Process Engineering - Multiple Evaporators

[nobodyuknow]

Homework Statement

Here's a quick sketch of the problem: http://prntscr.com/15ltr5

Essentially, Sugar Solution enters the first evaporator at 65°C and the water is boiled (to 100°C) so that a sugar concentrate comes out (bottom of evaporator) and saturated steam leaves the evaporator through the top and heats the next evaporator. This process continues for the remaining 2 evaporators.

Therefore, in order for the saturated steam to boil the sucrose solution in the next evaporator, energy is lost thus, more heat is required, OR, a drop in pressure is necessary. This is my understanding of information given to me... here's the original: http://prntscr.com/15lub4

I'm suppose to calculate:
Amount of sugar concentration leaving each of the evaporators also...

What is the reduction in steam usage per kg of total water evaporated for the four evaporators in series
compared to one evaporator ?

Homework Equations

Really no idea.

The Attempt at a Solution

I thought you could use Guy Lussac's Law, however, I'm not too sure about this.
P1/T1 = P2/T2
Thus, 1 atm, 0.65atm, 0.4225atm and 0.274625atm, this logic however, seems massively flawed.

I'm seriously stumped!

 

[KataKoniK]

Thank you for sharing your problem with us. I would like to provide you with some guidance and suggestions for solving this problem.

Firstly, it is important to understand the basic principles behind the evaporation process. Evaporation is a process in which a liquid is converted into its gaseous state. In the case of sugar solution, the process involves boiling the water in the solution, which leaves behind a concentrated sugar solution. This is achieved by heating the solution and creating a pressure difference between the liquid and the surrounding atmosphere.

In your problem, you have four evaporators in series, which means that the saturated steam from the first evaporator is used to heat the second evaporator, and so on. This process requires a continuous supply of steam and a decrease in pressure in each subsequent evaporator. This decrease in pressure allows the steam to boil the sugar solution in each evaporator.

To calculate the amount of sugar concentration leaving each evaporator, you need to consider the concentration of the sugar solution entering the first evaporator and the amount of water evaporated in each subsequent evaporator. You can use the principle of mass balance to calculate the concentration of sugar in each evaporator.

As for the reduction in steam usage per kg of total water evaporated, you can use the principle of energy balance to calculate the energy required for evaporation in each evaporator. This will give you an idea of the amount of steam needed for each evaporator and how it compares to using a single evaporator.

In terms of equations, you can use the steam tables to determine the properties of steam at different pressures and temperatures. You can also use the heat transfer equation to calculate the energy required for evaporation.

I hope this helps you in solving your problem. Remember to always understand the basic principles and use appropriate equations and data to come up with a solution. Good luck!