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LECTURE – 3

THE CONTENTS OF THIS LECTURE ARE AS FOLLOWS:

1.0 TYPES OF HYGROMETERS

1.1 Wall Mounted Type Hygrometer

1.1.1 Construction

1.1.2 Working

1.1.3 Precautions

1.2 Whirling Hygrometer or Sling Psychrometer

1.2.1 Construction

1.2.2 Working

1.2.3 Precautions

1.2.4 Limitations

1.3 Assmann Psychrometer

1.3.1 Construction

1.3.2 Working

1.3.3 Advantages

1.3.4 Precautions

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2.0 CALCULATING WATER VAPOUR CONTENT IN THE

UNSATURATED AIR

3.0 STEPS FOR CALCULATING WATER VAPOUR CONTENT

OF MOIST AIR

3.1 Method – I

3.2 Method – II

3.3 Method – III

REFERENCES

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1.0 TYPES OF HYGROMETERS

There are three types of hygrometers which employ the thermodynamic method of

measuring water content in the air. They are:

- Wall mounted type

- Whirling hygrometer or sling psychrometer

- Aspirated type or Assmann psychrometer

1.1 Wall Mounted Type Hygrometer

It is non-ventilated type in nature. It is fixed at suitable place in mine so that it is

well ventilated by mine air-current.

1.1.1 Construction

It has two thermometers mounted on it side by side. One of them is exposed

directly to mine air while the other has a wet muslin cloth all around the bulb. The

lower end of the muslin cloth is always immersed in some container having water.

This ensures continuous supply of the water to the muslin cloth (Fig. 1).

1.1.2 Working

It records dry and wet bulb temperatures using respective thermometers. Using a

barometer, barometric pressure is recorded. The three readings are used to

calculate the humidity.

1.1.3 Precautions

There should not be any source of heat nearby, while taking readings. Also bulbs of

thermometers should be wiped out properly so as to make it dust/dirt free. This is

done because impurities affects evaporation rate of water. Keeping this thing in

mind, it is better to use distilled water.

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Fig.1 Wall mounted hygrometer

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1.2 Whirling Hygrometer or Sling Psychrometer

1.2.1 Construction

It consists of a wooden frame with a handle attached to it. The handle is used for

rotating. Two thermometers are mounted in the wooden frame. They are mounted

such that they do not break when wooden frame is rotated. One of the

thermometers is directly exposed to atmosphere while the other has a muslin cloth

wrapped around the bulb. The muslin cloth has one end (lower) dipped in water

container. The water from container makes the muslin cloth wet by capillary action.

The former records dry-bulb temperature while the latter one records wet-bulb

temperature.

1.2.2 Working

The muslin cloth, wrapped around the bulb of the thermometer, is made wet using

distilled water. Then the wooden frame is rotated at a uniform speed of around 200

rpm for a span of 1-2 minute, so that a steady reading is obtained. This rotation

provides the air-current causing water to evaporate. Due to this, the temperature

of the thermometer with wet-muslin cloth is depressed.

1.2.3 Precautions

- While rotating the hygrometer, it should be kept away from the observer’s body to

avoid heat flow between observer’s body and the wet-muslin cloth. Same should be

applied while taking reading.

- The reading for the wet-bulb temperature should be taken as soon as possible

after stopping the rotation. This is because wet-bulb temperature starts fluctuating

while dry-bulb temperature remains steady. Therefore, wet-bulb temperature

should be recorded first.

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Fig.2. Whirling hygrometer (after Banerjee, 2003)

1.2.4 Limitations

The moisture evaporated from the muslin cloth affects both the thermometers,

unless an air-current of velocity 3 m/s or more is provided. That is why it is rotated

at around 200 rpm to provide an air-current of velocity equal to or more than 3

m/s. Actually the minimum velocity required is governed by the shape and size of

the bulb and the orientation of bulb with the direction of airflow.

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1.3 Assmann Psychrometer

1.3.1 Construction

It consists of two thermometers -one wet bulb and one dry bulb thermometer, and

a battery driven fan. The fan is at the top. The bulbs of the two thermometers are

covered by metal sleeves whose outer surface is coated with chromium. The two

thermometers are thermally insulated from each other through a central tube (as

shown in Fig.3). The two thermometers cover a range of 0 to 60°C.

Fig.3 Assmann psychrometer (after Banerjee, 2003)

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1.3.2 Working

When the fan is kept on, the air through inner sleeves (metal sleeves provided at

the bulb of each thermometer) and annular spaces enters the apparatus. The air

travels through the central tube and goes out of the apparatus through the slits

provided at the top near the fan. The fan is kept on for an interval of approximately

3 minutes. The fan should provide a velocity of more than 2m/s. This is done to

ensure that wet-bulb thermometer attains a constant temperature.

1.3.3 Advantages

i. It can measure humidity with an accuracy of ± 1%.

ii. The metal sleeves around the bulbs of the thermometers, shield the bulb

from any radiation. This ensures that using this, we can accurately

measure humidity in sunlit areas also.

iii. Easy to operate.

1.3.4 Precautions

i. The instrument requires calibration with respect to the fan speed and

hence the ventilation speed.

ii. The instrument should be hold away from observer’s body.

iii. The instrument should be held opposite to the direction of the flow when

experiment/survey is being carried out in a strong air-current.

We have repeatedly interchanged the words hygrometer and psychrometer in this

lecture. In general, the word ‘psychrometer‘ is used if the instrument gives result

with a higher degree of accuracy.

