Lesson 1: How Does Pressure Change With Depth?

1. What is the fundamental difference between a solid and a fluid?

Unlike solids which keep their shape, a fluid (which includes liquids and gases) is defined by its ability to flow and adapt to take the shape of whatever container it is in.

2. Why is pressure (P = F/A) considered a scalar quantity if force is a vector?

This is a common point of confusion. Pressure is a scalar because we only calculate it using the magnitude of the force acting perpendicular (normal) to the surface, ignoring direction. Physically, in a fluid, the force acts perpendicular to any surface it touches, regardless of orientation, so assigning a single direction to pressure itself is meaningless.

3. Does the shape of the container affect the pressure at the bottom?

No. The pressure at any specific depth depends only on that depth (h), gravity (g), and the fluid density (ρ). It has no relation to the container's shape or horizontal width.

4. What is the difference between "absolute pressure" and "gauge pressure"?

Absolute pressure is the total pressure at a point, which includes the atmospheric pressure acting on the fluid's surface. Gauge pressure is the pressure reading relative to the atmosphere; it is calculated by subtracting atmospheric pressure from the absolute pressure (p_gauge = p_absolute - p₀).

5. How does density differ between liquids and gases?

Gases are compressible, meaning their density changes significantly when you increase pressure because you are packing mass into a smaller space. Liquids are essentially incompressible; their density stays nearly constant even if you crank up the pressure.

Lesson 2: How do You Calculate Pressure Using a Manometer? & How Does a Mercury Barometer Work?

6. How does a mercury barometer actually measure air pressure?

It uses a long glass tube filled with mercury inverted into a reservoir. Atmospheric pressure pushes down on the reservoir, which supports the weight of the mercury column in the tube. The height (h) of this column tells us the atmospheric pressure using the formula p₀ = ρgh.

7. Does the width of the tube affect the reading in a barometer?

No. For a given pressure, the height of the mercury column is not affected by the cross-sectional area of the tube. The area does not appear in the final expression for pressure.

8. When I suck on a straw, am I pulling the liquid up?

No. When you suck on a straw, you expand your lungs to reduce the pressure in your mouth below atmospheric pressure. The higher outside atmospheric pressure then pushes the liquid up into the straw.

9. How do I use a U-tube manometer to find the pressure of a gas?

Connect one end of the U-tube to the gas container and leave the other open to the atmosphere. The gauge pressure of the gas is equal to the pressure difference caused by the height of the liquid column: p_g = ρgh.

10. Why do we ignore the space at the top of a mercury barometer?

That space is a near-vacuum containing only a tiny amount of mercury vapor. Its pressure is negligible compared to atmospheric pressure, so we treat it as zero (p₂ = 0) for practical calculations.

Lesson 3: Why is Pressure Equal Throughout a Fluid in Pascal’s Law?

11. What exactly does Pascal's Law state?

Pascal's Law states that a change in pressure applied to an enclosed, incompressible fluid is transmitted to every portion of the fluid and to the walls of its container.

12. How does a hydraulic lift allow me to lift a heavy car with a small force?

Because pressure is transmitted equally, a small force (F₁) on a small piston (A₁) creates a pressure that acts on a much larger piston (A₂). Since Force equals Pressure times Area, the larger area results in a much larger upward force (F₂ = F₁ × [A₂/A₁]).

13. Do hydraulic lifts create "free" energy?

No. While force is multiplied, energy is not. The volume of fluid moved is constant, so the small piston must move a large distance (d₁) to lift the heavy piston a small distance (d₂). The work input (F₁d₁) exactly equals the work output (F₂d₂).

Lesson 4:  Archimedes’ Principle: Why Objects Float or Sink

15. Why does a massive steel ship float?

It floats because of Archimedes' principle. A ship floats if its weight is less than the buoyant push of the water it displaces. At equilibrium, the weight of the water displaced by the ship is exactly equal to the ship's own weight.

16. Does the buoyant force depend on the mass of the object submerged?

No, this is a major misconception. The buoyant force depends only on the weight of the fluid displaced by the body, not the mass of the body itself.

17. How do I calculate the buoyant force if an object is only partially submerged?

If a body is partially immersed (e.g., 40% submerged), only that submerged portion counts toward the displaced volume. The buoyant force equals the weight of that specific volume of displaced fluid.

18. What is the condition for an object to sink?

An object sinks if the downward gravitational force (its weight) is greater than the magnitude of the upward buoyant force.

19. Why does a block of wood eventually stop sinking and start floating?

As the block sinks, it displaces more water, increasing the buoyant force. It stops sinking when the buoyant force grows large enough to exactly balance the block's weight.

20. What is the source of the buoyant force?

It comes from the pressure difference in the fluid. Pressure increases with depth, so the upward force on the bottom of an object is always greater than the downward force on its top.

Lesson 5: Bernoulli’s Principle (+ How does the Continuity Equation Relate to Bernoulli’s Equation)?

21. Why does pressure drop when fluid speed increases? Shouldn't it push harder?

If the pressure were higher at the faster point, it would push back against the flow and slow it down. The only way for fluid to speed up (accelerate) is if it moves from high pressure to low pressure. Thus, higher speed must correspond to lower pressure.

22. What are the three strict conditions for using Bernoulli's equation?

1. The flow must be steady (no sudden changes).
2. The fluid must have little viscosity (friction is ignored).
3. The fluid must be incompressible (constant density).
   

23. How is pressure considered a form of "energy" in Bernoulli's equation?

Pressure represents flow work per unit volume. It is the work done by the surrounding fluid to move a volume of fluid into or out of a region. Pressure has the same units as Energy divided by Volume (Joules per cubic meter).

24. What is the Continuity Equation?

It states that for an incompressible fluid, the volume flow rate is constant throughout a tube (A₁v₁ = A₂v₂). Whatever volume goes in one end must come out the other.

25. How do height changes affect fluid pressure according to Bernoulli?

Bernoulli's equation shows that pressure, speed, and height trade energy to keep a balance. Even if speed is constant, if a fluid moves up to a higher height against gravity, its pressure must drop to conserve energy.