Fluid Mechanics Basics

Grade 11 · Science · Study Guide

Explore pressure, buoyancy, fluid flow, and Bernoulli's principle for liquids and gases at an advanced introductory level.

Fluid mechanics describes the behavior of liquids and gases at rest (fluid statics) and in motion (fluid dynamics). Pressure in a fluid is defined as force per unit area: P = F/A, with SI unit Pascal (Pa). In a static fluid, pressure increases with depth: P = P0 + ρgh, where ρ is fluid density, g is gravitational acceleration, and h is depth. This hydrostatic pressure acts equally in all directions at any given depth.

Archimedes' Principle states that any object submerged in a fluid experiences a buoyant force equal to the weight of fluid displaced: F_b = ρ_fluid · V_displaced · g. An object floats when this buoyant force equals its weight.

For moving fluids, the continuity equation expresses conservation of mass: A1v1 = A2v2 for an incompressible fluid in a pipe. Where the pipe narrows, fluid speeds up; where it widens, fluid slows down.

Bernoulli's equation, a statement of energy conservation for ideal fluids, states: P + ½ρv² + ρgh = constant along a streamline. It explains why faster-moving fluid exerts lower pressure — the principle behind aircraft lift, carburetors, and Venturi meters. Bernoulli's equation assumes steady, incompressible, non-viscous flow along streamlines.

Viscosity measures a fluid's resistance to flow. Real fluids lose energy to viscous friction, described by Poiseuille's Law for pipe flow.

Key terms

Hydrostatic Pressure
Pressure at a depth h in a fluid: P = P0 + ρgh; increases linearly with depth.
Archimedes' Principle
The buoyant force on a submerged object equals the weight of fluid it displaces: F_b = ρ_fluid·V_sub·g.
Continuity Equation
A1v1 = A2v2 for incompressible flow; fluid speed increases where the cross-section narrows.
Bernoulli's Equation
P + ½ρv² + ρgh = constant; relates pressure, speed, and height along a streamline for ideal fluids.
Viscosity
A fluid's internal resistance to flow; high-viscosity fluids (like honey) flow more slowly than low-viscosity ones.
Buoyancy
The upward force exerted by a fluid on a submerged or partially submerged object due to pressure differences.

Flashcards

Pressure
P = F/A; force per unit area; SI unit is the Pascal (Pa = N/m²).
Hydrostatic Pressure Formula
P = P0 + ρgh; pressure at depth h below the surface with surface pressure P0.
Pascal's Principle
Pressure applied to an enclosed fluid is transmitted equally and undiminished in all directions.
Continuity Equation
A1v1 = A2v2; for incompressible flow, flow rate is constant throughout a pipe.
Bernoulli's Equation
P + ½ρv² + ρgh = constant; conservation of energy along a streamline for ideal fluid flow.
Torricelli's Theorem
Speed of fluid exiting a hole at depth h below the free surface: v = √(2gh); derived from Bernoulli's equation.
Reynolds Number
Re = ρvL/μ; dimensionless ratio predicting laminar (Re < 2000) vs. turbulent (Re > 4000) flow.
Hydraulic Press
Uses Pascal's principle: F1/A1 = F2/A2; small force on small area creates large force on large area.

Questions

  1. A pipe narrows from a cross-section of 4 cm² to 1 cm². If water enters at 2 m/s, what is its speed in the narrow section?

    1. 0.5 m/s
    2. 2 m/s
    3. 8 m/s
    4. 16 m/s
    Show answer

    Answer: 8 m/s

    Continuity: A1v1 = A2v2. (4)(2) = (1)(v2). v2 = 8 m/s.

  2. According to Bernoulli's principle, faster-moving fluid exerts lower pressure on its surroundings.

    Show answer

    Answer: True

    Bernoulli's equation shows that higher velocity corresponds to lower pressure: P + ½ρv² = constant (at same height). Higher v → lower P.

  3. The buoyant force on an object equals the weight of fluid _____.

    Show answer

    Answer: displaced

    Archimedes' Principle: F_buoyant = weight of fluid displaced = ρ_fluid·V_displaced·g.

  4. An object with density 600 kg/m³ is placed in water (density 1000 kg/m³). What fraction of the object is submerged?

    1. 40%
    2. 60%
    3. 100%
    4. 0%
    Show answer

    Answer: 60%

    For floating equilibrium: ρ_object/ρ_fluid = fraction submerged. 600/1000 = 0.6 = 60% submerged.

  5. Pascal's principle states that pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid.

    Show answer

    Answer: True

    Pascal's principle: any pressure change applied to an enclosed fluid is transmitted undiminished to all parts of the fluid and the container walls. This is the principle behind hydraulic systems.

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