Fluids, Pressure, and Hydraulics
Key Takeaways
- Pressure = Force / Area. The same force over a smaller area creates more pressure.
- Pascal's Principle: pressure applied to an enclosed fluid is transmitted equally in all directions.
- Hydraulic systems multiply force: a small piston pushing on fluid can create a large force at a bigger piston.
- Bernoulli's Principle: faster fluid flow = lower pressure. This is how airplane wings generate lift.
- Buoyancy: an object floats when it displaces fluid equal to its own weight (Archimedes' Principle).
Fluids, Pressure, and Hydraulics
Fluid mechanics questions appear regularly on the OAR MCT. These concepts are especially relevant for Navy and Marine Corps candidates since naval operations involve constant interaction with fluid systems.
Pressure
Definition
Pressure = Force / Area
P = F / A
| Variable | Unit |
|---|---|
| Pressure (P) | Pascals (Pa) = N/m², or PSI (lb/in²) |
| Force (F) | Newtons (N) or pounds (lb) |
| Area (A) | m² or in² |
Why Pressure Matters
The same force creates different effects depending on the area:
| Scenario | Force | Area | Pressure |
|---|---|---|---|
| Standing in boots | 800 N | 400 cm² | 2 N/cm² |
| Standing in high heels | 800 N | 2 cm² | 400 N/cm² |
| Nail point | 50 N | 0.01 cm² | 5,000 N/cm² |
This explains why:
- Knives cut because force is concentrated on a thin edge
- Wide tires spread weight for less ground pressure
- Snowshoes prevent sinking by distributing weight over a large area
Example: A 600 N crate sits on a 0.5 m × 0.4 m base. Pressure = 600 / (0.5 × 0.4) = 600 / 0.2 = 3,000 Pa
Atmospheric Pressure
Standard atmospheric pressure at sea level:
- 101,325 Pa (101.3 kPa)
- 14.7 PSI
- 1 atm
- 760 mmHg (millimeters of mercury)
Pressure increases with depth in a fluid: P = ρgh
Where ρ (rho) is fluid density, g is gravity, and h is depth.
Pascal's Principle
Pressure applied to an enclosed fluid is transmitted equally and undiminished to every point in the fluid and to the walls of the container.
Hydraulic Systems
This principle is the foundation of hydraulic systems.
F₁/A₁ = F₂/A₂
Or equivalently: F₂ = F₁ × (A₂/A₁)
| Component | Small Piston | Large Piston |
|---|---|---|
| Area | A₁ (small) | A₂ (large) |
| Force | F₁ (small) | F₂ (large) |
| Distance moved | d₁ (large) | d₂ (small) |
Example: A hydraulic jack has a small piston (area = 2 cm²) and a large piston (area = 50 cm²). If you push the small piston with 20 N, what force does the large piston exert?
F₂ = 20 × (50/2) = 20 × 25 = 500 N
The trade-off: you must push the small piston 25 times farther than the large piston moves.
Hydraulic Brake Systems
Car brakes use Pascal's Principle:
- You press the brake pedal (small force over small area)
- Hydraulic fluid transmits pressure to all brake calipers equally
- Large brake pistons squeeze the rotors with multiplied force
Bernoulli's Principle
In a flowing fluid, as speed increases, pressure decreases (and vice versa).
P₁ + 1/2ρv₁² + ρgh₁ = P₂ + 1/2ρv₂² + ρgh₂
For the OAR, the qualitative understanding is more important than the formula:
Fast flow = Low pressure | Slow flow = High pressure
| Application | How Bernoulli's Principle Applies |
|---|---|
| Airplane wing (airfoil) | Air moves faster over the curved top → lower pressure above → lift |
| Venturi tube | Narrow section → faster flow → lower pressure → suction effect |
| Curveball in baseball | Spinning ball creates faster flow on one side → curves toward low pressure |
| Shower curtain blows inward | Fast water flow creates low pressure inside → curtain pushed in |
| Chimney draft | Wind over chimney top → low pressure → draws smoke upward |
Continuity Equation
A₁v₁ = A₂v₂ (for incompressible fluids in a pipe)
Where A = cross-sectional area and v = flow velocity.
A narrower pipe → faster flow. Think of a garden hose: partially cover the opening and the water sprays faster.
Example: Water flows through a pipe at 2 m/s where the diameter is 10 cm. What is the speed where the diameter narrows to 5 cm?
- A₁ = π(5)² = 25π cm²
- A₂ = π(2.5)² = 6.25π cm²
- 25π × 2 = 6.25π × v₂
- v₂ = (25 × 2) / 6.25 = 8 m/s
Buoyancy and Archimedes' Principle
An object submerged in fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.
F_buoyant = ρ_fluid × g × V_displaced
Floating vs. Sinking
| Condition | Result |
|---|---|
| Object density < Fluid density | Floats (partially submerged) |
| Object density = Fluid density | Neutrally buoyant (hovers) |
| Object density > Fluid density | Sinks |
Why Ships Float
Steel is denser than water, so how do steel ships float? Because a ship's hull encloses a large volume of air, making the ship's average density less than water. The ship displaces a volume of water equal to its weight before becoming fully submerged.
Example: A block of wood (density = 600 kg/m³) is placed in water (density = 1,000 kg/m³). What fraction is submerged?
Fraction submerged = ρ_object / ρ_fluid = 600/1,000 = 0.6 (60% submerged)
Fluid Properties Summary
| Property | Definition | Key Relationship |
|---|---|---|
| Density | Mass per unit volume (ρ = m/V) | Determines floating vs. sinking |
| Viscosity | Resistance to flow | Higher viscosity = slower flow |
| Compressibility | How much volume changes under pressure | Liquids: nearly incompressible; Gases: compressible |
A hydraulic system has a small piston (area 5 cm²) and a large piston (area 100 cm²). If 30 N is applied to the small piston, what force does the large piston exert?
According to Bernoulli's Principle, what happens to pressure when fluid flows through a narrower pipe section?
A block with density 800 kg/m³ is placed in water (density 1,000 kg/m³). What percentage of the block is above the water surface?
Why does a sharp knife cut more easily than a dull knife?
How does an airplane wing generate lift according to Bernoulli's Principle?