I am looking for help on the following:

a) Given the system shown in the figure below, derive the steady flow energy equation from first principle.

b) Again using first principles, show how the energy equation would change for the case when the system is unsteady.

enter image description here

I am trying to learn this for upcoming exams.

But i can find nowhere on line which breaks down this sort of question. Which means i cant understand how to complete these sort of questions.

Can anyone help me complete this question please? So i can get an understanding of these types of questions.


  • $\begingroup$ There are two different equations I can think of . One with mass and one with energy, but don't really see how you can use the height in either of them. Also I am not certain what do you mean by unsteady state. Could you give an indication what is considered know and what unknown in this problem? $\endgroup$
    – NMech
    Oct 29, 2020 at 19:32
  • $\begingroup$ Thanks for the reply. This is a test question i was given. I have searched google and can fine no way to complete this. This is why i thought i would ask on here $\endgroup$ Oct 29, 2020 at 20:16
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    $\begingroup$ This looks like a homework question. In order for such questions to be answered in this site, we need you to add details describing the precise problem you're having. What have you tried to solve this yourself? Please edit your question to include this information. $\endgroup$
    – Wasabi
    Oct 30, 2020 at 1:39
  • $\begingroup$ @Wasabi i have tried to solve this. I am having a problem understanding all of the question. With help from people on here i was hoping to learn, and complete the question. So i have a better understanding of the subject $\endgroup$ Nov 5, 2020 at 20:07
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    $\begingroup$ @KyleAnderson I understand. But the best way for us to help you is if we actually understand where you're having trouble (do you understand what the question is asking? Do you have any idea of how to start trying to solve this problem?): the problem isn't that you can't solve this problem, it's that you have a knowledge gap which isn't letting you solve this problem. So we need to know what you've tried and where specifically you're stuck so that we can identify what specifically is the gap. This'll allow us to tailor our answers to focus on what you're actually having trouble with. $\endgroup$
    – Wasabi
    Nov 5, 2020 at 23:35

1 Answer 1


steady state process.

For the steady state process, there are two principles:

a) conservation of mass $$ \dot{m}_{in}- \dot{m}_{out} = \dot{m}_{system} = 0 $$

In your particular example: $$ \dot{m}_{1} + \dot{m}_{2} - \dot{m}_{3}= 0 $$

b)energy balance For a steady-flow process, the total energy content of a control volume remains constant. Therefore its rate of change should be equal to zero

$$\dot{E}_{in}- \dot{E}_{out} = \dot{E}_{system} = 0 $$

For a general steady-flow process, in your particular system the energy balance can be written as:

$$\underbrace{\left(\sum_{i=1}^2\dot{m}_{i}(h_i + g \;z_i) + \dot{Q}_{net}+ \dot{W}_{net} \right) }_{\dot{E}_{in}}- \dot{m}_{3}(h_3 + g \;z_3) = \dot{E}_{system} = 0 $$

unsteady process

The equations don't change much. The main difference is that the rate of the system does not have to be zero. i.e.:

a) conservation of mass $$ \dot{m}_{in}- \dot{m}_{out} = \dot{m}_{system} = 0 $$

In your particular example: $$ \dot{m}_{1} + \dot{m}_{2} - \dot{m}_{3}= \dot{m}_{system} $$

b)energy balance For a steady-flow process, the energy content of a control volume changes with time during an unsteady-flow process.

$$\dot{E}_{in}- \dot{E}_{out} = \dot{E}_{system} $$

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    $\begingroup$ Thank you @NMech i am going to look at this. And will reply when i have tried to understand a little more $\endgroup$ Nov 5, 2020 at 20:09

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