Fluids and Solids

Question 1

Density

Answer 1

Density: ρ=m/V

Question 2

Archimedes’ principle

Answer 2

buoyant force on an object = weight of the fluid displaced by the object.

Question 3

Buoyancy

Answer 3

F_B = weight_displaced = m_displacedg =ρ_fluidV_submergedg

Question 4

When do objects float, sink, and rise upward in a fluid?

Answer 4

• Things float when FB = Weight.
• Things will rise upward when FB > Weight.
• Things will sink when FB < Weight.

Question 5

Pascal’s Law

Answer 5

if you apply pressure on a liquid, the pressure is transmitted equally to all parts of the liquid.

Question 6

Pressure in relation to depth

Answer 6

• P=ρgh
• P is pressure, ρ is the density of the fluid; g is the gravitational constant, h is the height from the surface, or depth that the object is submerged.

Question 7

Viscosity: Poiseuille flow

Answer 7

When a viscous fluid flows through a pipe, the flow has a front that is shaped like a parabola bulging outward.

Question 8

Continuity equation

Answer 8

A·v = constant, where v is linear flow rate (velocity).

Question 9

Concept of turbulence at high velocities

Answer 9

• Low velocity -> laminar flow.
• High velocity -> turbulent flow, forms eddies.

Question 10

Surface tension

Answer 10

• Surface tension gives the surface of a liquid the ability to support things that are very light.
• For example, insects can walk on water due to surface tension.
• Surface tension is due to the attraction between the molecules of the solvent.

Question 11

Bernoulli’s equation

Answer 11

P + ½ρv² + ρgh = constant

Question 12

Elastic properties (elementary properties) of solids

Answer 12

• Stress: the pressure exerted on an object. σ = stress = F/A.
• Strain: the deformation of the object in the direction of the applied force divided by the original length. ε = strain = ΔL/L0.

Question 13

Young’s Modulus

Answer 13

• Young’s modulus = stress / strain.
• Young’s modulus, the ratio between stress and strain, is constant until you reach the elastic limit, where things get permanently deformed.

Question 14

Elastic Limit

Answer 14

The maximum stress something can handle before it breaks or become permanently deformed.

Question 15

Thermal expansion coefficient

Answer 15

Things expand when temperature rises, and contract when temperature falls.

ΔL = αL₀ΔT

ΔL is the change in length, L₀ is the initial length, ΔT is the change in temperature, and α is the coefficient of linear expansion.

Question 16

Expansion for area and volume

Answer 16

ΔV = βV₀ΔT = 3αV₀ΔT

ΔA = γA₀ΔT = 2αA₀ΔT

Question 17

Shear

Answer 17

• Shear = stress / shear ratio.
• Shear ratio = ΔL/L₀.
• When ΔL is very small compared to L₀, Shear ratio is approximately the same as the shear angle.
• Shear angle = tan^-1ΔL/L. Note: ΔL and L are perpendicular to each other.