Mechanics And Fluids Flashcards
Newton’s first law
A body at rest or in constant motion remains in that state until acted upon by an external unopposed force
Mechanics
The study of objects at rest or in motion and the effects of forces on a body
Newton’s second law
An unopposed forces causes a mass to accelerate
ΣF= ma
Newton’s third law
Every force has an equal and opposite reaction
Two divisions of mechanics
Statics
Dynamics
In statics, ΣF….
ΣF= 0
Because a=0
Statics is the study of…
Of forces acting on a non-accelerating body
Dynamics is the study of…
Motion of a body, both in translation and rotation
So ΣF cant be 0
Types of loading
- Tension: pull apart
- Compression: push together
- Moment: rotation
- Shear: distort shape
Scalar
Only has magnitude
Vector
Has magnitude and direction
Can be broken into x and y components
Adding vectors
Cx= Ax+Bx Cy= Ay+By C= sqrt(Cx^2 + Cy^2)
Multiplying vectors
Can only be multiplied by a scalar
Changes the vector’s magnitude
Does NOT change the vector’s diction
No negative numbers for the test
Unit vectors
i has magnitude of 1 in x direction
j has magnitude of 1 in y direction
When a vector component is multiplied by i or j
Magnitude of vector component is unchanged
The direction of the vector com pone is defined as parallel to the x or y axis
ΣF= Fxi + Fyj
When drawing FBDs
- Forces are detached from ground and other bodies
- All external forces are indicated (weight is applied at center of gravity)
- Indicate magnitude and direction of known external forces
- Include dimensions
Reaction forces in rollers/rockers
Perpendicular to the roller/rocker
Reaction forces in pins
Have x and y components
Truss
A simple skeletal structure (made of triangles
In theory, the individual members of a simple true are only subject to…
Tension (pulling) and compression (pushing)
No bending forces
Why structures are built with triangles
- Pinned triangles are naturally rigid
- Joint strength becomes less critical
- High stiffness can be achieved for small amount of material used
- Ease of construction
Members in tension
Tension forces tend to pull the member apart
Member tends to “stretch”
More economical
Can be made lighter/thinner
Members in compression
Compressive forces tend to “squeeze” the member
Long slender members tend to buckle easily and can only carry smaller loads
Shorter members can carry higher compressive loads
Assumptions for static analysis of truss bridges
- ΣF at each joint (node) must equal zero
- Each element is a “two force” member.
Tension: ⬅️➖➡️
Compression: ➡️➖⬅️ - Joints are pinned and frictionless (pins will not support a moment)
- Forces can only be applied at joints (no bending)
- No deformation occurs to change dimensions
- External reactions are statically determinant, and supports are frictionless
Solving for trusses by method of joints
- Draw FBD and determine reactions at supports
- Locate joint with 2 members and draw FBD of that pin. Determine unknown forces at the joint
- Locate a member where forces in only 2 members is still unknown. Draw FBD and solve
- Repeat
Joints under special loading conditions:
Forces in opposite member interesting 2 straight lines at a joint are….
Equal
Joints under special loading conditions:
The forces in two opposite members are equal when….
A load is aligned with a third member.
The third member force is equal to the load (including zero load)
Joints under special loading conditions:
The forces in 2 members connected at a joint are equal if…
The members are aligned and zero otherwise
Why learn about joints under special loading conditions?
Simplifies truss analyses
What is fluid mechanics?
Sumptuary of fluids in motion
Two classes of fluids
Liquids
Gases
Unlike solids, fluids can’t…
Resist shear stress
Assume the shape of containers
Pressure
Force per area
P= F/A
Fluid exerts a force perpendicular to a surface
THERE IS NO PARALLEL COMPONENT THAT WOULD CAUSE A FLUID AT REST TO FLOW
Varies with depth
What often drives fluid flow
Differences in pressure (gradients)
Temperature
Measure of internal energy
Ideal gas law
PV= nRT
Density equals:
ρ= m/V ρ= n/V= P/RT
Specific weight
Weight per unit volume
γ= ρg
Archimedes’s Principle:
If an object is submerged, there is a…
Net force on the one because the pressures at the top and bottom of it are different
Buoyant force
The upward force on the same volume of fluid that the object displaces
FB= F2-F1= ρgA(h2-h1)
FB= ρgV
FB= mg
The net force on a submerged object is…
The difference between the buoyant force and gravitational force
ΣF= FB-Fg
If an object’s density is less than that of water, there will be…
An upward ΣF on it
It will rise until it is partially out of the water
For a floating object, the fraction that is submerged is given by….
The ratio of the object’s density to that of the given fluid
Why do helium balloons rise?
Archimedes’s principle
For fluids in motion, we will deal with…
Laminar flow (no turbulence)
Mass flow rate
The mass that passes a given point per unit time
Flow rates at any two points must be equal, as long as no fluid is added or taken away
FR= V/t= Av
Equation of continuity
Because flow rates at any two points must be equal, as long as no fluid is added or taken away
ρ1A1v1 = ρ2A2v2
Bernoulli’s equation
Because fluid can also change its height
P + 1/2ρv^2 + ρgy= constant
Tells us that as the speed (v) increases, the pressure (P) decreases
Drag
Is a function of pressure and friction
Fdrag= 1/2CDρAv^2
Acts in opposite direction to the motion of the object
Drag coefficient
CD= CD,pressure - CD,friction
Depends on shape
Lift
Acts at right angles to drag
Caused by pressure differential between top and bottom wing
