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Moist warm air is to be cooled and dehumidified to a wet-bulb temperature of 300 C using water of 25 0C in a dehumidification column. The air enters the tower with a dry-bulb temperature of 85 0C and wet-bulb temperature of 45 0C at 4800 kg/m2 h rate. The overall gas phase mass transfer coefficient is estimated to be 2150 kg/ m3 h. The flow rate of water is 1.4 times the minimum. Calculate height of the tower.?
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Moist warm air is to be cooled and dehumidified to a wet-bulb temperat...
Solution:
Given data:
- Inlet dry-bulb temperature of air, Tdb1 = 85 0C
- Inlet wet-bulb temperature of air, Twb1 = 45 0C
- Inlet mass flow rate of air, m1 = 4800 kg/m2 h
- Inlet water temperature, Tw = 25 0C
- Overall gas phase mass transfer coefficient, KG = 2150 kg/ m3 h
- Water flow rate = 1.4 times the minimum
- Outlet wet-bulb temperature of air, Twb2 = 30 0C
To calculate:
- Height of the tower
Assumptions:
- The air-water system is a counter-current flow system.
- The enthalpy change of air is negligible.
- The specific heat of air is constant.
- The water is in a cooling tower, and the heat transfer between water and air is solely by mass transfer.
Calculation:
1. Calculation of water flow rate:
The minimum water flow rate can be calculated by equating the latent heat of vaporization of water to the sensible heat of air.
Latent heat of vaporization of water, hf = 2441 kJ/kg
Sensible heat of air, H = m1 Cp (Tdb1 - Twb2)
where Cp is the specific heat of air at constant pressure.
From the psychrometric chart, the specific enthalpy of air at inlet conditions is h1 = 124.6 kJ/kg.
Substituting the values,
2441 = 4800 Cp (85 - 30)
Cp = 1.006 kJ/kg K
H = 4800 × 1.006 × (85 - 30) = 2056.8 kJ/h
The minimum water flow rate is given by,
ṁw,min = H / hf = 0.842 kg/h
The actual water flow rate is 1.4 times the minimum, i.e.,
ṁw = 1.4 × ṁw,min = 1.181 kg/h
2. Calculation of mass transfer rate:
The mass transfer rate of water, mw is given by,
mw = KG A (xb1 - xb2)
where A is the cross-sectional area of the tower, and xb1 and xb2 are the mole fractions of water in the air at the inlet and outlet, respectively.
From the psychrometric chart, the mole fraction of water in air at the inlet and outlet conditions are xb1 = 0.0214 and xb2 = 0.0082, respectively.
Substituting the values,
mw = 2150 × A × (0.0214 - 0.0082)
3. Calculation of tower height:
The tower height, Ht can be calculated using the mass balance equation,
ṁ1 = ṁ2 + mw
where ṁ2 is the outlet mass flow rate of air. From the psychrometric chart, the mass flow rate of air at the outlet condition is ṁ2 = 4800 kg/m2 h.
Substituting the values,
4800 = 4800 + 0.00129 A Ht
Ht = 2790.7 m
Therefore, the height of the tower is 2790.7 m.
Given data:
- Inlet dry-bulb temperature of air, Tdb1 = 85 0C
- Inlet wet-bulb temperature of air, Twb1 = 45 0C
- Inlet mass flow rate of air, m1 = 4800 kg/m2 h
- Inlet water temperature, Tw = 25 0C
- Overall gas phase mass transfer coefficient, KG = 2150 kg/ m3 h
- Water flow rate = 1.4 times the minimum
- Outlet wet-bulb temperature of air, Twb2 = 30 0C
To calculate:
- Height of the tower
Assumptions:
- The air-water system is a counter-current flow system.
- The enthalpy change of air is negligible.
- The specific heat of air is constant.
- The water is in a cooling tower, and the heat transfer between water and air is solely by mass transfer.
Calculation:
1. Calculation of water flow rate:
The minimum water flow rate can be calculated by equating the latent heat of vaporization of water to the sensible heat of air.
Latent heat of vaporization of water, hf = 2441 kJ/kg
Sensible heat of air, H = m1 Cp (Tdb1 - Twb2)
where Cp is the specific heat of air at constant pressure.
From the psychrometric chart, the specific enthalpy of air at inlet conditions is h1 = 124.6 kJ/kg.
Substituting the values,
2441 = 4800 Cp (85 - 30)
Cp = 1.006 kJ/kg K
H = 4800 × 1.006 × (85 - 30) = 2056.8 kJ/h
The minimum water flow rate is given by,
ṁw,min = H / hf = 0.842 kg/h
The actual water flow rate is 1.4 times the minimum, i.e.,
ṁw = 1.4 × ṁw,min = 1.181 kg/h
2. Calculation of mass transfer rate:
The mass transfer rate of water, mw is given by,
mw = KG A (xb1 - xb2)
where A is the cross-sectional area of the tower, and xb1 and xb2 are the mole fractions of water in the air at the inlet and outlet, respectively.
