8.1 Internal Structure and Density
A fluid is any substance that can flow and alter its shape to match its container. In physics, this definition applies to both liquids and gases. Because fluids don't have a fixed shape, it's often more useful to talk about their mass in terms of how tightly packed it is, rather than total mass.
Density (ρ): The amount of mass contained in a given volume of a substance. It is an intrinsic property of a material.
Density Formula
- ρ (rho) = Density (kg/m3)
- m = Mass (kg)
- V = Volume (m3)
🎯 Common Reference Point: The density of pure water is widely used as a standard benchmark and is exactly 1,000 kg/m3.
8.2 Pressure
When a fluid is at rest, it exerts a force perpendicular to any surface it touches. Pressure is the macroscopic measurement of those microscopic particle collisions spread over an area.
General Pressure
Pressure is defined as Force divided by Area. The unit is the Pascal (Pa), which equals 1 N/m2.
Hydrostatic Pressure
The pressure at a depth h in a static fluid depends on the fluid's density and the gravity pulling it down.
In the hydrostatic pressure equation, P0 represents the pressure at the surface of the fluid (often atmospheric pressure, which is roughly 1.01 × 105 Pa).
⚠️ Depth, not Shape:
Fluid pressure depends ONLY on depth (h), not on the shape or total volume of the container. A diver 10 meters deep in a swimming pool experiences the exact same pressure as a diver 10 meters deep in the ocean!
8.3 Fluids and Newton's Laws
Because pressure increases with depth, the pressure pushing up on the bottom of a submerged object is always greater than the pressure pushing down on the top of it. This pressure difference results in an upward net force called the Buoyant Force.
Archimedes' Principle: The buoyant force exerted on an object fully or partially submerged in a fluid is equal to the weight of the fluid that the object displaces.
Buoyant Force Equation
- FB = Buoyant Force (N)
- ρfluid = Density of the fluid (not the object!)
- Vdisp = Volume of fluid displaced (m3)
If an object is floating in equilibrium, then by Newton's First Law, the upward Buoyant Force perfectly balances the downward Force of Gravity (FB = mg).
8.4 Fluids and Conservation Laws
When fluids begin to move, we transition from hydrostatics to fluid dynamics. In AP Physics 1, we assume fluids are "ideal"—meaning they are incompressible (constant density) and non-viscous (no internal friction).
The Continuity Equation (Conservation of Mass)
Because the fluid is incompressible, the volume of fluid entering a pipe per second must equal the volume of fluid exiting the pipe per second. Therefore, when a pipe narrows, the fluid must speed up.
Bernoulli's Principle (Conservation of Energy)
Bernoulli's equation is a statement of the conservation of energy applied to a moving fluid. It relates the pressure, flow speed, and height of a fluid at two points along a streamline.
Crucial Insight: The Venturi Effect
If a pipe remains perfectly horizontal (y1 = y2), those terms cancel out of Bernoulli's equation. If the pipe narrows, the fluid speeds up (v2 > v1). To keep the total energy constant, the pressure must drop. Faster moving fluids exert less lateral pressure!
Unit 8 Key Takeaways
Density is mass per unit volume (ρ = m/V).
Absolute pressure inside a fluid increases linearly with depth (P = P0 + ρgh).
Buoyant force equals the weight of the displaced fluid (Archimedes' Principle).
When a floating object is in equilibrium, Buoyant Force perfectly equals Gravity.
The Continuity Equation states that fluid flows faster through narrower sections.
Bernoulli's Principle shows that an increase in fluid speed results in a decrease in pressure.
End of Unit 8 Study Guide.