- #1

thermoPat

- 8

- 0

## Homework Statement

I want a detailed understanding of the temperature drop of a boiler when water is lost from a leak. I have a temperature recording of a leak that lasted for an hour and caused the temperature to drop from 170

^{o}C to 150

^{o}C when 2.55m

^{3}of water was lost. I have tried using steam tables to understand the temperature drop but my calculations show a slight temperature

*increase*instead of decrease, so obviously my approach is wrong.

I would appreciate some guidance on the correct way to calculate the theoretical temperature drop. This is the approach that I tried:

## Homework Equations

Steam table:

https://www.physicsforums.com/attachments/123054

## The Attempt at a Solution

Assumptions:

- 1m
^{3}of water weighs 1 tonne at the temperatures under consideration. - No energy was added to or removed from the system other than the energy in the lost water and work done to push it out of the leak hole.

- 6.55m
^{3}of water and 2.35m^{3}of saturated steam at 8 bar (116 psi). - From steam table www.engineeringtoolbox.com/saturated-steam-properties-d_457.html steam density is 4.16kg/m
^{3}, so mass of steam is 2.35 * 4.16 = 9.78kg - Enthalpy of water + steam is

6.55 * 721 + 9.78 * 2.77 = 4723 + 27 = 4750MJ

Water was cooling during the leak. Assume average temperature was 160. At that temp the specific enthalpy is 676, so total lost enthalpy is 1720MJ.

Work done in pushing the water out of the hole:

Average pressure is 6.5bar = 0.65MP = 0.65 MN/m

0.62MN moving 2.55m = 1.6MJ ------- Negligible

^{3}0.62MN moving 2.55m = 1.6MJ ------- Negligible

End conditions:

After the water leak the enthalpy of the system is the original enthalpy less the losses:

4750 - 1720 - 2 = 3028MJ.

To find the temperature of the system we search the steam table for the temperature of a system with an enthapy of 3028MJ and having 4t of water and 4.9m

We find this at 175

Something is wrong.

4750 - 1720 - 2 = 3028MJ.

To find the temperature of the system we search the steam table for the temperature of a system with an enthapy of 3028MJ and having 4t of water and 4.9m

^{3}of steam.We find this at 175

^{o}C, which is hotter than the initial temperature !??Something is wrong.