Eastern Mediterranean University
Department of Mechanical Engineering
LABORATORY WORK REPORT
COURSE:
MENG203 - Experimental Methods for Engineers
Semester: FALL 2015-2016
EXPERIMENT No:1
Name of Experiment: Measurement by Vernier Caliper
Instructor: Assoc. Prof. Dr. Hasan Hacişevki
Submitted by:
Student No:
Group No:
Date of submission:
EVALUATION
Filing/ Binding
10%
Contents/Research
40%
Discussion, Conclusion
20%
Presentation
30%
Overall Mark
Introduction
A Vernier caliper is a precision instrument that measures internal dimensions, outside
dimensions, and depth. It can measure at an accuracy of one thousandth of an inch and one
hundredth of a millimeter. The caliper has 2 sets of jaws on the upper portion and the lower
portion. Each set of jaws has a fixed jaw and a movable jaw. The upper set is designed to
measure inside dimensions. The lower set is designed to measure outside dimensions. It also has
a depth probe at the base or rear part, which functions as a depth measuring tool.
Types of Scales
There are 2 scales on a Vernier caliper. The main scale is typically found on the length of the
caliper. It functions much the same way as a ruler. The main scale is fixed on the device and
cannot be moved. The caliper also has a movable Vernier scale. The Vernier scale is the secret
to the instrument’s precision. It is divided into 10 sets, each of equal length. Below are the best
uses for a Vernier caliper.
1. Measuring Inside Dimensions
The upper set of jaws on the caliper can be used to measure inside dimensions, such as the
diameter of holes on a piece of wood or metal. Measuring the precise diameters of holes in
pipes, cylinders and other hollow objects is very important to any project or application. The
jaws of the caliper can be easily slid into the hole to get the precise measurement. The caliper
can also be used to measure inside dimension of holes with different shapes, e.g. square,
rectangular, cylindrical, or hexagonal. Lastly, the upper jaws can be used to measure the
distance between 2 objects. This can be done by simply putting the jaws of the caliper
between the objects to get a measurement.
Measuring Outside Dimensions
The lower set of jaws on the Vernier caliper can be used to measure outside dimensions. Outside
dimensions include the outer diameter of a cylinder and total length of an object. The outer
diameter of cylindrical objects can be measured by simply clamping the lower jaws of the
caliper around the object. The Caliper can also measure the length or width of an object by
placing the object between the caliper’s jaws.
Procedure:
In this experiment, we measured the inner and the outer diameter (mm) of 10 rings with
vernier caliper and recorded the data in the given table. In this report I am going to
calculate average dimensions and statistical analysis such as mean, standard deviation and
uncertainty analysis. Then I will use the error propagation formulas to compute the
uncertainty in quantities derived from the measurements. Then I will discuss and interpret
the results.
RESULTS
Inside diameter (mm)
(𝑥𝑖 − 𝑥𝑚 )
(𝑥𝑖 − 𝑥𝑚 )2
1
2
3
4
5
6
7
8
9
10
𝑛
1
𝑥𝑚 = ∑ 𝑥𝑖
𝑛
𝑖=1
∑𝑛 (𝑥𝑖 − 𝑥𝑚 )2
𝜎 = √[ 𝑖=1
]
𝑛
𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 𝜎 2
outside diameter (mm)
1
2
3
4
5
6
7
8
9
10
(𝑥𝑖 − 𝑥𝑚 )
(𝑥𝑖 − 𝑥𝑚 )2
Uncertainty Analysis:
𝜎
Uncertainty = ((Standard deviation) / (Number of reading))0.5 = √𝑛
Uncertainty for inner diameter =
Uncertainty for outer diameter =
So,
Inner diameter =
Outer diameter =
Standard Error = 𝑆𝑛 =
𝜎
√
= √[
𝑛
Standard Errorinner =
Standard Errorouter=
Discussion of Results
2
∑𝑛
𝑖=1(𝑥𝑖 −𝑥𝑚 )
(𝑛)(𝑛)
]