Thermodynamics - First Law (T-fitting)

[kaeser1]

Hey guys, I am having a problem trying to figure out what this question is asking for:

The air flow in a compressed air line is divided into two equal streams by a T-fitting in the line. The compressed air enters the 2.5cm diameter fitting at 1.6 MPa and 40 deg C with a velocity of 50 m/s. Each outlet has the same diameter as the inlet and the air at these outlets have a pressure of 1.4 MPa and temperature of 36 deg C. Determine the velocity of the air at the outlet and the rate of change of flow energy across the T-fitting.

I was able to figure out the velocities at the outlets but did not understand the rate of change of flow energy. If somebody could help me out, it would be great.

 

[ponjavic]

The problem obviously says first law, I believe you did not use the first law to find the velocities yeah? So try applying the first law. What variables are unknown? What is delta h?

 

[piercas]

Hello,

It seems like the question is asking for the application of the First Law of Thermodynamics in the context of a T-fitting in a compressed air line. The First Law states that energy cannot be created or destroyed, only transferred or converted from one form to another. In this case, the compressed air is entering the T-fitting with a certain amount of energy and is being divided into two streams, each with a different pressure and temperature.

To calculate the rate of change of flow energy across the T-fitting, you will need to use the equation for the First Law of Thermodynamics:

ΔE = Q - W

Where ΔE is the change in energy, Q is the heat transferred, and W is the work done. In this case, we can assume that there is no heat transfer (Q=0) and the work done is negligible. Therefore, the change in energy (ΔE) is equal to the change in flow energy.

To calculate the change in flow energy, you will need to use the equation:

ΔE = ΔU + ΔKE + ΔPE

Where ΔU is the change in internal energy, ΔKE is the change in kinetic energy, and ΔPE is the change in potential energy.

Since there is no change in height, we can assume that ΔPE = 0. Also, since the air is an ideal gas, we can assume that there is no change in internal energy (ΔU = 0). Therefore, the change in flow energy is equal to the change in kinetic energy (ΔKE).

To calculate the change in kinetic energy, you will need to use the equation:

ΔKE = ½ m (Vf² - Vi²)

Where m is the mass of the air, Vf is the final velocity, and Vi is the initial velocity.

Using this equation, you can calculate the change in kinetic energy for each outlet, and then add them together to find the total change in flow energy. This will give you the rate of change of flow energy across the T-fitting.

I hope this helps clarify the question and how to approach it. Let me know if you have any further questions. Good luck!