View Factor Orientation (or View factor or shape factor) plays an important role in radiation heat transfer. View factor is defined as, "fraction of radiation leaving surface 'i' and strike 'j' ". Summation Rule (View Factor) If there is are similar surfaces 'i' and 'j' , then: Blackbody Radiation Exchange Radiation Exchange between Opaque, Diffuse, Gray surfaces in an Enclosure 1. Opaque 2. Surfaces 3. Two surface enclosure Radiation Shield It is used to protect surfaces from radiation act like a reflective surface. References: Material from Class Lectures + Book named Fundamentals of Heat and Mass Transfer by Theodore L. Bergman + My knowledge. Photoshoped pics are developed. Some pics and GIF from Google. Videos from YouTube ( Engineering Sights ).
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Equilibrium of a Particle and Force System Resultants
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Equilibrium of a Particle
Equilibrium:
A particle is said to be in equilibrium if it remains at rest or moving with constant velocity and does not rotate about any axis.
This condition of rest or moving with constant velocity is also called Static Equilibrium.
Coplanar Force Systems:
If a particle is subjected to a system of coplanar forces that lie in the x-y plane then every forces can be resolved into its components.
Since, it is 2D so the equilibrium equations are:
Σ Fx = 0
Σ Fy = 0
3D Force System:
In case of three-dimensional force system, we can resolve the forces into their respective rectangular components.
So the equations of equilibrium are:
Σ Fx = 0
Σ Fy = 0
Σ Fz = 0
Force System Resultants
When a force is applied to a body it will produce a tendency of rotation of body about a point which us not on the line of action of force.
Moment of a Force (Scalar Formulation):
In this sense, the momen is considered as scalar and us calculated as:
Moment = (Force) × (Moment Arm)
M = Fd
Cross Product Formulation of Moment of A Force:
The moment of a force will be formulated using Cartesian vectors is given by:
Principle of Moment:
Principle of moment or Varignon's Theorem states that:
The moment of a force about a point is equal to the sum of the moments of the components of the force about that point.
This method is generally easier than finding the same moment using M = Fd.
Moment of a Force about a Specified Axis:
To determine the turning effect of a force, we can use scalar or vector analysis.
1. Scalar Analysis:
By using the scalar analysis of Turning effect of a force, we have:
M = Fd
2. Vector Analysis:
The vector analysis of moment of a force about an axis is given by:
Couple:
It is defined as:
Two parallel forces that have the same magnitude bit opposite directions and are separated by a distance (d).
Moment of Couple:
The moment produced by a couple is called Moment of a Couple.
We determine the moment of Couple of a system by the algebraic sum of moments acted on the object, which is given by:
M = Ma + Mb
Couple moment is a free vector, so it only depends on the position vector between the forces.
There are two analysis of formulating couple moment:
1. Scalar Formulation:
The moment of Couple by using scalar Formulation is given by :
M = Fd
2. Vector Formulation:
The moment of Couple by using vector Formulation is given by:
M = r × FΣ
Equivalent Couples:
If two couples produce a moment with the same magnitude and direction, then these two couples are equivalent.
Resultant Couple Moment:
Since, couple moments are vectors, their resultant can be determined by vector addition.
M = Σ(r × F)
Or
Resultant Force = ΣF
Resultant Moment = ΣM at origin + ΣM
Or
Resultant Force along x = ΣFx
Resultant Force along y = ΣFy
Resultant Moment at O = ΣMo + ΣM
Reduction of a Simple Distributed Loading:
A uniformly distributed load is a load that is distributed or spread across the whole region of an element. In other words, the magnitude of the load remains uniform throughout the whole element.
Magnitude of Resultant Force:
The Magnitude of resultant force Fr is equivalent to the sum of all the forces in the system, which is given by:
Location of Resultant Force:
The location of force or the geometric center or centroid of the area under the distributed loading is given by:
And, the location of centroid of area under distributive loading for different shapes are:
Projection: The term Projection is defined as: Presentation of an image or an object on a surface. The principles used to graphically represent 3-D objects and structures on 2-D media and it based on two variables: Line of Sight. Plane of Projection. Line of Sight & Plane of Projection: Line of sight is divided into 2 types: Parallel Projection Converging Projection & A plane of projection is an imaginary flat plane upon which the image created by the lines of sight is projected. Orthographic Projection: When the projectors are parallel to each other and perpendicular to the plane of projection. The lines pf sight of the observer create a view on the screen. The screen is referred to as the Plane of Projection (POP). The lines of sight are called Projection lines or projectors. Rules of Orthographic Projection: Edges that are parallel to a plane of projection appear as lines. Edges that are incl...
Types Of Lines And Its Uses: There are three types of types on the basis of thickness and they are: Visible Lines ↝ It represents features that can be seen in the current view. Hidden Lines ↝ It represents features that cannot be seen in the current view. Center Line ↝ It represents symmetry, path of motion, centers of circles,, axis of asymmetrical parts. Dimension and Extension Lines ↝ It indicates the sizes and location of features on a drawing. Placement Of Dimension Lines: Dimension should be outside the view. Dimension should be applied to one view. Dimension should be placed in a view that shows the distance in its true length. Dimension lines should be placed, in general 10 mm (1/2 in) away from the outlines from the view. Parallel lines should be placed uniformly. Values should be midway (auto centered) between the arrow heads, except when a center-line interferes. Dime...
Pressure: Pressure is defined as: ' Normal force per unit area of body'. There are different pressures which we described ahead: Atmospheric Pressure ⟺ Pressure exerted by atmosphere. Absolute Pressure ⟺ The actual pressure at a given point. It is calculated with respect to absolute zero pressure. Gage Pressure ⟺ It is difference between the absolute pressure and the local atmospheric pressure. Vacuum Pressure ⟺ Pressure below atmospheric pressure. Pressure At A Point In A Fluid: For the pressure at a point in fluid, consider a triangular area of fluid. Consider a free body diagram with in a fluid mass. The force and weight components along Z-axis is given by: So, pressure at a point of a fluid at rest or motion is independent of direction as long as there are no shearing stresses present. Types Of Forces: There are two types of forces which are described ahead: Body Forces ⟺...
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