Singapore H2 Physics Wiki

Fluid Forces and Resistive Motion

5 min read

Fluid Forces and Resistive Motion

Overview

Fluid Forces and Resistive Motion develops the parts of Forces involving liquids, gases, buoyancy, and motion through fluids.

This page focuses on:

  • pressure in fluids
  • hydrostatic pressure
  • atmospheric pressure and total pressure
  • upthrust
  • Archimedes’ principle
  • principle of floatation
  • drag / viscous resistive force
  • terminal velocity
  • worked examples
  • exam pitfalls

These ideas are important in mechanics, engineering, transport, and many real-world contexts.

Why It Matters

Fluid-force questions combine force balance, pressure ideas, and motion through fluids in a way that appears in many practical contexts.

Definition

Fluids can exert forces through pressure, buoyancy, and resistance to relative motion.

Key Representations

What is a Fluid?

A fluid is a substance that can flow and take the shape of its container.

Examples:

  • liquids (water, oil)
  • gases (air)

Fluids exert pressure on surfaces in contact with them.

Pressure

Pressure is a scalar quantity.

Defined as force per unit area:

where:

  • = pressure
  • = normal force on surface
  • = area

SI unit:

Key Ideas

  • Larger force gives larger pressure.
  • Smaller contact area gives larger pressure.
  • Pressure acts normal to surfaces.

Pressure in Fluids

A fluid at rest exerts pressure in all directions at a given point.

Pressure in a fluid increases with depth because deeper layers support more fluid above them.

Hydrostatic Pressure

For a liquid of density at depth :

where:

  • = density of fluid
  • = gravitational field strength
  • = vertical depth below surface

Important Notes

  • Depends on depth, not container shape.
  • Same depth in connected liquid gives same pressure.
  • Valid for static fluids.

Total Pressure Below Surface

If atmospheric pressure acts on the surface:

Often only pressure difference matters.

Why Pressure Increases With Depth

Greater depth means more fluid above the point.

More fluid weight produces greater force per unit area.

Hence pressure rises linearly with depth.

Upthrust

An immersed object experiences pressure on all sides.

Since pressure is greater lower down, the upward force on the bottom surface is larger than the downward force on the top surface.

This produces a resultant upward force called upthrust.

Symbol:

Archimedes’ Principle

The upthrust on a partially or fully immersed object equals the weight of fluid displaced.

where:

  • = fluid density
  • = volume of displaced fluid

This is one of the most important H2 results.

Floating and Sinking

Floating in Equilibrium

For a floating object:

where:

  • = upthrust
  • = weight of object

Hence:

Weight of object = weight of displaced fluid.

Sinking

If maximum possible upthrust is less than weight:

object sinks.

Rising

If:

object accelerates upward.

Principle of Floatation

A floating object displaces its own weight of fluid.

This explains why:

  • ships float
  • icebergs partly emerge
  • hydrometers work

Density and Floating

If Object Density < Fluid Density

Object can float.

If Object Density > Fluid Density

Object sinks when fully immersed.

If Equal

Neutral buoyancy possible.

Drag / Resistive Force

When an object moves through a fluid, the fluid exerts a resistive force opposing relative motion.

Common names:

  • drag
  • air resistance
  • water resistance
  • viscous force

Direction: opposite to velocity relative to fluid.

Factors Affecting Drag

Drag depends on:

  • speed
  • shape
  • surface roughness
  • frontal area
  • fluid density
  • fluid viscosity

Speed Dependence of Drag

At low speeds (laminar conditions), drag may be approximately proportional to speed:

At higher speeds, often:

In many exam questions, the relationship is given.

Terminal Velocity

When an object falls through a fluid:

  • weight acts downward
  • drag acts upward
  • upthrust may act upward

Initially:

  • speed small
  • drag small
  • acceleration downward large

As speed increases:

  • drag increases
  • resultant force decreases

Eventually:

So:

Acceleration becomes zero and speed becomes constant.

This constant speed is terminal velocity.

Motion Graph Ideas

Falling Object in Fluid

Velocity-Time

  • starts from zero
  • rises
  • levels off at terminal velocity

Acceleration-Time

  • starts near (if upthrust negligible)
  • decreases to zero

Resultant Force-Time

  • starts large downward
  • decreases to zero

Worked Examples

Example 1: Pressure at Depth

Water density:

Depth:

Then:

Example 2: Upthrust

A block displaces of water.

Example 3: Floating Object

Object weight:

Floating in water.

Then:

Example 4: Terminal Velocity

A skydiver reaches terminal speed.

Then:

(if upthrust negligible)

So resultant force is zero.

Common Exam Pitfalls

1. Using depth along slope

Use vertical depth in:

2. Forgetting pressure is scalar

Pressure has magnitude only.

3. Assuming heavier objects always sink

Density matters, not just mass.

4. Confusing upthrust with weight

They may be equal only in equilibrium.

5. Thinking terminal velocity means no forces

Forces still act, but resultant force is zero.

6. Using wrong displaced volume

Use volume of fluid displaced, not necessarily total object volume if floating partially.

7. Drag same direction as motion

Wrong. Drag opposes motion relative to fluid.

Summary

Core Equations

Pressure

Hydrostatic Pressure

Upthrust

Floating Equilibrium

Terminal Velocity

Big Ideas

  • pressure increases with depth
  • upthrust comes from pressure difference
  • floating depends on balance of forces
  • drag increases with speed
  • terminal velocity occurs when resultant force becomes zero

Related Links

Graph View

Backlinks