Converging nozzle temperature difference - Steady flow energy equation

[Nuclear_eng]

I come from a civil engineering background and I'm about to start a masters in nuclear energy. I have no experience in thermodynamics and I've been doing a bit of revision before the course commences to get me up to speed. I've been working my way through 15 revision questions and I only have a couple left now. I posted a question on this forum yesterday but I'm stuck again with a different type of question on flow processes. This is meant to be one of the easiest questions in my revision booklet but so far the answer has eluded me.

Homework Statement

A converging nozzle is used to accelerate a flow of air from 50m/s at the inlet to 150m/s at the exit. The air temperature is 25°C at the inlet. Assuming heat transfer to the air is negligible, use the steady flow energy equation to calculate the temperature at the exit.

Homework Equations

Steady flow energy equation:

h₁+0.5V₁²+gZ₁=h₂+0.5V₂²+gZ₂

The Attempt at a Solution

I've revised control volume analysis and steady flow processes but I'm not getting anywhere with this. I assume it will be a very simple calculation as all the other 'easy' revision questions have taken me about a minute or two.

The correct answer is 15.1°C

 

[Nuclear_eng]

Is there no one who can help me? I've been looking at this similar question I found on the forums and I can't get 184°C by using the SFEE. I think I must be making a mistake with the units or something really stupid.

https://www.physicsforums.com/showthread.php?t=249494

Could somebody please just plug the numbers in and show me how he got 184°C? I would imagine it will take less than a minute and it would be a massive help to me.

Thanks

 

[LawrenceC]

Use the energy equation you have above. The enthalpy is Cp*T. Ensure you get the units correct on the V^2/(2g) term.
15.1 C is indeed correct.

 

[Nuclear_eng]

Thank you very much Lawrence. I was getting my units for C_p messed up but I've now managed to get 15.1°C.

 

[Nickie]

, but I'm not sure how to get there using the steady flow energy equation. Can anyone provide some guidance or a step-by-step solution?

I understand your frustration with this problem and your desire to fully understand the concept before starting your masters in nuclear energy. The steady flow energy equation is a fundamental equation in thermodynamics and understanding it is crucial for many applications, including in nuclear energy.

First, let's break down the equation. The steady flow energy equation is a statement of energy conservation for a fluid flowing through a control volume. In this case, the control volume is the converging nozzle. The equation states that the total energy at the inlet (represented by h1, the enthalpy) plus the kinetic energy and potential energy at the inlet (represented by 0.5V12 and gZ1, respectively) is equal to the total energy at the exit (represented by h2) plus the kinetic energy and potential energy at the exit (represented by 0.5V22 and gZ2, respectively).

Now, let's apply this equation to the problem at hand. We know that the inlet velocity (V1) is 50m/s and the exit velocity (V2) is 150m/s. We also know that the inlet enthalpy (h1) is equal to the air temperature (T1) at the inlet, which is 25°C. However, we don't know the exit enthalpy (h2) or the potential energies (Z1 and Z2).

To solve for the exit enthalpy (h2), we need to use the ideal gas law, which states that the enthalpy of an ideal gas is only a function of its temperature. Therefore, we can use the ideal gas law to calculate the exit enthalpy (h2) based on the exit temperature (T2).

Once we have the exit enthalpy, we can plug in all the known values into the steady flow energy equation and solve for the exit temperature (T2). This should give us the correct answer of 15.1°C.

In summary, the key to solving this problem is understanding the steady flow energy equation and using the ideal gas law to relate temperature to enthalpy. I hope this explanation helps and best of luck in your studies!