13.1.6. Basic Conservation Laws

Now, as you might have solved a lot of physics problems on solid body translations, rotations and all, the basic concept of linear momentum equations you apply, which is, you know, force is rate of change of momentum flux. That is the Newton’s second law of motion and you have been using that to solve many problems in twelfth level of the class in physics or fluid mechanics type of problems.

Now, when you consider a system that means these three conservation principles they are quite valid. When we consider an isolated system like, as I have given examples, the virtual fluid balls, they are isolated systems, okay? They can move at different times. Like, for example, if I consider a system of a set of fluid particles or a set of virtual fluid balls, as you can understand it, there is no change, no other type of mass decaying function is there. The mass will remain constant.

That means what will happen is mass at the system level at t is equal to mass at the system level at t will be the same, but they can have simple space at this location, but when it comes to t level they can fragment and they can occupy very complex surface at t times. So, mass conservation is a very simple thing. You just know it, the mass remains constant at t and t if you are considering an isolated system where you have n number of fluid particles or virtual fluid balls, that number will remain the same whether you have t time or t time.

Conservation of mass is a fundamental principle in fluid mechanics. It states that for an isolated system, the total mass remains constant over time. This means that, even as the individual fluid particles move and change location, the overall mass of the system does not change. This principle is crucial when analyzing fluid flow in various systems, as it allows us to conclude that the mass entering a system must equal the mass leaving it, given that no mass is created or destroyed. Therefore, any calculations involving fluid dynamics often start with the assumption that mass conservation applies.

Consider a balloon filled with air. If you were to squeeze the balloon, you would notice that the volume of the balloon changes, but the total amount of air inside it stays the same unless you let some air escape. This is a practical demonstration of mass conservation; no air is lost as you change the shape and size of the balloon.

Now, as you might have solved a lot of physics problems on solid body translations, rotations and all, the basic concept of linear momentum equations you apply, which is, you know, force is rate of change of momentum flux. That is the Newton’s second law of motion and you have been using that to solve many problems in twelfth level of the class in physics or fluid mechanics type of problems.

The conservation of momentum states that in an isolated system, the total momentum remains constant unless acted upon by an external force. In fluid mechanics, this is expressed mathematically via the momentum equations derived from Newton's second law, indicating that the change in momentum of fluid particles depends on the net force exerted on them. When analyzing fluid flows, we often calculate the net forces acting on a volume of fluid to determine how its motion changes over time. This concept is essential in designing systems where fluid motion is crucial, such as pipelines or nozzles.

Think about a game of billiards. When the cue ball strikes a stationary ball, it transfers momentum to the other ball, causing it to move. If no outside forces (like friction) acted on the balls, their total momentum before and after the collision would remain the same. This illustrates the conservation of momentum well, showing how momentum is transferred between objects but the overall momentum remains constant in the absence of external forces.

Now coming to the energy conservation equation, see, if you look at the energy conservation, you know very well, energy is conserved unless otherwise you have very particular cases. That means, if I have a system like, for example, let us have a pump system here, okay. And it is connected to the inflow, also it is connected to the outflow. That means two pipes we have, connected to that I have a pump.

So, if you look at that, the pump is giving energy to this fluid, okay. We convert from mechanical energy to potential energy. The pump is giving additional energy or work done by the mechanical to the fluid, okay. So, we have exchange of work to this system. Also, as you feel it, if you touch any pumping system, just the outlet level and the inlet pipe, you can see there will be a temperature different. If there is a temperature difference, that means heat transfer is happening.

So, work done is there and also heat transfer is there.

The conservation of energy principle conveys that energy cannot be created or destroyed, only transformed from one form to another. In fluid dynamics, this means that the total energy of a fluid system remains constant unless influenced by external work or heat transfer. For instance, in a pump system, mechanical energy is converted into the potential energy of the fluid. Understanding energy conversion helps engineers design efficient systems. Identifying energy losses, such as friction in pipes or heat loss, is necessary for optimizing performance.

Consider riding a bicycle uphill. You need to exert energy to pedal against gravity. Your muscles do work (mechanical energy), which is transformed into potential energy as you gain height. If you stop pedaling, your bike will eventually slow down and stop. This represents energy conservation; energy is not lost but converted and transferred, similar to how a pump transfers energy to fluid.

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