Chapter 5: Fluids and Solids Flashcards
Fluid
Ability to flow and conform to the shape of its container; liquids and gases
Solid
Does not flow; rigidity helps it retain a shape independent of that of any container
Common characteristics of fluids and solids
Both can exert forces perpendicular to their surface, only solids can withstand shear (tangential forces)
Density
- scalar quantity
- (rho) = m/V
- units = kg/m^3
Calculating weight using density
W = mg m = (rho)V W = (rho)Vg
Specific gravity
Ratio of the density of a substance to the density of water; density of H2O = 1000 kg/m^3 = 1g/cm^3
- if specific gravity > 1, substance more dense than water
- if specific gravity < 1, substance less dense than water
Pressure
P = F(N)/A
- unit = Pascal (1 Pa = 1 N/m^2)
- other units: 1.013 x 10^5 Pa = 1 atm = 760 torr = 760 mm Hg
- scalar quantity
Absolute pressure
- the total pressure that is exerted on an object that is submerged in a fluid
P = P(0) + (rho)gh
Gauge pressure
- the difference between absolute and atmospheric pressure; the pressure in a closed space above atmospheric pressure
P(g) = P - P(atm) = [P(0) + (rho)gh] - P(atm)
Hydrostatics
the study of fluids at rest and the forces and pressures associated with standing fluids
Pascal’s principle
For fluids that are incompressible, when a change of pressure is applied to an enclosed fluid, that pressure change will be transmitted undiminished to every portion of the fluid and to the walls of the containing vessel
P = F(1)/A(1) = F(2)/A(2)
F(2) = F(1) [A(2)/A(1)]
V = A(1)d(1) = A(2)d(2)
d(2) = d(1) [A(1)/A(2)]
W = P∆V = F(1)/A(1) [A(1)d(1) = F(2)/A(2) [A(2)d(2)]
W = F(1)d(1) = F(2)d(2)
Archimedes principle
A body wholly or partially immersed in a fluid will be buoyed up by a force equal to the weight of the fluid that displaces it
- force directed upward = buoyant force
F(buoy) = V(fluid displaced)[rho(fluid)]g = V(object submerged)[rho(fluid)]g
- an object will float, no matter what it is made of and no matter how much mass it has, if its average density is less than or equal to the density of the fluid into which it is placed; an object will sink if its average density is greater than the density of fluid displaced
Molecular forces in liquids
Surface tension = causes liquid surface to form a thin, but strong, layer, results from cohesion
Cohesion = attractive force that a molecule of liquid feels toward other molecules of the liquid
Adhesion = attractive force that a molecule of liquid feels toward the molecules of some other substance
Hydrodynamics
the study of fluids in motion
Viscosity
The resistance of a fluid to flow; fluid friction
- ideal fluids have no viscosity
Laminar and turbulent flow
- Laminar flow = smooth and orderly, imagine concentric layers of fluid that flow parallel to each other
- Turbulent flow = rough and disorderly; causes the formation of eddies; can arise when the velocity of the fluid exceeds a certain critical velocity [v(c)]
v(c) = N(R) (eta) / [(rho)D]
Streamlines
- representations of the molecular movement
- indicate the pathway followed by tiny fluid elements as they move
Volumetric flow rate for changing cross-sectional area
- volumetric flow rate (ie. units of volume per units of time) is constant for a closed system and is independent of changes in cross-sectional area
Linear velocity
- units = m/s
- measure of the linear displacement of a fluid particle in a given amount of time
Continuity equation
v(1)A(1) = v(2)A(2) = constant
- fluids will flow more quickly through narrow passages and more slowly through wider ones
Bernouilli’s Equation
- Fluids have higher velocities through narrower tubes
P(1) + [(rho)v(1)^2/2] + (rho)gy(1) = P(2) + [(rho)v(2)^2/2] + (rho)gy(2) = constant
- dynamic pressure = pressure associated with the movement of the fluid = (rho)v(1)^2/2 and (rho)v(2)^2/2
- static pressure = P + (rho)gy(1) and P + (rho)gy(2)
- for an incompressible fluid not experiencing friction forces, the sum of the static pressure and dynamic pressure will be constant within a closed container
Young’s modulus
- When a stretching (tensile) or pushing (compression) force is exerted against an object, the object will experience a change in length
- applied pressure = stress
- change in length per unit length = strain
Y = (F/A) ÷ (∆L/L)
Shear modulus
- If a force is applied parallel to an object’s surface, the object will experience a shape change known as a shear; causes a lateral shift in the direction of the force
S = (F/A) ÷ (x/h)
Bulk modulus
- the degree to which a material will experience a change in its volume in relation to an applied pressure
- Solids and liquids have large bulk moduli, gases have relatively small bulk moduliB = (F/A) ÷ (∆V/V)
- Speed of sound is proportional to the square of the root of the bulk modulus, sound will travel fastest through solids and slowest through gases
