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Formula Sheets / Physics

Chapter 12

Mechanical Properties of Fluids

Revise with flashcards Download this chapter (PDF) All Physics formulas (PDF)

Pressure and buoyancy Fluid dynamics and Bernoulli's theorem Viscosity Surface tension and capillarity

Pressure and buoyancy

$P = P_{0} + ρ g h,$ $F_{B} = ρ_{fluid} V_{sub} g$
Floating
$\frac{V _{sub}}{V} = \frac{ρ _{body}}{ρ _{fluid}}$
Accelerating container
$tan θ = \frac{a}{g}$ (free surface, horizontal $a)$

Fluid dynamics and Bernoulli's theorem

Continuity
$A_{1} v_{1} = A_{2} v_{2}$
Bernoulli
$P + \frac{1}{2} ρ v^{2} + ρ g h =$ constant
Torricelli
$v = 2 g h;$ range $= 2 h (H - h)$

Viscosity

$v_{t} = \frac{2 r ^{2} ( ρ - σ ) g}{9 η}$ $F_{Stokes} = 6 π η r v$
Terminal velocity
$v_{t} = \frac{2 r ^{2} ( ρ - σ ) g}{9 η}$
Poiseuille
$Q = \frac{π Δ P r ^{4}}{8 η l}$
Reynolds number
$R_{e} = \frac{ρ v D}{η}$

Surface tension and capillarity

$T = \frac{F}{L},$ $W = T Δ A$
Excess pressure
drop $\frac{2 T}{r};$ soap bubble $\frac{4 T}{r}$
Capillary rise
$h = \frac{2 T cos θ}{r ρ g}$

Mechanical Properties of Solids Thermal Properties of Matter