1. Compare One column of water has twice the diameter as another water column. If the pressure at the bottom
of each column is the same, how do the heights of the
two columns compare?
2. Explain why the height of the liquid column in a
barometer changes as atmospheric pressure changes.
3. Classify the following as fluids or solids: warm butter,
liquid nitrogen, paper, neon gas, ice.
4. Explain how the pressure at the bottom of a container
depends on the container shape and the fluid height.
5. Think Critically Explain how the diameter of a balloon
changes as it rises higher in the atmosphere.

1. The height of both water column are the same

2. When the atmospheric pressure increases, the height of the water column increases and vice versa

3. Warm butter = Fluid

Liquid nitrogen = Fluid

Paper = Solid

Neon gas = Fluid

Ice = Solid

4. The pressure and the fluid height are directly proportional and the pressure is independent of the shape of the container

5. Increase in altitude decreases the atmospheric pressure on the balloon and increases the diameter

Explanation:

1. The static pressure head, P, formula is P = ρ × h × g

Where;

ρ = The density of the water

h = The height of the water column

g = The acceleration due to gravity = Constant

Therefore, given that the static pressures, and the density of both waters are the same, P₁ = P₂, ρ₁ = ρ₂, we have;

P₁ = ρ₁ × h₁ × g = P₂ = ρ₂ × h₂ × g

ρ₁ × h₁ × g = ρ₂ × h₂ × g, where ρ₁ = ρ₂, we have;

h₁ = ρ₂ × h₂ × g/(ρ₁ × g) = ρ₂ × h₂ × g/(ρ₂ × g) = h₂

h₁ = h₂

Therefore, the height of both water column are equal

2. From P = ρ × h × g, the height of the liquid column in a barometer is directly proportional to the pressure, therefore, as the atmospheric pressure that supports the water column changes, the height of the water column changes

3. Warm butter = Fluid

Liquid nitrogen = Fluid

Paper = Solid

Neon gas = Fluid

Ice = Solid

4. The pressure at the bottom of the container, P = ρ × h × g, therefore, the pressure is directly proportional to the fluid height and is independent of the shape of the container

5. As a balloon rises in the atmosphere, the pressure of the atmosphere on the walls of the balloon reduces while the pressure of the gas in the balloon  remains relatively the same, therefore, the balloon expands and the diameter increases