Average || Important Formulas and Shortcuts of Average

          Dear readers, we all know that speed and accuracy in calculation is much needed for Quantitative Aptitude section of various competitive exams and if we know enough Short Tricks in Quantitative Section, we will surely score better in the section. So, let us make it easy for all of you through these Simple and Easy tricks on Average which will not only make quantitative questions easy but  also save our time. The tricks will be helpful for the upcoming Indian RRB Exam , SSC CGL Exam and much more.

What is Average?

          Average is obtained by adding several quantities together and then dividing this total by the number of quantities given. 

The main term of average is equal distribution of a value among all which may distribute persons or things.

Here is average based some fact and formula and some average shortcut tricks examples.

Formula:

· Average = (Sum of observations / Number of observations).

Find the Average Speed

· Average Speed = (Total Distance Covered/Total Time Taken).

· If a person travels a distance at a speed of x km/hr and the same distance at a speed of y km/hr then the average speed during the whole journey is given by-   

· If a person covers A km’s at x km/hr and B km’s at y km/hr and C km’s at z km/hr, then the average speed in covering the whole distance is- 

· If value of each term increases/decreases by ‘x’, then the average of the group also increases/decreases by ‘x’.

· There are two batches A and B in a class. If we have to find the average of the whole class use the formula:
Batch A: Number of students = a
                  Average of batch A = x
Batch B: Number of Students = b
                  Average of batch B = y

Average of whole class (Batch 1 and Batch 2) = (ax + by)/(a + b)

When a person leaves the group and another person joins the group in place of that person then-

· If the average age is increased,
Age of new person = Age of separated person + (Increase in average × total number of persons)

· If the average age is decreased,
Age of new person = Age of separated person – (Decrease in average × total number of persons)

When a person joins the group 

In case of increase in average age

· Age of new member = Previous average + (Increase in average × Number of members including new member)

In case of decrease in average age

· Age of new member = Previous average – (Decrease in average × Number of members including new member)

If the numbers are in Arithmetic Progression there are two cases

· when the number of terms is odd the average will be the middle term.

· when the number of terms is even then the average will be the average of two middle terms.

PROBLEMS ON AVERAGE - 1

Suction couch roll

          Couch roll (also known as “cooch”) is used in paper machine to remove water by application of vacuum. It acts as the last “wrap” where the wet web leaves the forming wire (wire part) and enter into the wet-press section (press part). On the surface of the couch roll we found rows of small holes to suck the water. Inside the roll baffles (long and end strips) are present. These baffles direct the vacuum towards the portion of the roll where the wet web of paper is on the fabric. Below of the long baffle strips air tubes are present for strip movement. Below the end baffle strips springs are present to seal the roll for vacuum suction creation. In the vacuum box one shower will present, it cools the rubber material on the roll. In vacuum boxes if we increase the vacuum we need more power to drive the forming fabric. But in couch roll if we applied too high vacuum it produces visible suction-hole “shadows” due to the movement of fines within the sheet.

Is it necessary to Align A Flexible Coupling?

          When I started my career as a maintenance engineer i got a doubt, is it necessary to align flexible coupling too?? we are using flexible coupling instead of fixed or rigid couplings because they don't have to be aligned??.

Later I read some articles and found some useful information. Today I wanna share this information with you people.

Courtecy : T B Woods Inc

For every coupling its manufacture give some common value of alignment specification:

According to T.B Woods Sureflex Coupling (with an 8je insert) 

--> Cost : about $XXX per sleeve or insert

--> Maximum  RPM : 4500

--> Parallel Misalignment : 0.020 in

--> Angular Misalignment : 0.094 in (about 0.012"/inch)

          Based on these manufactures recommendations the coupling can bear or tolerate some sort of misalignment. and also the insert (i.e rubber) is inexpensive then why we have to go precision alignment??

          Because we are aligning shafts -- we are not aligning couplings. The coupling sleeve or Insert that we use can tolerate that misalignment but the bearings on the shafts, oil seals, gears and also shafts can't tolerate.

