Thermo 1st Law open system question

[Abi_mecheng]

Homework Statement

An insulated nozzle receives are at a negligible velocity at a pressure of 150kpa and temp of 25 degrees C. if the flow passing through the nozzle expands to 100kpa in an isentropic process, calculate the temperature and velocity of the air leaving the nozzle.

The Attempt at a Solution

Solution is attached but I don't understand how 1/2 becomes 1/2000 in the equation m(dot)[h2-h1)+1/2(v2^2 - v1^2)

Thanks

 

[SteamKing]

Be advised that the solution has P1 = 130 kPa, not 150 kPa.

 

[SteamKing]

The Attempt at a Solution

Solution is attached but I don't understand how 1/2 becomes 1/2000 in the equation m(dot)[h2-h1)+1/2(v2^2 - v1^2)

Thanks

Look at the units of the various parts of this equation. The additional factor of 1000 comes about to convert kg-m^2/s^2 to kJ (1 J = 1 kg-m^2/s^2).

 

[Abi_mecheng]

Ohh ok totally missed that, thanks for pointing that out much appreciated.

 

[rezeew]

for sharing the problem and the solution. In order to better understand the solution and the use of the 1/2 term, let's break down the equation:

m(dot): This represents the mass flow rate of the air passing through the nozzle. It is measured in units of mass per unit time (e.g. kg/s).

[h2-h1]: This term represents the change in enthalpy of the air passing through the nozzle. Enthalpy is a measure of the total energy of a system, and it includes both the internal energy of the system and the work done by or on the system. In this case, the air is expanding and doing work as it passes through the nozzle, so the enthalpy will change. This term is multiplied by the mass flow rate to give the total change in energy (in units of energy per unit time).

1/2(v2^2 - v1^2): This term represents the change in kinetic energy of the air passing through the nozzle. Kinetic energy is a measure of the energy of motion, and it is dependent on the velocity of the air. In this case, the air is expanding and its velocity will change. This term is multiplied by the mass flow rate to give the total change in kinetic energy (in units of energy per unit time).

Now, to answer your question about why 1/2 becomes 1/2000 in the equation, it is because the mass flow rate (m(dot)) is given in units of kg/s, while the velocity (v) is given in units of m/s. In order to have consistent units, we need to divide the velocity term by the mass flow rate, which gives us 1/2000. This allows us to have units of energy per unit time on both sides of the equation, which is necessary for the equation to be balanced.

I hope this explanation helps to clarify the use of 1/2 in the equation. If you have any further questions or concerns, please do not hesitate to ask. As scientists, it is important to fully understand the equations and solutions we use in our work. Keep up the good work!