 | 0.77 | 0.46 |
| 300 | - | - | 7.80 | 4.90 | 2.81 | 1.92 | 1.08 | 0.65 |
| 350 | - | - | 10.37 | 6.52 | 3.74 | 2.56 | 1.44 | 0.86 |
| 400 | - | - | - | 8.35 | 4.79 | 3.28 | 1.85 | 1.11 |
| 450 | - | - | - | - | 5.95 | 4.07 | 2.30 | 1.38 |
| 550 | - | - | - | - | - | 5.91 | 3.33 | 1.67 |
| 600 | - | - | - | - | - | - | 3.91 | 2.72 |
| 650 | - | - | - | - | - | - | 4.54 | 3.12 |
| 750 | - | - | - | - | - | - | 5.21 | 3.54 |
| 800 | - | - | - | - | - | - | - | 3.99 |
Pressure losses in the sprinkler cart must be computed. The pressure loss in the traveler depends on the flow rate, speed of travel, type of power unit, and machine design. Performance for a specific machine must be obtained from the manufacturer. Some travelers use water pressure through a turbine to power the hose reel to rewind the hard hose. Other systems use an engine to power the reel. About ten psi is required to power the turbine. The pressure and discharge relationships for a typical traveler powered with a turbine is shown in Figure 12.21. The upper portion of the figure shows the pressure discharge relationships for the 1.83-inch nozzle used with the gun and the input pressure required for a given discharge from the traveler— developed from manufacturer’s data. The difference in the pressure between the nozzle and inlet to the hose reel for the same discharge represents the friction loss in the hose reel, turbine, hard hose, and the sprinkler cart. The pressure loss is quite substantial for travelers. The pressure requirement of the traveler is significant, so operating costs for travelers are high. The lower portion of Figure 12.21 shows the friction loss in the 4.5-inch hard hose and the cart and the reel system with a turbine powered traveler. Most of the loss occurs in the hose, especially at high flow rates.
Figure 12.21. Pressure versus discharge and friction loss relationships for a traveler with a 1.83-inch nozzle.
