KLIMATOLOGI PERTANIAN

( Kuliah Minggu Ke 7 )

Oleh

Suardy Mandung

Equation 1:

                                                                                   where

P = Static pressure (pascals)T = Standard temperature (kelvins)L = Standard temperature lapse rate (kelvins per meter)h = Height above sea level (meters)R * = Universal gas constant for air: 8.31432×103 N·m / (kmol·K)g0 = Gravitational constant (9.80665 m/s²)

M = Molar mass of Earth's air (28.9644 g/mol)

Barometric formula

whereP = Static pressure (inches of mercury)T = Standard temperature (kelvins)L = Standard temperature lapse rate (kelvins per foot)h = Height above sea level (feet)R * = Universal gas constant (using feet and kelvins and gram moles: 8.9494596×104 kg·ft2·s-2·K-1·kmol-1)g0 = Gravitational constant (32.17405 ft/s²)M = Molar mass of Earth's air (28.9644 g/mol)

Subscript b

Height Above

Sea Level

Static Pressure Standard

Temperature(K)

Temperature Lapse Rate

(m) (pascals) (K/m)

0 0 101325 288.15 -0.0065

1 11,000 22632.1 216.65 0.0

2 20,000 5474.89 216.65 0.001

3 32,000 868.019 228.65 0.0028

4 47,000 110.906 270.65 0.0

5 51,000 66.9389 270.65 -0.0028

6 71,000 3.95642 214.65 -0.002

                                       

                                        where

ρ = Mass Density (kg/m3)T = Standard temperature (kelvins)L = Standard temperature lapse rate (kelvins per meter)h = Height above sea level (geopotential meters)R * = Universal gas constant for air: 8.31432×103 N·m / (kmol·K)g0 = Gravitational constant (9.80665 m/s²)

M = Molar mass of Earth's air (28.9644 g/mol)

Density Equations

Or converted to English units:[1]Where

ρ = Mass Density (slugs/Ft3)T = Standard Temperature (degrees Kelvin)L = Standard Temperature Lapse Rate (degrees Celsius per foot)h = Height above Sea Level (geopotential feet)R * = Universal Gas Constant (converted to English units: 8.9494596 X 104 Ft2/sec2 K)go = Gravitational Constant (32.17405 Ft/sec2)M = Molar Mass of Earth's Air (28.9644 grams per mole)

Subscrip

t b

Height Above Sea Level (h)

Mass Density (ρ) Standard

Temp.(T)(K)

Temperature Lapse Rate (L)

(m) (kg/m3) (K/m)

0 0 1.2250 288.15 -0.0065

1 11,000 0.36391 216.65 0.0

2 20,000 0.08803 216.65 0.001

3 32,000 0.01322 228.65 0.0028

4 47,000 0.00143 270.65 0.0

5 51,000 0.00086 270.65 -0.0028

6 71,0000.00006

4214.65 -0.002

Derivation ideal gas law:              

When density is known:                  

And assuming that all pressure is hydrostatic:                 

Substituting the first expression into the second we get:                   

Integrating this expression from the surface to the altitude z we get:                          

Assuming constant temperature, molar mass, and gravitational acceleration, we get the barometric formula:

                    

n this formulation, R is the gas constant, and the term RT / Mg gives the scale height (approximately equal to 7.4 km for the troposphere).

Penyebaran tekan uap air

(dry season)

Penyebaran tekan uap air

(wet season)

Water Vapor Pressure

                           

                                                                               

Where

The temperature Tv is in degrees Celsius

The pressure p is in pascals.

Absolute humidity

Absolute humidity is the density of water in a particular volume of air. The most common units are grams per cubic meter,

he amount of vapor in that cube of air is the absolute humidity of that cubic

meter of air. More technically: the mass of water vapor mw, per cubic meter of

air, Va .              volumetric humidity. "absolute humidity." Most humidity charts are given in

g/kg or kg/kg,

Mixing ratio / Humidity ratio

Mixing or Humidity ratio is expressed as a ratio of kilograms of water vapour, mw, per kilogram of dry air, md, at a given pressure

That ratio can be given as:               

Specific humidity

Specific humidity is the ratio of water vapor to air (dry air plus water vapor) in a particular volume of air. Specific humidity ratio is expressed as a ratio

of kilograms of water vapor, mw, per kilogram of air, ma .That ratio can be given as:

             Specific humidity is related to mixing ratio (and vice versa) by:

                   

                   

Relative humidity

Relative humidity is defined as the ratio of the partial pressure of water vapor in a gaseous mixture of air and water vapor to the saturated vapor pressure of water at a given temperature. Relative humidity is expressed as a percentage and is calculated in the following manner:

                           where

        is the partial pressure of water vapor in the gas mixture;

        is the saturation vapor pressure of water at the temp of the gas mixture

     is the relative humidity of the gas mixture being considered.

Contoh PerhitunganPengamatan suhu udara dengan alat psikrometer

1. TBK = 32,5OC

2. TBB = 27,5OC

3. Tekanan udara = 1 005 mb

4. Tetapan psikometer = 0,000667

Tentukan :

1. Tekanan uap (mb)

2. Suhu Titik embun (OC)

3. Kelembaban Nisbi (%)

4. Kelembaban Spesifik (g/kg)

5. Nisba Campuran (g/kg)

6. Defisit Tekanan Uap (mb)

1. Tekanan Uap Air

TBB ( nilai ini digunakan pada perhitungan RH pad rumus Regnault )

es * = 6,1078 e

(17,239 T / ( T + 237,3 ))

es * = 6,1078 e (17,239 x 27,5 / ( 27,5 + 237,3 ))

es * = 6,1078 e 1,7903

es * = 6,1078 x 5,9913 es * = 36,59 mb

TBB ( nilai ini digunakan pada perhitungan RH pada rumus Regnault )

e = es * - req p ( TBK – TBB)

e = 36,59 – (0,000667) (1 005) ( 32,5 – 27,5 )

e = 36,59 – 3,3351

e = 33,2548 mb (Nilai ini adalah Tekanan Uap air)

2. Suhu Titik Embun

Td = ( 237,3 x Y ) / ( 17,237 – Y )

Y = ln ( e / 6,1078 )

Y = ln ( 33,2548 / 6, 1078 )

Y = 1,6946

Td = ( 237,3 x 1,6948 ) / ( 17,237 – 1,6948 )

Td = 25,88OC

3. Tekanan Uap Air JenuhTBK

es * = 6,1078 e

(17,239 T / ( T + 237,3 ))

es * = 6,1078 e (17,239 x 32,5 / ( 32,5 + 237,3 ))

es * = 6,1078 e 2,0766

es * = 6,1078 x 7,9773 es * = 48,72 mb

4. Kelembaban Nisbi Udara

RH = ( e / es ) x 100%

RH = ( 33,25 mb / 48,72 mb ) x 100%

RH = 68 %

5. Kelembaban Spesifik

SH = ( 622 e ) / (1,622 p )

SH = ( 622 x 33,25 ) / ( 1,622 x 1 005 )

SH = 12,6872 g/kg

6. Nisbi Campuran

SH = 622 ( e / ( p - e ))

SH = 622 ( 33,25 / ( 1005 - 33,25 ))

SH = 21,28 g/kg

7. Defisit Tekanan Uap

DTU = e - es

DTU = 33,25 - 48,72

DTU = 16,47 mb

Pan Evaporimeter Class A