2.0 CALCULATING WATER VAPOUR CONTENT IN THE UNSATURATED AIR

We have already learnt that at equilibrium when the wet bulb temperature becomes

constant, the heat loss (latent) by the bulb is equal to the sensible heat gained by

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it. We are interested in knowing the amount of heat lost at equilibrium by the wet

bulb. This can be better understood by Fig.4

Fig. 4 Heat balance on a wet bulb thermometer (after, McPherson, 1993)

Fig.4 shows that some mass of unsaturated air when passes through a wet muslin

cloth, it becomes saturated. Let X be the specific humidity of unsaturated air. To

attain saturation, the specific humidity should be ‘Xs’. Then mass of water vapour

evaporating from the wet muslin cloth is (Xs– X) per kg of dry air. Therefore, heat

loss (latent) from wet-bulb surface is

q = L × m(Xs − X) joule … … … … (a)

Where,

L= latent heat of vapourization (J/kg)

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m= mass of dry air (kg)

X = specific humidity of unsaturated air (kg/kg dry air)

Xs=specific humidity of saturated air (kg/kg dry dir)

q= heat lost (J)

Now, we require to know, the amount of heat gained by wet-bulb from the

unsaturated air passing through the muslin cloth. Let the mass of dry air in the

unsaturated air be ‘m’.

Then total mass of the moist/unsaturated air is m(1+X) kg. Therefore heat gain is

q = mass of unsaturated air × specific heat of unsaturated air at constant pressure

× difference between the dry bulb and wet bulb temperature

Therefore, q = m(1 + X) × Cpm × (td − tw) joule … … … … . (b)

Where,

q= heat lost (J)

X = specific humidity of unsaturated air (kg/kg dry air)

m= mass of dry air (kg)

Cpm = specific heat of moist air at constant pressure (J/kg℃)

td = dry bulb temperature (℃)

tw = wet bulb temperature (℃)

Now, when the wet bulb temperature attains a constant value, the heat gain and

loss by the wet-bulb surface is equal. Equating equation (a) and (b), we have:

L(Xs − X) = (1 + X) × Cpm × (td − tw) J per kg dry air … … . (1)

Substituting the expression of Cpm = Cpd+XCpv

1+X in equation (1) we get,

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L(Xs − X) = (1 + X) × Cpd+XCpv

1+X× (td − tw) J per kg dry air … … . (2)

The above equation results in

X = LXs − Cpd × (td − tw)

Cpv × (td − tw) + L

kg

kg dry air

This gives the specific humidity of moist/unsaturated air.

3.0 STEPS FOR CALCULATING WATER VAPOUR CONTENT OF MOIST AIR

In all methods described below, unit of pressure is Pa and temperature is °C, unless

and otherwise stated.

3.1 Method – I

a. Record/measure td, tw and Pb

b. Evaluate e, esw and esd using following equations.

es = 610.6 exp (17.27 ∗ t

237.3 + t) Pa

{replace t by td and tw for esd and esw respectively }

and

e = esw − 0.000644 Pb(td − tw) Pa

c. Evaluate

Specific humidity (X) = 0.622e

Pb −e

kg

kg dry air and

Relative humidity(rh) = e

esd × 100 %

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3.2 Method – II

a. Measure Pb , td and tw

b. Evaluate esw and esd using following equations.

es = 610.6 exp (17.27 ∗ t

237.3 + t) Pa

{replace t by td and tw for esd and esw respectively }

c. Evaluate

(Xs) = 0.622esw

Pb − esw

kg

kg dry air

d. Evaluate latent heat of vaporization at wet bulb temperature, ‘Lw’ using equation

LW = (2502.5 − 2.386tw) × 1000 J/kg

e. Evaluate ‘X’ by substituting the values of constants used in the following

equation

Specific humidity (X) = LwXs − Cpd × (td − tw)

Cpv × (td − tw) + L

kg

kg dry air

f. Evaluate

Relative humidity(rh) = e

esd × 100% {e can be calculated using X }

3.3 Method – III

a. Measure Pb , td and tw

b. Evaluate esw and esd using following equations.

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es = 610.6 exp (17.27 ∗ t

237.3 + t) Pa

{replace t by td and tw for esd and esw respectively }

c. Evaluate

(Xs) = 0.622esw

Pb − esw

kg

kg dry air

d. Evaluate latent heat of vaporization at wet bulb temperature, ‘Lw’ using equation

LW = (2502.5 − 2.386tw) × 1000 J/kg

e. Evaluate sigma heat ‘S’ using formula given below

S = (LwXs + 1005tw) J

kg dry air

f. Evaluate specific humidity (X) of the moist air

X =S − 1005td

Lw + 1884(td − tw) =

LwXs − 1005(td − tw)

Lw + 1884(td − tw)

kg

kg dry air

g. Evaluate

Relative humidity(rh) = e

esd × 100% {e can be calculated using X }

REFERENCES

Banerjee S.P. (2003); “Mine Ventilation”; Lovely Prakashan, Dhanbad, India.

Deshmukh, D. J. (2008); “Elements of Mining Technology, Vol. – II”; Denett & Co.,

Nagpur, India.

Hartman, H. L., Mutmansky, J. M. & Wang, Y. J. (1982); “Mine Ventilation and Air

Conditioning”; John Wiley & Sons, New York.

Le Roux, W. L. (1972); Mine Ventilation Notes for Beginners”; The Mine Ventilation

Society of South Africa.

McPherson, M. J. (1993); Subsurface Ventilation and Environmental Engineering”;

Chapman & Hall, London.

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Misra G.B. (1986); “Mine Environment and Ventilation”; Oxford University Press,

Calcutta, India.

Vutukuri, V. S. & Lama, R. D. (1986); “Environmental Engineering in Mines”;

Cambridge University Press, Cambridge.