Mechanical Properties of Fluids mind map

Mechanical Properties of Fluids: what the chapter covers

The main idea of each topic with its first key points. Open a branch above for everything, or read the full notes.

1. 1Chapter Overview

   Mechanical Properties of Fluids studies liquids and gases at rest and in motion. Fluids cannot sustain shear stress at rest, so they flow and exert pressure normally on surfaces. The chapter begins with pressure in fluids, hydrostatic pressure and Pascal's law, which explains hydraulic lift and hydraulic press. Moving fluids are described using streamline flow, turbulent flow, continuity equation and Bernoulli's principle. Real fluids show viscosity, leading to drag, terminal velocity and Reynolds number. At the liquid surface, molecular forces produce surface tension, surface energy, capillary rise or fall and excess pressure in drops and soap bubbles. For NEET, this chapter is formula-rich, application-based and highly scoring.

   • Pressure in a fluid at rest is the same in all directions at the same point.
   • Fluid pressure depends on depth, density and gravity, not on container shape.
   • In streamline flow through a narrow region, speed increases and pressure generally decreases.
   Read Chapter Overview notes

2. 2Pressure & Pascal's Law

   Pressure is the normal force acting per unit area. In a fluid at rest, pressure at a point acts equally in all directions and always normal to any surface. Hydrostatic pressure increases with depth because lower layers support the weight of fluid above them. At depth h below an open surface, pressure is P = P0 + ρgh, where P0 is atmospheric pressure. Pascal's law states that pressure applied to an enclosed incompressible fluid is transmitted equally and undiminished throughout the fluid. This explains hydraulic lift and hydraulic press, where a small force on a small piston produces a large force on a larger piston. The machine multiplies force, not energy.

   • Pressure is scalar although force is vector.
   • Fluid pressure at rest depends on depth, fluid density and gravity.
   • Pressure does not depend on container shape or base area alone.
   Read Pressure & Pascal's Law notes

3. 3Fluid Flow

   Fluid flow describes the motion of liquids and gases. In streamline flow, each fluid particle follows a smooth path, and the velocity of fluid at a point remains constant with time. In turbulent flow, the motion is irregular, chaotic and contains eddies. The equation of continuity is based on conservation of mass. For steady incompressible flow, the volume of fluid crossing every cross-section per second is the same, so A1v1 = A2v2. Thus, fluid moves faster through narrow sections and slower through wider sections. The volume flow rate is Q = Av. Ideal fluid assumptions include incompressible, non-viscous, steady and irrotational flow, which are important before applying Bernoulli's principle.

   • Continuity equation comes from conservation of mass.
   • For incompressible fluid, density remains constant.
   • If streamlines crossed, a fluid particle at one point would have two velocities, which is impossible.
   Read Fluid Flow notes

4. 4Bernoulli's Principle

   Bernoulli's principle is the conservation of mechanical energy for ideal fluid flow. For steady, incompressible, non-viscous flow along a streamline, the sum P + 1/2ρv² + ρgh remains constant. These terms represent pressure energy, kinetic energy and potential energy per unit volume. At the same height, when fluid speed increases, pressure decreases. This pressure-velocity relationship explains many applications: a venturimeter measures flow speed using pressure difference, airplane wings produce lift due to pressure difference, and atomizers and carburetors use fast air to reduce pressure and draw liquid into the air stream. NEET frequently asks direct formulas and conceptual applications.

   • Bernoulli's equation is applied along a streamline.
   • Pressure energy per unit volume is P.
   • Kinetic energy per unit volume is 1/2ρv².
   Read Bernoulli's Principle notes

5. 5Viscosity & Stokes' Law

   Viscosity is the internal friction of a fluid that opposes relative motion between its layers. A more viscous fluid, such as honey, flows slowly compared with water. The coefficient of viscosity, η, measures the viscous nature of a fluid. When a small spherical body moves slowly through a viscous fluid, it experiences viscous drag given by Stokes' law: F = 6πηrv. As a sphere falls through a fluid, its speed increases until weight is balanced by buoyant force and viscous drag. Then acceleration becomes zero and it moves with terminal velocity. Reynolds number predicts whether fluid flow is streamline or turbulent. These ideas are important in raindrops, sedimentation, blood flow and oil flow.

   • Viscosity arises due to relative motion between fluid layers.
   • Liquids generally become less viscous when temperature increases.
   • Gases generally become more viscous when temperature increases.
   Read Viscosity & Stokes' Law notes

6. 6Surface Tension & Capillarity

   Surface tension is the property of a liquid surface by which it behaves like a stretched elastic membrane. It arises because molecules at the surface experience unbalanced cohesive forces. Surface tension is defined as force per unit length or surface energy per unit area. It explains spherical drops, floating needles, soap bubbles and insects walking on water. The angle of contact decides whether a liquid wets a solid surface. In a narrow capillary tube, liquid may rise or fall depending on adhesive and cohesive forces. Water rises in glass because angle of contact is acute, while mercury falls because its angle is obtuse. Curved liquid surfaces create excess pressure inside drops and bubbles, which is very important for NEET.

   • Surface tension decreases with increase in temperature.
   • Soap solution has lower surface tension than pure water.
   • A liquid drop tends to be spherical to minimize surface area.
   Read Surface Tension & Capillarity notes