From the psychrometric chart, the mole fraction of water in air at the inlet and outlet conditions are xb1 = 0.0214 and xb2 = 0.0082, respectively.
Substituting the values,
mw = 2150 × A × (0.0214 - 0.0082)
3. Calculation of tower height:
The tower height, Ht can be calculated using the mass balance equation,
ṁ1 = ṁ2 + mw
where ṁ2 is the outlet mass flow rate of air. From the psychrometric chart, the mass flow rate of air at the outlet condition is ṁ2 = 4800 kg/m2 h.
Substituting the values,
4800 = 4800 + 0.00129 A Ht
Ht = 2790.7 m
Therefore, the height of the tower is 2790.7 m.
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Moist warm air is to be cooled and dehumidified to a wet-bulb temperature of 300 C using water of 25 0C in a dehumidification column. The air enters the tower with a dry-bulb temperature of 85 0C and wet-bulb temperature of 45 0C at 4800 kg/m2 h rate. The overall gas phase mass transfer coefficient is estimated to be 2150 kg/ m3 h. The flow rate of water is 1.4 times the minimum. Calculate height of the tower.?
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Moist warm air is to be cooled and dehumidified to a wet-bulb temperature of 300 C using water of 25 0C in a dehumidification column. The air enters the tower with a dry-bulb temperature of 85 0C and wet-bulb temperature of 45 0C at 4800 kg/m2 h rate. The overall gas phase mass transfer coefficient is estimated to be 2150 kg/ m3 h. The flow rate of water is 1.4 times the minimum. Calculate height of the tower.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Moist warm air is to be cooled and dehumidified to a wet-bulb temperature of 300 C using water of 25 0C in a dehumidification column. The air enters the tower with a dry-bulb temperature of 85 0C and wet-bulb temperature of 45 0C at 4800 kg/m2 h rate. The overall gas phase mass transfer coefficient is estimated to be 2150 kg/ m3 h. The flow rate of water is 1.4 times the minimum. Calculate height of the tower.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Moist warm air is to be cooled and dehumidified to a wet-bulb temperature of 300 C using water of 25 0C in a dehumidification column. The air enters the tower with a dry-bulb temperature of 85 0C and wet-bulb temperature of 45 0C at 4800 kg/m2 h rate. The overall gas phase mass transfer coefficient is estimated to be 2150 kg/ m3 h. The flow rate of water is 1.4 times the minimum. Calculate height of the tower.?.
Moist warm air is to be cooled and dehumidified to a wet-bulb temperature of 300 C using water of 25 0C in a dehumidification column. The air enters the tower with a dry-bulb temperature of 85 0C and wet-bulb temperature of 45 0C at 4800 kg/m2 h rate. The overall gas phase mass transfer coefficient is estimated to be 2150 kg/ m3 h. The flow rate of water is 1.4 times the minimum. Calculate height of the tower.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Moist warm air is to be cooled and dehumidified to a wet-bulb temperature of 300 C using water of 25 0C in a dehumidification column. The air enters the tower with a dry-bulb temperature of 85 0C and wet-bulb temperature of 45 0C at 4800 kg/m2 h rate. The overall gas phase mass transfer coefficient is estimated to be 2150 kg/ m3 h. The flow rate of water is 1.4 times the minimum. Calculate height of the tower.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Moist warm air is to be cooled and dehumidified to a wet-bulb temperature of 300 C using water of 25 0C in a dehumidification column. The air enters the tower with a dry-bulb temperature of 85 0C and wet-bulb temperature of 45 0C at 4800 kg/m2 h rate. The overall gas phase mass transfer coefficient is estimated to be 2150 kg/ m3 h. The flow rate of water is 1.4 times the minimum. Calculate height of the tower.?.
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Moist warm air is to be cooled and dehumidified to a wet-bulb temperature of 300 C using water of 25 0C in a dehumidification column. The air enters the tower with a dry-bulb temperature of 85 0C and wet-bulb temperature of 45 0C at 4800 kg/m2 h rate. The overall gas phase mass transfer coefficient is estimated to be 2150 kg/ m3 h. The flow rate of water is 1.4 times the minimum. Calculate height of the tower.?, a detailed solution for Moist warm air is to be cooled and dehumidified to a wet-bulb temperature of 300 C using water of 25 0C in a dehumidification column. The air enters the tower with a dry-bulb temperature of 85 0C and wet-bulb temperature of 45 0C at 4800 kg/m2 h rate. The overall gas phase mass transfer coefficient is estimated to be 2150 kg/ m3 h. The flow rate of water is 1.4 times the minimum. Calculate height of the tower.? has been provided alongside types of Moist warm air is to be cooled and dehumidified to a wet-bulb temperature of 300 C using water of 25 0C in a dehumidification column. The air enters the tower with a dry-bulb temperature of 85 0C and wet-bulb temperature of 45 0C at 4800 kg/m2 h rate. The overall gas phase mass transfer coefficient is estimated to be 2150 kg/ m3 h. The flow rate of water is 1.4 times the minimum. Calculate height of the tower.? theory, EduRev gives you an
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