Sometimes coupling will bend, but also it resists bending, for this it need some good amount of energy to oppose that force. That enegy is produced within itself by:

1) Increased heat due to friction

2) Increase in load on bearings, shafts, and seals.

          So finally i got to an conclusion, "is it necessary to align a flexible coupling?"- we should not worry about it but aligning the shafts to precision alignment is necessary. because, by this we will increase the machine life,  decrease vibrations, reduce energy consumption and also the couplings life. 

ALIGNMENT CONDITIONS

In general there are 4 alignment conditions:

           1) Perfect alignment

           2) Parallel or offset misalignment

           3) Angular or Face misalignment

           4) Skewed or combination misalignment (i.e., offset and parallel)

PERFECT ALIGNMENT :

          When the two shafts are perfectly aligned they will be colinear and operate as a solid shaft when coupled. Without performing alignment procedure we saw rarely perfectly aligned shafts. Regular checking is necessary to maintain the perfect alignment condition. Regular checking is the key condition in preventing maintenance.

Image Credits: www.myodesie.com

OFFSET or PARALLEL MISALIGNMENT :

          When there is a distance between shaft center lines, it is referred as Offset or parallel misalignment. Generally this alignment is measured in thousandths of an inch. In this condition the shafts are parallel to each other but not colinear. Offset may present in either the vertical or horizontal plane. Theoretically, offset is measured at coupling center line.

ANGULAR MISALIGNMENT :

          Angular misalignment also referred as face misalignment. Angular misalignment is the condition when the shafts aren't parallel (Angular offset) however they are in same plane with no offset. Angularity is the angle between the two shaft centerlines, which usually expressed as a "slope", or "rise over run" of so many thousandths of an inch per inch (i.e., unit less) rather than as an angle in degrees. It should be determined both in the vertical and horizontal planes.

COMBINATION OR SKEWED MISALIGNMENT :

          Skewed or Combination misalignment  occurs when both Offset and Angular misalignment occurs. In this type of misalignment shafts are not parallel and also they wont intersect at the coupling. This type of misalignment can occur in both the horizontal and vertical planes or either in the horizontal or vertical planes.  

SHAFT ALIGNMENT - ALIGNMENT PLANES

          Before we start learning alignment this is very important to know the types of misalignment planes and types of misalignment.

Generally there are two misalignment planes that we have to correct: 

          1) Vertical and 

          2) Horizontal.

In general there are two types of misalignment.

          1) Parallel (also known as Offset)

          2) Angular (also known as Gap).

Therefore, in the case of making a machine-train by using at least two machines, four types of misalignment can occur: 

          a) Vertical Offset

          b) Vertical Angularity

          c) Horizontal Offset, and

          d) Horizontal Angularity.

These can occur in any combination and in many cases, all four are present.

Vertical:

          Vertical misalignment means that the misalignment of the shafts in the vertical plane. In vertical misalignment both angular and offset misalignment can occur.

          Offset (Parallel) vertical misalignment happens when the motor shafts is moved vertically away from the pump shaft, but both shafts still operate in the same vertical plane and parallel.

          Gap (Angular) vertical misalignment occurs when the motor shaft is at an angle with the pump shaft, However, both shafts still operate within the same vertical plane.

          Vertical misalignment, which is corrected by the employment of Shims.

MIS-ALIGNMENT PLANES-- VIEW

Horizontal:

          Horizontal misalignment means that the misalignment of the shaft in the horizontal plane. Just like vertical misalignment, in horizontal misalignment also both angular and offset misalignment can occur.

          Offset (Parallel) horizontal misalignment happens when the motor shaft is moved horizontally away from the pump shaft, but both shafts still operate in the same horizontal plane and parallel.

          Gap (Anhular) horizontal misalignment occurs when the motor shaft is at an angle with the pump shaft. However both shafts operate within the same horizontal plane. 

          Horizontal misalignment, which is not corrected by employing Shims. This type of misalignment is corrected by physically moving the MTBM.

Alignment Tolerances:

ALIGNMENT TOLERANCES