Picture an airplane flying around to a certain destination that can't be reached by land-based vehicles. While picturing this, let me ask you, have you ever wondered how these huge metal machines are able to maintain a certain degree of altitude for extended periods of time. Yes, you may say that the jet or propeller engine is responsible for that. In reality though, it is the air that passes under, over, and all around the plane in the sky that really keeps it in the air. This airflow can be computed through streamlines which is typically the change of the velocity vector in relation to the line preceding it prior to forcefully contacting a physical thing, an airplane for this matter. In other words, if there is a continuous flow of air and something external is added to the mix, the direction of the flow or streamline will change. Computing for these changes will consist of you using a number of equations that involves the functional stream formula. Bear in mind that this equation is only applicable streamlines that are in a steady state that cannot be compressed.
- Single out the parts of the velocity vector. The velocity vector is the original flow or line the air is following. In order to calculate the streamlines, you will need to determine and point out each part of the velocity vector first. The equations to use here is V=2Y+4XJ where 2Y represents the U component and 4X represents the Y component.
- Use the stream function equation. For as long as you know the velocity vector components, you can use the stream function equation to calculate the stream function. In order to do this, input all the necessary numerical figures for the components into the equation. If you are unfamiliar with the equation, then read up more on it here.
- Determine the stream function. With both equations in tow and with results, combining them will provide you with the stream function which will assist you in plotting the streamlines or trajectories of a particular flow.
- Solve for the Y constant. If the stream function that you derive is equal to 0, then consider solving for Y in the equation to determine the streamline or trajectory of the particular flow.
- Repeat the process. The process is pretty much the same for every kind of streamline. The bottom line is that you need to solve for Y. If the math is more understandable and simple, then computing for X is a process worth doing. In any case, keep with the process in computing streamlines within the same flow field. You may need to input other constants in order to effectively solve the equation and find out what Y represents.
As soon as you have calculated the streamlines and have the numerical results, you can now translate the figures into a graph to make the whole ordeal much more understandable to the non-mathematical people. Bear in mind, this aspect of math and physics is pretty complex yet it is a vital cog in all the laws of motion we all enjoy today.