# Steam generation thermodynamics

1. May 1, 2017

### Ali Ahmad

a cylindrical tank with volume V
a volume of water is inside the tank and the rest is air
now if coal combustion is releasing heat into the tank Qin
and when the gauge reads a certain pressure "P", the valve is opened which allows steam to exit the boiler
what's the mass flow rate of the steam?

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2. May 1, 2017

### Staff: Mentor

Is this a homework problem?

3. May 1, 2017

### Staff: Mentor

The mass flow out will depend most strongly on the size of the valve and the outlet pipe. The flow rate will also vary with time.

If that is homework, there is too little information given to solve it.

4. May 1, 2017

### Staff: Mentor

I think they want him to assume that the rate of heating is constant.

5. May 2, 2017

### Ali Ahmad

this is a part of a senior project that im working on.
you can assume anything to simplify it
assume it's a bachelor's degree level question

6. May 2, 2017

### Staff: Mentor

What is your analysis of this so far?

7. May 2, 2017

### Ali Ahmad

Ignore the previous question.
now let's say that the tank is vacuumed and has a volume "Vt", and the valve is closed
then a volume "Vw" of water at T1=20C is added to the tank
water is heated using an external heat source (coal combustion) until its temperature reaches T2=120C
what is the mass of steam generated in the tank, and when the valve is opened, what is the flow rate of steam? what is the pressure in the tank?
assume the cross-sectional area of the pipe is "Ap" and ignore heat losses

8. May 2, 2017

### Staff: Mentor

What are your thoughts on how this would be approached?

9. May 2, 2017

### Ali Ahmad

after t seconds, the heat rate is:
Qdot = mw . (cp2 . T2 - cp1 . T1) / t
control volume thermodynamics
Ein - Eout = dE/dt (assuming steady)
Ein = Eout
Qdot = mout . u2 -------eq1
at T2=120C
P2=gauge pressure reading just before opening the valve
then from steam tables, we get u2 and substitute in eq1 to find mout
and how do I find the amount of vapor generated after t seconds?

10. May 2, 2017

### Staff: Mentor

Is this what you are asking: I have water in a constant volume tank, and I am supplying heat at a constant rate. When the pressure gets to a certain value, I start removing mass at a rate necessary to hold the pressure at this constant value, while continuing to supply heat?

11. May 6, 2017

### Ali Ahmad

yes

12. May 6, 2017

### Staff: Mentor

The simplest solution makes use of energy conservation. Can you write expressions for the total energy in and the total energy out?

13. May 6, 2017

### Staff: Mentor

Are you currently learning about the open system (control volume) version of the first law of thermodynamics?

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