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Fluid Statics (Fluids at Rest)〰️

a) Density (ρ)

Defined as mass per unit volume
ρ = m / V
Unit: kg/m³


b) Pressure in Fluids

Pressure is the force applied per unit area:
P = F / A
Unit: Pascal (Pa)


c) Pressure due to a Column of Fluid

P = ρgh
Where:

ρ = density of the fluid

g = gravitational acceleration

h = height/depth of the fluid



d) Pascal’s Principle

A change in pressure applied to an enclosed fluid is transmitted equally throughout the fluid.
Used in hydraulic systems.


e) Archimedes’ Principle

A body submerged in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid.
F_b = ρ_fluid × g × V_displaced


f) Conditions of Floating and Sinking

✅Floating: Weight = Buoyant force

✅Sinking: Weight > Buoyant force

✅Suspended: Weight = Buoyant force (object remains at equilibrium)

Heart Chambers

✅The human heart has four chambers

1. Right Atrium – receives deoxygenated blood from the body via the vena cava.


2. Right Ventricle – pumps deoxygenated blood to the lungs through the pulmonary artery.


3. Left Atrium – receives oxygenated blood from the lungs via the pulmonary veins.


4. Left Ventricle – pumps oxygenated blood to the body through the aorta.



💡 The atria (plural of atrium) are the upper chambers and have thin walls, while the ventricles are the lower chambers and have thick, muscular walls—especially the left ventricle, which pumps blood to the whole body.

@ethiohigh_school ☑️

❓What is the correct sequence of blood flow through the heart chambers, starting from the body?(USSLCE 2016)

A. Right atrium → Right ventricle → Lungs → Left atrium → Left ventricle → Body

B. Left atrium → Left ventricle → Lungs → Right atrium → Right ventricle → Body

C. Right ventricle → Right atrium → Lungs → Left ventricle → Left atrium → Body

D. Right atrium → Left atrium → Right ventricle → Left ventricle → Body

🧠comment @ethiohigh_school ☑️

Matrices

☛ A matrix is a rectangular array of numbers arranged in rows and columns.

☛ A matrix is usually denoted by capital letters (e.g., A, B, C).

☛ Each number in a matrix is called an element or entry.


⊙Notation
☛ If a matrix A has m rows and n columns, we write it as Aₘₓₙ (m by n matrix).

✔️ Types of Matrices

☑Row matrix: Only one row (e.g., [2 3 5])

☑Column matrix: Only one column

☑Square matrix: Same number of rows and columns

☑Zero (Null) matrix: All elements are 0

☑Diagonal matrix: Only diagonal elements are non-zero

☑Scalar matrix: Diagonal matrix with same diagonal values

☑Identity matrix (Iₙ): Diagonal = 1, rest = 0

☑Symmetric matrix: A = Aᵗ (transpose)

☑Skew-symmetric matrix: A = -Aᵗ


✔ Matrix Operations

a) Addition and Subtraction

☛ Only possible if matrices have same order

☛ Add/subtract corresponding elements


b) Scalar Multiplication

☛ Multiply each element by a scalar (number)


c) Matrix Multiplication

Multiply Aₘₓₙ × Bₙₓₚ results in Cₘₓₚ

Rule: Multiply row by column

@ethiohigh_school ☑️