Padeepz E-Learning Materials MA8151 Engineering Mathematics 1 we have provided the sample materials in this page. If you like the sample and want to buy the full subject the procedure is also provided in this page.
Partial derivatives:-
A partial derivative of a function of several variables is the ordinary derivative with respect to one of the variables, when all the remaining variables are kept constant. Consider a function u=f(x,y). Here , u is the dependent variable and x & y are independent variables. The partial derivative of u=f(x,y) with respect to x is the ordinary derivative of u w.r.to x, keeping y constant. It is denoted by
Padeepz E-Learning Materials PH8151 Engineering Physics we have provided the sample materials in this page. If you like the sample and want to buy the full subject the procedure is also provided in this page.
Modulus of elasticity
Types of moduli of elasticity:
Based on the 3 types of strain, elastic modulli of solids are.
(i) young’s Modulus:
Within elastic limit, ratio of longitudinal stress to longitudinal strain
consider a wire, length – L
Area of cross section – a
One end is fixed at top and load is applied at the bottom. Force acting along the length of wire is `F’. Let – elongation in length of the wire due to force applied.
Longitudinal stress = F/A
(II) Bulk Modulus:
Within elastic limit, ratio of bulk stress to bulk stress.
Bulk Modulus (k) = Bulk stress / Bulk Strain
Consider a body of volume ‘v’ and area of cross section A let ‘F’ the force applied to the whole surface of the body. This results in the change in volume but no change in shape of the body. Let v he the change in volume.
Bulk modules is sometimes called in compressibility its reciprocal is compressibility =1/k
(iii)Rigidity Modulus
Within elastic limit, ratio of sharing stress to shearing strain
Consider cube ABCDEFGH . lower ABCD is fixed and force is applied 11l to surface EFGH. So the body is sheared by angle o . Let ‘L’ he the length of the cube and sL be the change in length of the upper surface
Shearing stress = F/A
Poisson’s Ratio:
When a body is subjected to a force, the deformation is not only in one direction but all along.
Ex: If a wire is stretched, besides undergo extension along the direction of force, it also undergoes contraction in perpendicular direction strain produced along the direction of force longitudinal strain
Similarly, strain produced in perpendicular direction is lateral strain
Within elastic limit, ratio, of lateral strain to the longitudinal strain is called poisson’s ratio ‘’
Let us consider a body which is subjected to an uniformly increasing stress Due to the application of stress, strain is developed If we plot a graph b/w stress & strain we get a curve and is called stress. Strain diagram
Itis found that the bodyobey’s Hooke’s law up to the region OA called elastic lang
As soon as the yieldpt‘B’ is crossed, the strain & rapidly than the stress
Atthis stage the body remains partly elastic and partly plastic which is represented by BC
Noweven if a small external face is applied, the body will take a new path CD and remains plastic called plastic law where D is the ultimate strength.
Afterthis, the body will not some to its Original state and the body acquires a permanent residual strain I and it breaks down at aptl/ called a breaking stress indicated by EF.
Padeepz E-Learning Materials CY8151 Engineering Chemistry we have provided the sample materials in this page. If you like the sample and want to buy the full subject the procedure is also provided in the Video.
Boiler Feed Water
The water fed into the boiler for the production of steam is called boiler feed water
REQUIREMENTS
It should be free from
Dissolved gases (O2,CO2,carbonic acid etc)
Suspended impurities, oil and turbidity
Dissolved salts, hardness causing substances and alkalinity
It should be zero hardness
If the water is untreated, it leads to some troubles in the boiler
Formation of deposits in steam boilers and heat exchangers (scale and sludge)
Priming and foaming ( carry over )
Caustic embrittlement
Boiler corrosion
Hi Padeepz.com is a place where we make Engineering Students to understand their subjects in an easy and in a effective way. Which leads to greater knowledge in the subject and Provide plenty of time spending in innovative ideas.
