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), po: air pressure at the free surface (N/m2), p: pressure created by the weight of liquid above, pB: total pressure at the depth h

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

Pascals Principle

PS: pressure on the surface

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$$p_A = p_s + pgh$$

Application

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

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

Archimedes Principle

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

$$F_b = d.V = pgV$$

Flow Rate

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

$$Q = A_1 v_1 = A_2 v_2$$