A Derivation of the Hydrostatic Equation

[@b.m.khalidhasandrobo9982]

Explained very simply and promptly! Thanks a lot !

[@dy--dx]

Thank you for the clear and concise explanation!

[@reinhardt0731]

thanks for making this simple I finally understand

[@JamesCharbonneau]

@@reinhardt0731 Glad you found it helpful!

[@hidanakatsuki3624]

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[@hidanakatsuki3624]

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[@hidanakatsuki3624]

Step by step

[@mambrinox]

This "proof" assumes that the pressure at an area only depends on the weight of the cylinder over that area. To prove that you need the hydrostatic equation that you derive. The proof assumes the proof. No proof at all.

[@JamesCharbonneau]

You are correct, it is not a proof, it is a derivation. One thing that separates physics from math, and one thing that many people who want an axiomatic, proof-like structure struggle with in physics, is that physics always requires a jump in intuition to connect what we observe in the world to the math we use to describe it. You are correct that we made an assumption that the weight on the top of the cylinder is only from the fluid directly above it. This isn’t a ridiculous assumption. The weight that a bathroom scale measures is from the objects on it, and not beside it. However, fluids are different, and it’s a valid question. The thing is though, when we make this assumption we this equation that turns out correct. The “proof” comes when we verify this equation using experiments. But even this isn’t a “proof” you would get in math that this equation is exactly correct, but it is the best we can do in physics. The reality is that all of physics is constructed out of circular logic. You could derive a formula for the hydrostatic equation making a different starting assumption. For instance, you might think that the weight on the top of the cylinder is given by all the fluid in the container above the cylinder, and derive your equation. You then need to test it. This equation fall aparts very quickly when you run an experiment. If the pressure were equal to the weight of all the water in the container above you, then when you submerse yourself in the ocean you would get crushed by all the water above you. You have probably done this one yourself-when you submerse yourself in the ocean you do not get crushed. So because of that we can rule out this assumption. There are many other assumptions you could make and check, but the one that works and reproduces the measurements we see in the real world is the one we start this derivation with. You are right it is not a proof. But you should be aware that all of physics is similarly circular. There is not a single equation that you can derive from first principles. They all have an assumption or intuitive leap that has survived experimental tests.

[@hidanakatsuki3624]

Please make it simple

[@JamesCharbonneau]

Sorry, this is a video for my course I teach at UBC. It’s meant to be viewed in context of a course where many concepts have already been introduced. I just post it hear because KZbin is easy to host videos on. However, If you have specific I questions about steps you feel are missing, I’m happy to answer them for you.

[@hidanakatsuki3624]

Sir thank you. For ur concern I am an aeronautical diploma 🎓🗞 Student. And I have this concept in my cyllabus So can u simplify these concept Mean full explanation , written explanation for each step. If u can I'm glad sir.

[@JamesCharbonneau]

@@hidanakatsuki3624 Sorry, I personally can’t do it much more clear than in the video without specific questions. I’m going to be honest, you’re probably much better off doing practice problems and getting a feel for it rather than having a more detailed explanation of this derivation. After some practice using the equation, come back and check to see if the conceptual aspects of where it comes from makes sense.

[@veronicanoordzee6440]

The force of the atmosphere is the force at sea-level. Force is weight (F = m.g). At sea-level the force is the weight of all the stuff (above the cylinder) in the atmosphere. In the water the force and therefore the pressure is equal over any horizontal plane, according Pascal's Law: en.wikipedia.org/wiki/Pascal%27s_law