Fluids Study Guide and Practice Questions

Definition of a Fluid

• Fluid: Any substance that flows, including liquids and gases.

Viscosity

• Definition: Measures a fluid's resistance to flow.
• Characteristics:
  • High viscosity = slow flowing
  • Low viscosity = fast flowing
  • Gases have ultra-low viscosity
• Factors Affecting Viscosity:
  1. Temperature
  2. Particle Size and Mass
  3. Particle Complexity
  4. Particle Properties (e.g., Polarity)

Mass vs Weight

• Mass:
  • Measures amount of matter in an object
  • Variable: "m"
  • Units: grams (g) or kilograms (kg)
  • Consistent regardless of location
• Weight:
  • Measures gravitational force on an object
  • Variable: "Fg"
  • Units: Newtons (N)
  • Varies with location
• Formulas:
  • ( Fg = m \times g )
  • ( m = \frac{Fg}{g} )
  • ( g = \frac{Fg}{m} )
  • Mass in formulas is in kg.

Density

• Definition: Ratio of mass to volume; indicates how tightly matter is packed.
• Comparisons:
  • Same mass: more dense object takes up less volume
  • Same volume: more dense object has more mass
• Units: g/ml or g/cm³
• Formulas:
  • ( D = \frac{m}{V} )
  • ( m = D \times V )
  • ( V = \frac{m}{D} )
  • Mass in formulas is in grams (g)
• Conversions:
  • Grams to kilograms: divide by 1000
  • Kilograms to grams: multiply by 1000

Buoyancy

• Definition: Lifting force experienced by objects in a fluid.
• Requires Gravity:
• Archimedes’ Principle:
  • "The buoyant force on an object is equal to the weight of the fluid it displaces."
• States of Buoyancy:
  1. Positive: buoyant force > object’s weight → rises
  2. Negative: buoyant force < object's weight → sinks
  3. Neutral: buoyant force = object's weight → stays in place
  4. Special Case: Partially submerged due to density ratio
• Floating Principle:
  • Less dense object than fluid will float; if denser, will sink.

Pressure

• Definition: Caused by force acting on an area.
• Formula:
  • ( P = \frac{F}{A} )
• Units: N/m² or Pascal (Pa)

Pascal’s Law

• Principle: Any force applied to an enclosed liquid is transmitted equally without reduction throughout the liquid.
• Hydraulic Systems:
  • Formula: ( F_1 \times \frac{A_2}{A_1} = F_2 )

Practice Problems

1. Weight on Mars: Calculate the weight of a 350kg box on Mars (( g = 3.7 , N/kg )).
2. Mass on Pluto: Determine the mass of an object weighing 2000N on Pluto (( g = 0.62 , N/kg )).
3. Density Calculation: Find the density of a material with a 400ml volume and 640g mass.
4. Volume of Copper: Calculate the volume of a 3000g copper block (( D = 8.96 , g/ml )).
5. Weight of Gold: Determine the weight of a 2500ml gold block (( D = 19.3 , g/ml )) on Earth (( g = 9.8 , N/kg )).
6. Buoyancy Check: Calculate the weight of water displaced by a 500ml block of aluminum (( D = 2.7 , g/ml )). Determine if it floats in water.