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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Vectors
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Vectors:
It is defined as;
Quantity having magnitude and direction are called vectors and they are represented by arrow over the letters.
Types of Vectors:
Types of vectors are as follows:
1. Free Vectors:
Vector having magnitude and direction and can be applied at any point in the space is called Free vector.
2. Sliding Vectors:
Thsee vectors have a line of action in space but no particular point if application
3. Fixed Vectors:
Vectors having specific point of application are called fixed vectors.
Pallelogram Law of Vector Addition:
If two vectors ate considered to be the adjacent sides of a parallelogram, then the resultant of two vectors is given by drawing the diagonal between the vectors.
The formula used for the Parallelogram Law of Vector Addition is:
Resolution of Vectors:
It is defined as;
The converting of a vector into its rectangular components.
1. For 2-dimensional Space:
Now the rectangular componets of vector a are:
ax = a cosθi
ay = a sinθj
And, the rectangular components of vector b are:
bx = b cosαi
by = b sinαj
Now, the resultant X and Y comoments are:
Rx = a cosθi + b cosαi
Ry = a sinθj + b sinαj
And, the resultant vector and angle is given by:
R = √ Rx² + Ry²
ɸ = tan⁻¹ ( Rx / Ry )
2. For 3-dimensional Space:
Where,
Ax, Ay, Az are the projections of vector A
α, β, ɣ are direction cosines
Now, the vector form of vector A is given b:
Vector A = Axi + Ayj + Azk
The magnitude of resultant vector A is given by:
A = √ Ax² + Ay² + Az²
The respective angles are given by:
cosα = vector Ax / A
cosβ = vector Ay / A
cosɣ = vector Az / A
The unit vector is given by:
Unit vector Ua = cosα + cosβ + cosɣ
Or
Vector A = A × (unit vector Ua)
Vector A = Acosα + Acosβ + Acosɣ
And,
A = √ Ax² + Ay² + Az²
A = √ (Acosα)² + (Acosβ)² + (Acosɣ)²
A = A √ (cosα)² + (cosβ)² + (cosɣ)²
cosα² + cosβ² + cosɣ² = 1
Position Vector:
It is defined as;
Vector which specifies the position of point in space is called Position Vector.
TAPING CORRECTIONS There are two types of corrections depending upon the type of errors in tape due to the different conditions. 1. Systematic Errors : Slope Erroneous tape length Temperature Tension Sag 2. Random Errors : Slope Alignment Marking & Plumbing Temperature Tension & Sag 1. Temperature Correction It is necessary to apply this correction, since the length of a tape is increased as its temperature is raised, and consequently, the measured distance is too small. It is given by the formula, C t = 𝛼 (T m – T o )L Where, C t = the correction for temperature, in m. 𝛼 = the coefficient of thermal expansion. T m = the mean temperature during measurement. T o = the tempe...
Solid Mechanics OR Mechanics of Materials OR Strength of Materials: It is the study of mechanics of body i.e. forces and their effects on deformable solids under different loading conditions. Deformable Body Mechanics: It is the study of non-rigid solid structures which deform under load. Deformation/Distortion ⇾ change of shape and size OR have some relative displacement or rotation of particles. It happens when we apply combined load. Rigid Body Motion ⇾ Translation or rotation of particles but having constant distance between particles. Since deformation occur at particular load. Below this load, every body is considered as rigid body . Types of Load: Point Load ⇾ Load apply on a single point i.e. concentrated load. Uniformly Distributed Load (UDL) ⇾ Load remains uniform throughout an area of element like beam. Varying Distributed Load (VDL) ⇾ Load varies with length with constant rate. Moment ⇾ It measures the tend...
Strain Transformation Principal Strain and stresses can occur in the same directions. Material Properties Relation (Young, bulk Rigidity Modulus) ⇼ Hooke's Law General State of Strain ⇼ Є X , Є Y , Є Z and ૪ X , ૪ Y , ૪ Z . Stress (normal or shear)/ Strain (normal or shear) ⇼ vary with element orientation. Transformation equations for Plane strain derived from: Interpretation of Experimental measurements Represent in graphical form for plane strain (Mohr's Circle). Geometry and independent of material properties. Mohr's Circle It is defined as., " A graphical method for determining normal and shear Shear stresses without using the stress transformation equations " . While considering the circle CCW ⇼ Shear strain positive upward & Normal strain positive towards right. The construction of Mohr's circle (with normal and shear stresses are known) is quite easy which include following steps: Draw a set o...
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