List of formulas related to mechanics of fluid

Density

m: mass of a volume V

$$ \rho = \frac{m}{V}(kg/m^3) $$

Pressure

F: force applied on area of A

$$ p = \frac{F}{A}(N/M^2) $$

Pressure Of Liquids

d: specific gravity(N/m³), p_o: air pressure at the free surface (N/m²), p: pressure created by the weight of liquid above, p_B: total pressure at the depth h

Pressure Of Liquids

$$ p = d.h = pgh $$ $$ p_B = p_o + d.h = p_o + pgh $$ $$ p_A = p_B; p_C = p_D $$

Pascals Principle

P_S: pressure on the surface

Pascals Principle

$$ p_A = p_s + pgh $$

Application

A₁, A₂: area of small and large cylinders; F₁, F₂: applied and upward forces

Pascals Principle application

$$ p = \frac{F_1}{F_2} = \frac{A_1}{A_2} $$

Archimedes Principle

d: specific gravity of liquid (N/m³), V: volume of object, F_b: buoyant force

Archimedes Principle

$$ F_b = d.V = pgV $$

Flow Rate

A: cross sectional area (m²), v: flow velocity (m/s), Q: flow rate (m³/s)

Flow Rate

$$ Q = A_1 v_1 = A_2 v_2 $$