I have seen multiple times and places that many ideal laws are easily made applicable on real life situations. For example, Bernoulli's equation or principle is made as a good equipment in solving real life question regarding lift of aeroplane, blowing out of roofs of houses during storm, vacuum brakes in trains, and many more. The problem with me is that why and how we directly apply a theorem for ideal situation to a condition which is non-ideal? Do we do it just to get answer or is there any approximation? If there is, then what are the assumptions we've made? Furthermore, there are some more ideal equations which are directly applied on real life situations which are non-ideal, but we follow them blindly? Why so? Is there any good logic behind?
Engineers produce analytical models of situations which would ideally return exact solutions for quantities such as pressure etc.
The skill to this is being aware of the assumptions made through deriving certain theorems, such as Bernoulli's principle, and knowing when they can be applied and when they can't be.
In many cases, the scenario will be too complex to model perfectly, so approximations are made. It is important to be aware whether your approximations will lead to an overestimate or an underestimate. For example, you may approximate a fluid to be inviscid to simplify a flow scenario and allow you to apply Bernoulli's principle.
Another example would be neglecting friction in a dynamics analysis. Being aware that there is an additional decelerating force would allow you to confirm that any result you obtained from your theoretical model would be an overestimate.
Engineers do not follow these models "blindly" - they are aware of any assumptions they have made and apply a suitable safety factor to their results that ensures any design decisions based on these values are exaggerated to allow for the calculated value to be different to the actual value experienced in reality.
For example, when the cross sectional area of a bar of known material is calculated to support a known load without yielding, a safety factor of 2 or maybe 4 would be applied so that the bar will not yield if even 4 times the design load is experienced in reality. This accounts for any approximations or untrue assumptions made in the theoretical model.
According to https://en.wikipedia.org/wiki/Bernoulli%27s_principle, The following assumptions must be met for this Bernoulli equation to apply:
- The flow must be steady, i.e. the fluid properties (velocity, density, etc...) at a point cannot change with time
- The flow must be incompressible – even though pressure varies, the density must remain constant along a streamline
- Friction by viscous forces has to be negligible.