Mechanical Properties of Fluids — Complete Formula

Pressure

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Pressure	[P = \dfrac{F}{A}]	[P] = pressure, [F] = force, [A] = area	Pa	Force per unit area ⭐
Hydrostatic Pressure	[P = \rho gh]	[\rho] = density, [g] = gravity, [h] = depth	Pa	Increases with depth ⭐
Total Pressure	[P = P_0 + \rho gh]	[P_0] = atmospheric pressure	Pa	Absolute pressure

💡 Memory Hint:
Pressure in fluid depends only on depth, not shape

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Pascal’s Law	[P_1 = P_2]	—	—	Pressure transmitted equally ⭐
Hydraulic Lift	[\dfrac{F_1}{A_1} = \dfrac{F_2}{A_2}]	[F] = force, [A] = area	—	Force multiplication ⭐

💡 Memory Hint:
Small force → large force using area difference

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Buoyant Force	[F_b = \rho g V]	[F_b] = buoyant force, [V] = displaced volume	N	Upward force ⭐
Apparent Weight	[W’ = W – F_b]	[W] = actual weight	N	Weight reduces in fluid ⚠️
Floating Condition	[\rho_{body} \leq \rho_{fluid}]	—	—	Body floats ⭐

💡 Memory Hint:
Buoyant force = weight of displaced fluid

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Continuity Equation	[A_1 v_1 = A_2 v_2]	[A] = area, [v] = velocity	m³/s	Mass conservation ⭐

💡 Memory Hint:
Area ↓ → Velocity ↑

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Bernoulli Equation	[P + \dfrac{1}{2}\rho v^2 + \rho gh = \text{constant}]	[v] = velocity, [h] = height	Pa	Energy conservation ⭐
Horizontal Flow	[P + \dfrac{1}{2}\rho v^2 = \text{constant}]	—	Pa	Height same

💡 Memory Hint:
Velocity ↑ → Pressure ↓ ⚠️

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Viscous Force	[F = \eta A \dfrac{dv}{dx}]	[\eta] = viscosity, [dv/dx] = velocity gradient	N	Opposes motion ⭐
Stokes’ Law	[F = 6\pi \eta r v]	[r] = radius	N	For spherical body ⭐
Terminal Velocity	[v = \dfrac{2r^2(\rho – \sigma)g}{9\eta}]	[\sigma] = fluid density	m/s	Constant speed ⚠️

💡 Memory Hint:
Viscosity = internal friction of fluid

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Surface Tension	[T = \dfrac{F}{l}]	[T] = surface tension, [l] = length	N/m	Force per unit length ⭐
Energy Relation	[T = \dfrac{E}{A}]	[E] = energy, [A] = area	J/m²	Energy per unit area
Excess Pressure (Drop)	[\Delta P = \dfrac{2T}{r}]	[r] = radius	Pa	Single surface ⭐
Soap Bubble	[\Delta P = \dfrac{4T}{r}]	—	Pa	Double surface ⚠️

💡 Memory Hint:
Bubble → double pressure of drop

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Capillary Rise	[h = \dfrac{2T\cos\theta}{\rho g r}]	[\theta] = contact angle	m	Depends on radius ⭐

💡 Memory Hint:
Narrow tube → higher rise

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