Physics: Fluids

1. University of Zululand
April 25, 2023
Fluids and forces acting on it

2. Pressure varies with height
• For fluid at rest, all portions of a fluid should be in static equilibrium. That is parts of fluid
(particles consisting a fluid) must be at rest, otherwise fluid will flow from high pressure region to
lower pressure region.
• When the fluid surface is exposed or open to air/atmosphere, atmospheric pressure 𝑃0 = 𝑃𝑎𝑡𝑚 =
1.013 × 105
𝑃𝑎 exerts a force on fluid
• When immersing a volume of object in fluid, weight of it has gravitational force in a direction of
𝑃0 and fluid exerts forces on the faces of that object whose net resultant force is upward.
• Hence pressure of fluid varies with magnitude of height, 𝑃𝑖 = 𝑃0 + 𝜌𝑔ℎ𝑖
• Particles consisting a fluid and at same height (with reference to fluid surface) have the same
pressure 𝑃1 = 𝑃0 + 𝜌𝑔ℎ1, 𝑃2 = 𝑃0 + 𝜌𝑔ℎ2, 𝑃3 = 𝑃0 + 𝜌𝑔ℎ3 and so on

3. Newton’s 2nd law applies to fluid too. Forces acting on the block
immersed in a fluid shown on the left figure have resultant,
𝑃2𝐴 − 𝑃1𝐴 − 𝑀𝑔 = 𝑚𝑎 = 0 (Equilibrium case, at rest)
But 𝑀 = 𝜌𝑉 (fluid mass)
𝑃2𝐴 − 𝑃1𝐴 = 𝜌𝐴𝑔 𝑦1 − 𝑦2
𝑃2 = 𝑃1 + 𝜌𝑔 𝑦1 − 𝑦2 (pressure at bottom, 𝑦2)
• Therefore for any fluid open to the atmosphere or air, the
pressure at different height is given by
𝑃 = 𝑃0 + 𝜌𝑔ℎ (1)
• This implies fluid particles at height ℎ below the surface has a
pressure of 𝜌𝑔ℎ in addition to atmospheric pressure 𝑃0

4. Buoyant force and Archimedes principle
• What keeps object afloat in fluid?
• Object immersed in fluid such as water is partial supported by upward force known as buoyant
force.
• Buoyant force is a result of pressure difference, 𝐹𝐵 = (𝑃2−𝑃1)𝐴 surrounding the material
• Magnitude of buoyant force is independent of a material being immersed in fluid, but on the
mass of the displaced fluid, i.e., 𝐹𝐵 = 𝑀𝑔 = 𝑔 𝜌𝑉 𝑓𝑙𝑢𝑖𝑑