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 ).
Get link
Facebook
X
Pinterest
Email
Other Apps
Differential Analysis of Fluid Flow_A
Get link
Facebook
X
Pinterest
Email
Other Apps
-
Fluid Element Kinematics
We need to know inlet and outlet conditions ⇋ Integral or CV Analysis or No flow properties.
We need to follow fluid particles ⇋ Flow domain or Differential analysis.
Ques: How fluid flows (i.e. all four types of motion)?
All these motion take place all at a time because of difference in velocities (evidence: velocity profile in a pipe is look like parabolic i.e. velocity change).
OR
Pressure due to the fluid or wall friction changes.
Linear Motion & Deformation
Angular Motion & Deformation
For Pure rotation ⇋ Ý = 0 & Pure angular deformation ⇋ ω = 0.
The continuity equation reflects the fact that mass is conserved in any non-nuclear continuum mechanics analysis.
The equation is developed by adding up the rate at which mass is flowing in and out of a control volume, and setting the net in-flow equal to the rate of change of mass within it.
Change in the stream function is related to volume flowrate.
If lines of constant stream function plotted with provided the family of streamlines ⇋ help in visualization of flow pattern.
Velocity Potential Function
Velocity Potential Function⇋ consequence of irrotationality of flow field, 3D flow.
Stream Function⇋ consequence of mass conservation, 2D flow.
Basic or Elementary or Plane Potential Flows
Plane potential flows is defined as, "the inviscid, incompressible, irrotational, 2D flows".
For simplicity → only 2D plane flows will be considered.
A. Uniform Flow
It is defined as, "Flow in which streamlines are all straight and parallel, the magnitude of the velocity is constant".
B. Source Flow
It is defined as, "Fluid flows radially outward from a line (point) through origin perpendicular to x-y plane".
Streamlines are straight lines directed radially outward from a point.
Strength of source: m = 2πrVr.
C. Sink Flow
It is defined as, "Fluid flows radially inward from a point towards the origin (i.e. opposite to source flow".
Same as Source flow but opposite sign.
D. Free Vortex Flow
It is defined as, "streamlines are in the form of concentric circles".
Fluid particles do not rotate while revolving around the vortex center.
Strength of Vortex: K' = 2πrVӨ.
Tangential velocity varies inversely with the distance from the origin.
Method of Superposition
It is defined as, "the combination of basic velocity potential and stream functions to yield a streamline that corresponds to a particular body shape of interest which describe flow around the body".
Potential flows are governed by Laplace's equation, which is a linear partial differential equation.
1. Source & Sink Pair
2. Doublet
It is formed by combining a source and sink in a special way infinitely close to each other.
Uniform flow and source → flow past a half body.
Uniform flow and a Source and Sink pair → flow past a Rankine Oval.
3. Uniform Flow and Doublet
A doublet combine with a uniform flow in positive X-direction can be used to represent a flow around a stationary circular cylinder.
Pressure Distribution & Resultant Force on the Cylinder Surface
Pressure distribution on the cylinder surface is obtained from the Bernoulli equation by neglecting elevation differences.
These results indicate that both drag and lift are predicted by Potential Theory.
For a fixed cylinder in a uniform flow → Fx and Fy = 0.
From experience, there is a significant drag developed on a cylinder when it is placed in a moving fluid.
This discrepancy is known as D' Almbert's Paradox.
4. Uniform Flow, Doublet and Free Vortex
An additional potential flow can be developed by adding free vortex to the flow around a cylinder → Flow past a rotating cylinder.
This flow field type can be approximately created by placing a rotating cylinder in a uniform stream.
Because of viscosity, the fluid in contact with the rotating cylinder would rotate with the same velocity as the cylinder.
Pressure Distribution & Resultant Force on the Cylinder Surface
Pressure distribution on the cylinder surface is obtained from the Bernoulli equation by neglecting elevation differences.
For the rotating cylinder, no force in the direction of the uniform flow is developed → FX = 0.
Lift is developed equal to the product of fluid density, upstream velocity and circulation → Lift Force.
References:
Material from Class Lectures + Book named Fundamentals of Fluid Mechanics by Munson, Young & Okiishi's (8th Edition) + my knowledge.
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...
Moving Boundary Work: The expansion and compression work associated with a piston cylinder device in which boundary moves is called Moving Boundary Work. Area under the Process curve on a PV Diagram: From the above figure, the differential area is the product of pressure and differential volume. So the area under the Process curve is given by: The area under the Process cure on a PV Diagram is Moving Boundary Work. Moving Boundary Work in A constant Volume Process: Moving boundary work is given by: Moving Boundary Work for a Constant Pressure Process: Moving Boundary Work is given by: Moving Boundary Work for an Isothermal Process: A thermodynamic process in which temperature remains constant durine the heat transfer is called Isothermal Process. Moving Boundary Work is given by: Where; PV = mRT If temperature is constant,then PV = c P = c/V Moving Boundary Work for P...
Center of Gravity: It is defined as; The resultant weight of a system which passes through a single point is called Center of Gravity ( G ). Center of Mass: It is defined as; The point at which the whole mass of the system acts. The concept of center of mass is cleared from the video given below: Centroid of a Volume: Objects having three dimensions have the centroid which is its geometric centre. Centroid of an Area: Objects having two dimensions have the centroid which is its geometric centre. Centroid of a Line: Objects having linear dimensions have the centroid which is its geometric centre. Composite Bodies: A composite body consists of a series of connected simpler shaped Bodies which may be rectangular, triangular, semicircular, etc. References: www.youtube.com www.wikipedia.com http://web.aeromech.usyd.edu.au/statics/doc/friction/Friction1.htm From Book Engineering Mechanics sta...
Comments
Post a Comment
HI, we wI'll contact you later