Fluid Statics & Fluid Dynamics: NEB Class 12 Physics Guide

Curriculum boundary

Separate the fluid models in the Grade 12 scope

The CDC Grade 12 Physics page and secondary curriculum control the Nepal scope. This unit includes fluid pressure and hydrostatics, Pascal’s law, buoyancy/flotation, surface phenomena and moving-fluid ideas such as continuity, Bernoulli, viscosity and flow resistance at the stated level.

Prerequisites are density, pressure units, equilibrium, energy and algebra. Review physical quantities and units and work and energy. Do not mix equations before stating whether the fluid is static, ideal/incompressible/steady, or viscous.

Pressure and depth

A static fluid transmits normal stress

Pressure P=F⊥/A is scalar at a point and acts normal to a surface. SI unit Pa=N m⁻². In a uniform static liquid, pressure rises with depth: P=Psurface+ρgh. Points at the same horizontal level in the same connected stationary fluid share pressure, provided other imposed conditions match.

Absolute pressure is measured from vacuum; gauge pressure is relative to local atmospheric pressure. A manometer compares pressure using column-height differences. Container shape does not change pressure at a given depth, though total force depends on area.

Pascal’s principle states that a pressure change applied to enclosed fluid is transmitted undiminished. In an ideal hydraulic system F₁/A₁=F₂/A₂; larger output force comes with larger output-area displacement tradeoff so energy is not created. See OpenStax Pascal’s principle.

Archimedes and flotation

Buoyancy comes from pressure difference

Pressure on an immersed object’s lower surface is greater than on its upper surface, creating net upward buoyant force. Archimedes’ principle gives FB=ρfluid g Vdisplaced. The force exists whether an object floats, sinks or is held submerged.

For floating equilibrium, FB=weight, so the displaced-fluid weight equals object weight. Fraction submerged for a uniform floating object is approximately ρobject/ρfluid. A dense steel ship floats because its overall average density including enclosed air is less than water and it displaces sufficient volume.

Check the institutional Archimedes treatment. Apparent weight in a fluid equals true weight minus buoyant force when acceleration is zero.

Surface effects

Cohesion, adhesion and curvature affect liquids

Surface tension is force per unit length along a liquid surface, also interpretable as energy per unit area. Cohesive forces favour smaller surface area; adhesion to a solid helps determine contact angle and whether a liquid rises or falls in a capillary.

For a circular contact line, count the number of liquid surfaces correctly: a soap film has two surfaces. Capillary rise depends on surface tension, tube radius, contact angle, density and g. Narrower clean tubes show larger rise when wetting conditions are similar.

Mass conservation

Continuity connects area and average speed

Volume flow rate Q=dV/dt=Av for uniform average speed. For steady incompressible flow in one connected stream tube, A₁v₁=A₂v₂. Narrower cross-section requires greater speed. For compressible flow, mass-flow conservation uses ρAv.

The OpenStax flow-rate section links volume rate and speed. Continuity alone does not determine pressure; combine it with an appropriate momentum or energy model.

Ideal-flow energy

Bernoulli’s equation is an energy statement with conditions

Along a streamline for steady, incompressible, non-viscous flow without added/removed shaft work, P+½ρv²+ρgh is constant. Pressure, kinetic and gravitational terms are energy per unit volume. If height is constant and speed increases, static pressure decreases under these assumptions.

Do not use “fast fluid always has low pressure” as a universal slogan. Pumps, viscosity, turbulence, compressibility, changing streamlines and unsteady flow require additional terms or different models. State points 1 and 2 and keep heights referenced consistently.

See OpenStax Bernoulli’s equation for its energy basis.

Real-fluid resistance

Viscosity dissipates mechanical energy

Viscosity describes internal fluid friction. Laminar flow has orderly layers; turbulent flow contains mixing and eddies. Reynolds number compares inertial and viscous effects, but transition depends on geometry and disturbances, so quoted thresholds are guides rather than universal switches.

Stokes’ drag for a small sphere in slow laminar flow is Fd=6πηrv. Terminal speed occurs when net force becomes zero: weight, buoyancy and drag balance. Poiseuille flow through a long circular tube under laminar assumptions gives Q=ΔPπr⁴/(8ηL). The fourth-power radius dependence makes tube size extremely influential.

Use the OpenStax viscosity and Poiseuille section for model conditions and examples.

Problem method

Model → points → conservation → losses → check

1. Identify static, ideal moving or viscous fluid.
2. Draw surfaces/stream tube and label depths, areas and velocities.
3. Choose gauge or absolute pressure consistently.
4. Apply force equilibrium, continuity, Bernoulli or viscous law with conditions.
5. Keep density, area and pressure units coherent.
6. Check direction, bounds and limiting behaviour.

Common mistakes include using h as container height instead of vertical depth difference, equating pressure with force, forgetting displaced volume, applying continuity to unrelated flows, using Bernoulli across a pump/loss without modification and confusing radius with diameter.

For online or physical NEB tuition, call 9846662070. The MKS Education panel supports SAT/IELTS/PTE/DET and study-abroad pre-counselling after Grade 12.

Checked sources

References and related learning

• CDC Nepal: Physics Grade 12
• CDC Nepal: Secondary Level Curriculum
• OpenStax: Fluid Statics
• OpenStax: Pressure with Depth
• OpenStax: Archimedes’ Principle
• OpenStax: Flow Rate and Continuity
• OpenStax: Bernoulli’s Equation
• OpenStax: Viscosity and Poiseuille’s Law

Continue with the Fluid Study Guide and Practice Set. Curriculum and institutional pages were checked on 2 August 2026; follow current CDC, NEB and school notices if requirements change.

Model contrast

Use one water tank to separate three kinds of reasoning

In a closed stationary tank, compare pressure at two depths using hydrostatics. Open a small outlet and idealise a large reservoir: continuity and Bernoulli relate the falling surface, outlet speed and pressure. Feed the outlet through a long narrow tube: viscosity creates a pressure loss and Poiseuille-type resistance may matter if the flow is laminar. The physical apparatus is similar, but the model changes with motion, geometry and dissipation.

This contrast prevents the hydrostatic paradox from becoming a slogan: pressure at a depth is independent of container shape, yet the force on a wall also depends on area and pressure distribution. It also prevents Bernoulli from being used inside every pipe regardless of pump work or friction. Always ask what energy enters, leaves or becomes internal energy.