Fluids: Pressure, Pascal and Archimedes

Formulas (3)

• Pressure as force per area, and its units · Pressure
  $$p = \frac{F}{A}$$
• Pressure at a depth in a liquid (Stevin's law) · Pressure at depth h
  $$p = p_0 + \rho g h$$
• Pascal's principle and the hydraulic press · Hydraulic press
  $$\frac{F_1}{A_1} = \frac{F_2}{A_2} \qquad A_1 d_1 = A_2 d_2$$

Watch out for (4)

• Square millimetres are not a thousandth of a square metre
  → Pressure as force per area, and its units
• Doubling the pressure means doubling the absolute pressure
  → Pressure at a depth in a liquid (Stevin's law)
• A still liquid pushes perpendicular to the wall
  → Pressure at a depth in a liquid (Stevin's law)
• A hydraulic press multiplies force, not energy
  → Pascal's principle and the hydraulic press

Formulas (2)

• Archimedes' principle: the size of the upthrust · Upthrust
  $$F_B = \rho_{\text{fluid}}\, V_{\text{sub}}\, g$$
• Floating and sinking by comparing densities · Fraction submerged when floating
  $$\frac{V_{\text{sub}}}{V} = \frac{\rho_{\text{object}}}{\rho_{\text{liquid}}}$$

Watch out for (3)

• The upthrust uses the liquid's density
  → Archimedes' principle: the size of the upthrust
• A sunken object still feels upthrust
  → Floating and sinking by comparing densities
• For a floating object, the upthrust equals the weight in every liquid
  → Floating and sinking by comparing densities