Fluids and Solids

Question 1

Specific Gravity

Answer 1

• Specific gravity of a material is defined as the ratio of its density to the density of water at 4 ^oC
  
  • Also known as relative density

Question 2

Pascal’s Principle

P_total

Answer 2

• States that pressure applied to an enclosed fluid is transmitted equally throughout the fluid and to the walls of the fluid’s container
• P₁ - P₂ = ρ(y₂ - y₁)g
• P_total = P_atm + ρgh

Question 3

Archimede’s Principle

Answer 3

• States that the buoyant force acting upon an object is equal to the weight of the fluid it displaces
• B = (ρ_fluid)(V_{fluid displaced})(g)

Question 4

Floating Object

Answer 4

• W_object = B
  
  • (ρ_object)(V_object)(g) = (ρ_fluid)(V_{fluiddisplaced})(g)
  • (ρ_object)(V_object) = (ρ_fluid)(V_{fluid displaced})
  • (V_{fluid displaced})/(V_object) = (ρ_object)/(ρ_fluid) < 1
  • ρ_fluid > ρ_object
• Relative densities = % submerged

Question 5

Sunken Object

Answer 5

• B = apparent weight loss
  
  • W_object = B + N_object
    
    • Object underwater seems lighter
  • W/B = (ρ_object)/(ρ_fluid)
• Relative densities = W to B ratio = specific gravity of object if in water

Question 6

Surface Tension

Answer 6

• The force associated with this tendancy of the surface of a liquid to pull inward and shrink in area is known as the surface tension
• If a membrane stretches, the surface tension of the membrane decreases

Question 7

Viscosity

Answer 7

• The viscosity (η) of a fluid defines the friction within fluids
• The greater the viscosity, the slower the rate of flow
• Increasing temperature generally decreases viscosity

Question 8

Flow Rate

Answer 8

• Fluid flows fastest at the center of a pipe
• Flow rate (Q) is the volume V of a fluid that passes through a pipe per unit of time t

Question 9

Poiseuille’s Principle

Answer 9

• Q = ((πr⁴)(P₁- P₂))/(8ηL)
  
  • If the radius of a pipe is doubled, the flow rate increases by a factor of 16

Question 10

Continuity Equation

Answer 10

• Q = A₁v₁ = A₂v₂

Question 11

Bernoulli’s Equation

Answer 11

• Fluids flow from a region of high pressure to low pressure
• P₁ - P₂ = ρ/2(v₂² - v₁²) + ρg(y₂ - y₁)
• Simplified form
  
  • k = P_{against inner walls} + ρ/2(v)² + ρgh

Question 12

Bernoulli’s Equation Meaning

Answer 12

• As a fluid’s velocity increases, it’s pressure against an inner wall decreases
• Fluids want to move from an area of higher pressure to lower pressure
  
  • Explains the lift generated by airfoils

Question 13

Stress and Strain

Answer 13

• Stress (σ) refers to the force per unit area that causes deformation in an object
  
  • σ = F/A
• Strain (ε) refers to the deformation that results from the applied stres
  
  • ε = ΔL/L

Question 14

Young’s Modulus (Modulus of Elasticity)

Answer 14

• Y = E = stress/strain = σ/ε = (F/A)/(ΔL/L) = (FL)/(AΔL)
• Young’s modulus (Y) is the proportionality constant that relates the stress to the strain

Question 15

Bulk Modulus

Answer 15

• Bulk modulus (B) of an object relates how much the volume of a solid object changes as the pressure surrounding it changes
• B = (-ΔP)/(ΔV/V₀)
• Involves forces that are perpendicular to the surface of the object’s walls

Question 16

Shear

Answer 16

• Shear refers to the deformation resulting from forces acting parallel to the object’s walls