This chapter explores the mechanical properties of fluids, including their behavior under various forces and conditions. Understanding these properties is essential for applications in engineering and environmental science.
Mechanical Properties of Fluids – Formula & Equation Sheet
Essential formulas and equations from Physics Part - II, tailored for Class 11 in Physics.
This one-pager compiles key formulas and equations from the Mechanical Properties of Fluids chapter of Physics Part - II. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
P = F / A
P represents pressure (in pascals), F is the normal force (in newtons), and A is the area (in square meters). This formula defines pressure as force acting per unit area.
ρ = m / V
ρ denotes density (in kg/m³), m is mass (in kg), and V is volume (in m³). This formula is crucial for understanding the mass distribution of fluids.
P = P₀ + ρgh
P is the pressure at a depth, P₀ is the atmospheric pressure at the surface, ρ is the fluid density, g is gravitational acceleration, and h is the depth. This relationship is fundamental for calculating pressure variations with depth.
A₁v₁ = A₂v₂
A₁ and v₁ are the area and velocity of fluid flow at one point, while A₂ and v₂ are at another. This continuity equation ensures that the mass flow rate remains constant in incompressible fluid flow.
P₁ + (1/2)ρv₁² + ρgh₁ = P₂ + (1/2)ρv₂² + ρgh₂
This is Bernoulli's equation, linking pressure, kinetic energy, and potential energy along a streamline for incompressible fluids in steady flow.
F = 6πηav
F is the drag force (in newtons), η is the viscosity of the fluid (in Pa·s), a is the radius of the sphere (in meters), and v is the velocity (in m/s). Stokes' law expresses the resistance a sphere experiences as it moves through a fluid.
h = (2S cos θ) / (ρg)
h is the capillary rise (in meters), S is the surface tension (in N/m), θ is the contact angle, ρ is the liquid density, and g is gravitational acceleration. This formula relates surface tension to height of liquid rise in a capillary tube.
P_i - P_o = 4S/r
P_i and P_o are the internal and external pressures; S is the surface tension, and r is the radius of the bubble. This formula helps find excess pressure in a soap bubble.
ΔP = ρgh
ΔP denotes the change in pressure (in pascals) due to a height change h in a fluid of density ρ. It is essential for determining pressure differences in a fluid column.
v_t = (2a²(ρ - σ)g) / (9η)
v_t refers to the terminal velocity of a sphere falling through a fluid, a is the radius of the sphere, ρ is the sphere's density, σ is the fluid's density, g is gravitational acceleration, and η is the fluid's viscosity. This equation predicts the constant speed of the sphere in turbulent flow.
Equations
P = F / A (Pressure)
Defines pressure as force divided by area.
ρ = m / V (Density)
Describes the mass per unit volume of a fluid.
P = P₀ + ρgh (Hydrostatic Pressure)
Relates pressure at depth to gauge pressure.
A₁v₁ = A₂v₂ (Continuity Equation)
Ensures mass conservation in fluid dynamics.
Bernoulli's Equation: P₁ + (1/2)ρv₁² + ρgh₁ = P₂ + (1/2)ρv₂² + ρgh₂
Relates pressure, kinetic energy, and potential energy in flowing fluids.
F = 6πηav (Stokes' Law)
Gives the viscous drag force on a sphere in a fluid.
h = (2S cos θ) / (ρg)
Calculates capillary rise in fluids.
P_i - P_o = 4S/r (Excess Pressure in Bubble)
Finds the pressure inside a bubble due to surface tension.
ΔP = ρgh
Determines pressure difference related to a height change.
v_t = (2a²(ρ - σ)g) / (9η)
Predicts terminal velocity of a sphere in viscous fluid.
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