Physics
Chapter 11: Fluid Mechanics

Motivation
Fluid mechanics is a branch of physics that deals with behavior of fluids and the forces acting on them.

Introduction
Fluid is basically a substance, as a liquid or gas, that can flow and change it's shape.
- A liquid is a fluid that has a definite volume but no definite shape.
- A gas is a fluid that has neither a definite volume nor a definite shape.

Pressure
A simply analogy for the pressure formula is:
A nail can stab into wood, but your finger can't even with the same force?
And why won't the nail work if you press it too gently?
You have discovered pressure, it is defined as force applied per unit area: \( P = \frac{F}{A} \)
(P = pressure (Pa), F = force (N), A = area (m²))

Static pressure of a fluid
\( P = h \rho g \) (derived using \(P = \frac{F}{A}\), derivation below)
(P = pressure (Pa), h = height (m), \( \rho \) = density of fluid (kg/m³), g = 9.81 m/s²)

If atmospheric pressure is included, the equation becomes:
\( P = P_0 + h \rho g \).
(P_0 = atmospheric pressure (Pa))

Buoyant Force
When an object is placed in a fluid, it experiences an upward force called the buoyant force.
This is why objects feel lighter in water.

The formula for buoyant force is \( F_b = \rho V g \).
(\(F_b\) = buoyant force (N), \( \rho \) = density of fluid (kg/m³), \( V \) = volume of fluid displaced (m³), \( g \) = 9.81 m/s²)

If the buoyant force is greater than the object's weight, it floats.
If less, it sinks.

Pascal's law
To easier understand Pascal's law, look at the beautiful diagram below:

Pascal's law states that for a fluid at rest in a closed container, a pressure change in one part is transmitted without loss to the other side.
To simply put, if you push down all the fluid in the left side on the diagram, it will appear same amount of fluid on the right.

Formula for Pascal's law is: \( \frac{F_1}{A_1} = \frac{F_2}{A_2} \).
(\(F_1\) and \(F_2\) = force applied on left and right respectively (N), \(A_1\) and \(A_2\) = area of left and right respectively (m²))

Bernoulli's Equation
Bernoulli's equation simply put is the conversation of energy formula for fluids.
It's a pretty important equation, as it pretty much combines all the formula before and sums it into one formula.

The formula for bernoulli's equation is:
\(P + \frac{1}{2} \rho v^2 + \rho g h = \text{constant}\)
(\( P \) = pressure (Pa), \( h \) = height (m), \( \rho \) = density (kg/m³), \( v \) = velocity (m/s), \( g \) = 9.81 m/s²)

That's all, now go practice question on book 🔥🔥