MÉTODO DE PENMAN
Datos:
𝑇 π‘š(º𝐢) = 16
𝐻𝑅 π‘šπ‘’π‘‘π‘–π‘Ž (%) = 53%
𝐻𝑅 π‘šπ‘Žπ‘₯π‘–π‘šπ‘Ž (%) = 60%
π‘Žπ‘™π‘‘π‘–π‘‘π‘’π‘‘ π‘šπ‘’π‘‘π‘–π‘Ž π‘£π‘–π‘’π‘›π‘‘π‘œ = 4π‘š/𝑠𝑒𝑔
π‘ˆ (
π‘˜π‘š
π‘‘π‘–π‘Ž
) = 132
π‘Žπ‘™π‘‘π‘–π‘‘π‘’π‘‘ = 2000
𝑛 = 8
π‘™π‘Žπ‘‘π‘–π‘‘π‘’π‘‘ π‘ π‘’π‘Ÿ = 14º𝐢
π‘šπ‘’π‘  = π‘šπ‘Žπ‘¦π‘œ
π‘£π‘’π‘™π‘œπ‘π‘–π‘‘π‘Žπ‘‘ 𝑑𝑒 π‘£π‘–π‘’π‘›π‘‘π‘œ = 3π‘š/𝑠𝑒𝑔
π‘ˆ π‘‘π‘–π‘Ž
π‘ˆ π‘›π‘œπ‘β„Žπ‘’
=
3
1
𝛼 = 0.30
π’”π’π’π’–π’„π’Šπ’π’:
 𝑁 (π‘‘π‘Žπ‘π‘™π‘Ž 2.20 𝑏)
𝑁 = 11.76 β„Žπ‘œπ‘Ÿπ‘Žπ‘ /π‘‘π‘–π‘Ž
𝑛
𝑁
=
8
11.76
= 0.68
𝑅 π‘Ž = 12.10 π‘šπ‘šπ»π‘” (π‘‘π‘Žπ‘π‘™π‘Ž 2.19 𝑏)
𝑅 𝑠 = (0.25 + 0.50 βˆ— 𝑛/𝑁)𝑅 π‘Ž
𝑅 𝑠 = (0.25 + 0.50 βˆ—
8
11.76
) βˆ— 12.10
𝑅 𝑠 =7.14 mm/dΓ­a
𝑅 𝑛𝑠 = (1βˆ’βˆ) βˆ— 𝑅 𝑠
𝑅 𝑛𝑠 = (1 βˆ’ 0.30) βˆ— 12.10
𝑅 𝑛𝑠 = 4.99
π‘šπ‘š
π‘‘π‘–π‘Ž
𝑒 π‘Ž = 18.20π‘šπ‘π‘Žπ‘Ÿ π‘‘π‘Žπ‘π‘™π‘Ž 2.16
𝑒 𝑑 =
𝑒 π‘Žβˆ—π»π‘…%
100
𝑒 𝑑 =
18.20βˆ—53
100
𝑒 𝑑 = 9.65π‘šπ‘π‘Žπ‘Ÿ
𝑓(𝑑)=13.8 π‘‘π‘Žπ‘π‘™π‘Ž 2.22
𝑓(𝑒𝑑)=0.202 (Se interpola)
𝑓(𝑛/𝑁)=0.666 (Se interpola)
𝑅(𝑛𝑙)= 𝑓(𝑑) βˆ— 𝑓(𝑒𝑑) βˆ— 𝑓(𝑛/𝑁)
𝑅(𝑛𝑙)=13.8 βˆ— 0.202 βˆ— 0.666
𝑅(𝑛𝑙)=1.86
π‘šπ‘š
π‘‘π‘–π‘Ž
𝑅(𝑛)= 𝑅 𝑛𝑠 βˆ’ 𝑅(𝑛𝑙)
𝑅(𝑛)=4.99 βˆ’ 1.86
𝑅(𝑛)=3.13
π‘šπ‘š
π‘‘π‘–π‘Ž
𝑓(𝑧)=0.88 π‘‘π‘Žπ‘π‘™π‘Ž 2.17
π‘ˆπ‘§ = 𝑓(𝑧) βˆ— π‘ˆ
π‘ˆπ‘§ = 0.88 βˆ— 132
π‘ˆπ‘§ = 116.16
π‘˜π‘š
π‘‘π‘–π‘Ž
𝑓(𝑒)=0.27 βˆ— (1 +
π‘ˆ 𝑧
100
)
𝑓(𝑒)=0.27 βˆ— (1 +
116.16
100
)
𝑓(𝑒)=0.584
𝐹𝐴𝐢𝑇𝑂𝑅 𝐢 π‘‘π‘Žπ‘π‘™π‘Ž 2.23
∴ 𝐢 = 0.998 (Se interpola)
W= 0.690 π‘‘π‘Žπ‘π‘™π‘Ž 2.18
𝐸𝑇𝑃 = 𝐢{(π‘Š βˆ— 𝑅(𝑛)) + (1 βˆ’ π‘Š) βˆ— [𝑓(𝑒)(𝑒 π‘Ž βˆ’ 𝑒 𝑑)]}
𝐸𝑇𝑃 = 0.998{(0.69 βˆ— 3.13) + (1 βˆ’ 0.69) βˆ— [0.629 βˆ— (18.20 βˆ’ 9.65)]}
𝐸𝑇𝑃 = 3.819 π‘šπ‘š/π‘‘π‘–π‘Ž

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Metodo de penman

