Fluids Study Guide

Level High SchoolReview time ~10 hours

Fluids are just materials that flow, and two ideas — pressure and energy conservation — explain nearly all of it. From floating ships to flying wings, this guide organizes the principles, the formulas, and the traps.

Key formulas

Bernoulli's Equation — P + ½ρv² + ρgh = constant

Along a streamline, pressure plus kinetic-energy density plus gravitational-energy density stays constant.

Kinetic Energy Formula — KE = ½mv²

Kinetic energy equals one-half times mass times velocity squared.

Pressure — P = F/A

Pressure equals force divided by the area it acts on.

Work Formula — W = Fd

Work equals force times distance moved in the direction of the force.

Topic checklist

Density

Use $\rho = m/V$ with consistent units.
Rank materials by density to predict floating versus sinking.
Explain why ice floats on water.

Pressure

Apply $P = F/A$ and hydrostatic $P = \rho gh$ .
Add atmospheric pressure for absolute pressure ( $P_{abs} = P_{atm} + \rho gh$ ).
Convert between pascals, atmospheres, and bar.

Buoyancy

State Archimedes' principle: buoyant force equals the weight of displaced fluid.
Set $F_b = mg$ for floating objects to find the submerged fraction.
Explain why ships float and submarines dive.

Continuity and Bernoulli

Apply continuity $A_1v_1 = A_2v_2$ to pipes and nozzles.
Use Bernoulli's equation along a streamline.
Explain lift, curveballs, and shower curtains with pressure differences.

Viscosity and drag

Distinguish laminar from turbulent flow.
Explain viscosity as internal friction between fluid layers.
Describe how drag grows with speed.

Surface tension and hydraulics

Explain surface tension as unbalanced molecular attraction at the surface.
Give examples: water striders, droplets, capillary rise.
Relate Pascal's principle to hydraulic lifts ( $F_1/A_1 = F_2/A_2$ ).

Common mistakes

Mistake: Mixing gauge and absolute pressure.

Fix:

Gauge pressure omits the atmosphere; absolute includes it. Tire gauges read gauge pressure, but gas laws need absolute. Add 101 kPa when the problem demands absolute.

Mistake: Setting buoyant force equal to the object's volume times fluid weight in all cases.

Fix:

Floating means $F_b$ equals the object's weight — always. The displaced volume adjusts itself until they match. Only a fully submerged object displaces its whole volume.

Mistake: Quoting 'faster means lower pressure' without conditions.

Fix:

Bernoulli compares points on the same streamline in steady, incompressible flow. Faster fluid means lower pressure only when elevation and the other terms are accounted for — write the full equation.

Mistake: Thinking pressure changes cause velocity changes in pipes (it is the reverse).

Fix:

Continuity says volume flow rate is constant ( $Av$ = constant), so squeezing a hose speeds the water up. The pressure drops as a consequence via Bernoulli — cause and effect run through velocity first.

Mistake: Confusing viscosity with density.

Fix:

Viscosity resists flow between layers; density is mass per volume. Honey is viscous but barely denser than water; mercury is dense but flows easily. The words measure different things.

Exam tips

Draw the fluid system and mark two points before writing Bernoulli's equation.
For buoyancy, write the force balance first: what equals what?
Watch units: $\rho gh$ needs density in kg/m³ and height in meters for pascals.
In manometer problems, equal horizontal levels in a continuous fluid share pressure.