Calculating Mass Flow Rate of Water in a Natural Draught Cooling Tower

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Discussion Overview

The discussion revolves around calculating the mass flow rate of water entering a natural draught cooling tower, considering factors such as evaporation loss, inlet and outlet conditions of air and water, and energy transfer. The scope includes theoretical and mathematical reasoning related to thermodynamics and fluid mechanics.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a problem involving the calculation of mass flow rate, noting uncertainty about finding the enthalpy for water at the outlet.
  • Another participant suggests using the average heat capacity (Cp) and temperature difference (ΔT) instead of enthalpy for the calculations.
  • A participant questions how to apply CpΔT without knowing the outlet temperature for water.
  • There is a suggestion to assume standard cooling tower outlet temperatures, such as 25 or 30°C, and inquire about design parameters that might guide this assumption.
  • One participant argues that the energy required to heat the air leaving the cooling tower can help determine the initial water flow rate, emphasizing that the problem does not require finding the cooled water temperature.
  • Another participant points out the challenge of having one equation with two unknowns, suggesting the need to consider the 3% mass loss due to evaporation in their calculations.
  • A participant expresses frustration about how to utilize the 3% loss and determine enthalpy, indicating they are stuck in their reasoning.
  • One participant advises that the problem does not focus on energy calculations, suggesting to use psychrometric charts to find moisture content and calculate mass flow based on the 3% loss.

Areas of Agreement / Disagreement

Participants express differing views on how to approach the problem, particularly regarding the use of enthalpy versus heat capacity, the assumptions about outlet temperatures, and the relevance of energy calculations. There is no consensus on a single method to solve the problem.

Contextual Notes

Participants highlight limitations such as the unknown outlet temperature for water and the dependence on assumptions regarding cooling tower design parameters. The discussion reflects various approaches to the problem without resolving the mathematical uncertainties involved.

chelonege
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A natural draught cooling tower is designed to have a 3% loss of the mass of the water entering the tower by evaporation into the atmosphere. Atmospheric air enters the tower at a volume flow rate of 4 m^3/s a temp of 10C and a relative humidity of 50%. Air leaves the tower in a saturated condition at a temp of 34C. The atm pressure is 0.995 bar. The water enters the tower at a temperature of 36C. Find the mass flow rate of water entering the tower.

The problem is I don't know how to find the h for the water at the outlet, any suggestions? Thx~
 
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Have you considered using CpΔT instead of enthalpy? This should be close enough if you use the average heat capacity between temperatures.
 
The point is if i don't know the outlet temp for water how will i be able to do CpT
 
I guess you need to assume standard cooling tower outlet conditions - 25 or 30 C maybe. Are there any design parameters to go by?
 
You know the inlet and outlet conditions for the air. You know the inlet conditions of the water, and that a certain amount of the water is lost due to evaporation. Don't you think you can determine how much water enters the tower based on the amount of energy required to heat the air leaving the cooling tower? The problem does not ask you to find the temperature of the cooled water, only how much enters initially.
 
But there's one equation and 2 unknowns. So the duty the air supplies, Q = water flow*Cp*(T1-T2). We don't have T2 and mass flow of water. We need to take a different path. We have to use the 3% loss in water mass that leaves the tower as steam.
 
i agree with Mrmiller, but how can I actually use the 3% and find H... I have been stuck here
 
You're not trying to find energy here, so I'm not sure what direction you guys are going with the problem. You have the inlet and outlet conditions of the air, so just read from a table or psych chart the moisture content at each, subtract, then convert to mass (then divide by 3%).
 

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