13.1.8. Conservation of Momentum

Now, as you know from your twelfth level of knowledge in fluid mechanics as well as solid mechanics, the three basic conservation laws we follow which are mass conservation, momentum conservation which is part of Newton’s second law of motion, then we have the third law which talks about energy conservation, that is the first law of thermodynamics.

In physics, conservation laws are fundamental principles that describe how certain quantities remain constant in a closed system. Mass conservation means that the total mass in a system cannot change over time; it can only change forms (like from solid to liquid) but the total amount will remain the same. Momentum conservation, linked to Newton's second law, states that the total momentum of a closed system remains constant unless acted upon by external forces. Energy conservation asserts that energy can neither be created nor destroyed but only transformed from one form to another.

Consider a game of billiards. When you strike the cue ball, it transfers momentum to the other balls, and their combined momentum before and after the strike remains the same unless some external force (like friction or a cushion) acts upon them. This is a practical demonstration of momentum conservation.

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.

In a controlled or isolated environment, the principles of conservation apply more strictly. For instance, if we think of a collection of virtual fluid balls as a system, each ball experiences forces internally but collectively maintains the total mass and momentum unless disturbed. This implies that, in a defined timeframe, no matter how individual particles move and interact, the overall properties of the system remain constant.

Imagine a sealed jar filled with marbles. If you shake the jar, the marbles will bounce around and change positions but the total number of marbles (mass), their collective 'kinesis' (momentum), and energy they possess will remain constant unless something external (like opening the jar) affects them.

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.

This highlights that the momentary distribution and arrangement of the particles can change, but the total number remains constant - this is the crux of conservation. The concept can also be related to momentum, where the total momentum before an interaction is the same as the total momentum after the interaction, given that no external forces are acting on the system.

Think of a fireworks display, where individual fireworks explode and scatter in different directions. Each firework represents a particle within our system; while they disperse and change locations, the overall number of fireworks (or 'mass' in our analogy) stays the same until the display ends.

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.

Energy conservation relates to momentum in that it establishes the energy transfer or work done on the system influences its momentum. Here, the pump system does work on the fluid, adding energy to it. The relationship between energy, work, and fluid motion can be expressed mathematically, allowing for increases in momentum due to energy input.

Consider a water slide. As you slide down, gravitational potential energy is converted into kinetic energy, causing you to go faster. In this case, your increased speed (momentum) is a direct effect of the energy transferred by gravity, similar to how fluid systems exchange energy through pumps.

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