  • 1. MΓ‰TODO DE PENMAN Datos: 𝑇 π‘š(º𝐢) = 16 𝐻𝑅 π‘šπ‘’π‘‘π‘–π‘Ž (%) = 53% 𝐻𝑅 π‘šπ‘Žπ‘₯π‘–π‘šπ‘Ž (%) = 60% π‘Žπ‘™π‘‘π‘–π‘‘π‘’π‘‘ π‘šπ‘’π‘‘π‘–π‘Ž π‘£π‘–π‘’π‘›π‘‘π‘œ = 4π‘š/𝑠𝑒𝑔 π‘ˆ ( π‘˜π‘š π‘‘π‘–π‘Ž ) = 132 π‘Žπ‘™π‘‘π‘–π‘‘π‘’π‘‘ = 2000 𝑛 = 8 π‘™π‘Žπ‘‘π‘–π‘‘π‘’π‘‘ π‘ π‘’π‘Ÿ = 14º𝐢 π‘šπ‘’π‘  = π‘šπ‘Žπ‘¦π‘œ π‘£π‘’π‘™π‘œπ‘π‘–π‘‘π‘Žπ‘‘ 𝑑𝑒 π‘£π‘–π‘’π‘›π‘‘π‘œ = 3π‘š/𝑠𝑒𝑔 π‘ˆ π‘‘π‘–π‘Ž π‘ˆ π‘›π‘œπ‘β„Žπ‘’ = 3 1 𝛼 = 0.30 π’”π’π’π’–π’„π’Šπ’π’:  𝑁 (π‘‘π‘Žπ‘π‘™π‘Ž 2.20 𝑏) 𝑁 = 11.76 β„Žπ‘œπ‘Ÿπ‘Žπ‘ /π‘‘π‘–π‘Ž 𝑛 𝑁 = 8 11.76 = 0.68 𝑅 π‘Ž = 12.10 π‘šπ‘šπ»π‘” (π‘‘π‘Žπ‘π‘™π‘Ž 2.19 𝑏) 𝑅 𝑠 = (0.25 + 0.50 βˆ— 𝑛/𝑁)𝑅 π‘Ž 𝑅 𝑠 = (0.25 + 0.50 βˆ— 8 11.76 ) βˆ— 12.10 𝑅 𝑠 =7.14 mm/dΓ­a 𝑅 𝑛𝑠 = (1βˆ’βˆ) βˆ— 𝑅 𝑠 𝑅 𝑛𝑠 = (1 βˆ’ 0.30) βˆ— 12.10 𝑅 𝑛𝑠 = 4.99 π‘šπ‘š π‘‘π‘–π‘Ž
  • 2. 𝑒 π‘Ž = 18.20π‘šπ‘π‘Žπ‘Ÿ π‘‘π‘Žπ‘π‘™π‘Ž 2.16 𝑒 𝑑 = 𝑒 π‘Žβˆ—π»π‘…% 100 𝑒 𝑑 = 18.20βˆ—53 100 𝑒 𝑑 = 9.65π‘šπ‘π‘Žπ‘Ÿ 𝑓(𝑑)=13.8 π‘‘π‘Žπ‘π‘™π‘Ž 2.22 𝑓(𝑒𝑑)=0.202 (Se interpola) 𝑓(𝑛/𝑁)=0.666 (Se interpola) 𝑅(𝑛𝑙)= 𝑓(𝑑) βˆ— 𝑓(𝑒𝑑) βˆ— 𝑓(𝑛/𝑁) 𝑅(𝑛𝑙)=13.8 βˆ— 0.202 βˆ— 0.666 𝑅(𝑛𝑙)=1.86 π‘šπ‘š π‘‘π‘–π‘Ž 𝑅(𝑛)= 𝑅 𝑛𝑠 βˆ’ 𝑅(𝑛𝑙) 𝑅(𝑛)=4.99 βˆ’ 1.86 𝑅(𝑛)=3.13 π‘šπ‘š π‘‘π‘–π‘Ž 𝑓(𝑧)=0.88 π‘‘π‘Žπ‘π‘™π‘Ž 2.17 π‘ˆπ‘§ = 𝑓(𝑧) βˆ— π‘ˆ π‘ˆπ‘§ = 0.88 βˆ— 132 π‘ˆπ‘§ = 116.16 π‘˜π‘š π‘‘π‘–π‘Ž 𝑓(𝑒)=0.27 βˆ— (1 + π‘ˆ 𝑧 100 ) 𝑓(𝑒)=0.27 βˆ— (1 + 116.16 100 ) 𝑓(𝑒)=0.584 𝐹𝐴𝐢𝑇𝑂𝑅 𝐢 π‘‘π‘Žπ‘π‘™π‘Ž 2.23 ∴ 𝐢 = 0.998 (Se interpola) W= 0.690 π‘‘π‘Žπ‘π‘™π‘Ž 2.18
  • 3. 𝐸𝑇𝑃 = 𝐢{(π‘Š βˆ— 𝑅(𝑛)) + (1 βˆ’ π‘Š) βˆ— [𝑓(𝑒)(𝑒 π‘Ž βˆ’ 𝑒 𝑑)]} 𝐸𝑇𝑃 = 0.998{(0.69 βˆ— 3.13) + (1 βˆ’ 0.69) βˆ— [0.629 βˆ— (18.20 βˆ’ 9.65)]} 𝐸𝑇𝑃 = 3.819 π‘šπ‘š/π‘‘π‘–π‘Ž