ME305 EndSemKEY 22112017

NATIONAL INSTITUTE OF TECHNOLOGY, WARANGAL
(An Institution of National Importance)

DEPARTMENT OF MECHANICAL ENGINEERING
III B.TECH. (MECHANICAL ENGINEERING) I SEMESTER
ME305 - MECHANICAL MEASUREMENTS
END SEMESTER EXAMINATION, NOVEMBER - 2017
Date: 22.11.2017 Max. Marks: 50
Note: 1. There are 9 questions on this paper, 2. Assume missing data if any, suitably, 3. Answer to the point.
1. Explain Accuracy, Precision, Calibration, Least count and Sensitivity. (5 marks)
Scheme:
1 mark for each definition/explanation
2. Derive an equation to show manometer as a second order system. Give expressions for its time constant
and damping ratio. (5 marks)
Scheme:
List of forces acting
When pressure ΔP is applied, the forces acting on L are
1. Force due to acceleration of the liquid – Fa
2. Force supporting the change in height – Fs
3. Weight of column of liquid – W
4. Friction force due to viscosity – Ff
𝑑2𝑥
𝐹𝑎 = 𝜌𝑚 𝑎𝐿 − − − −(1)
𝑑𝑡 2
𝐹𝑠 = 𝑎∆𝑃 − − − −(2)
𝑊 = 𝜌𝑚 𝑎𝑥𝑔 − − − −(3)
𝐹𝑓 = 𝑎∆𝑃𝑓 − − − −(4)
2 marks for the above steps
Getting frictional pressure drop from flow rate and using it in (4) we get
𝑑𝑥
𝐹𝑓 = 𝜌𝑚 𝑎2 𝑅 − − − −(5)
𝑑𝑡
𝐹𝑎 = 𝐹𝑠 − 𝑊 − 𝐹𝑓 − − − −(6)
𝑑2 𝑥 𝑑𝑥
𝜌𝑚 𝑎𝐿 2
= 𝑎∆𝑃 − 𝜌𝑚 𝑎𝑥𝑔 − 𝜌𝑚 𝑎2 𝑅 − − − −(7)
𝑑𝑡 𝑑𝑡
𝐿 𝑑2 𝑥 𝑎𝑅 𝑑𝑥 ∆𝑃
2
+ +𝑥 = − − − −(8)
𝑔 𝑑𝑡 𝑔 𝑑𝑡 𝜌𝑚 𝑔
2marks for the above steps

Characteristic time is defined as τ = (1/ωn) which is given by
1 𝐿
𝜏= =√
𝜔𝑛 𝑔
And the damping ratio
𝑎𝑅
𝜁=
2𝑔𝜏
Then (13) becomes
𝑑2𝑥 𝑑𝑥 ∆𝑃
𝜏2 2
+ 2𝜁𝜏 +𝑥 = − − − −(9)
𝑑𝑡 𝑑𝑡 𝜌𝑚 𝑔
1 mark for the above steps
3. Calculate the value of the quantity X and its uncertainty from the measured values of a, b and c in each of
the following:
(i) X =6a+ 4b , a =40 ± 2, b =20 ± 2
(ii) X =a – 2b , a =50 ± 1, b =24 ± 0.5
(iii) X =a3 , a =10 ± 0.3, b =0
(iv) X =a/(b) (1/2) a =100 ± 4, b =50 ± 2
2
(v) X =ab /c , a =0.2 ± 0.004, b =0.1 ± 0.003, c = 0.05 ± 0.002 (5 marks)
Scheme:
1 mark for each correct answer
S.No X Wx
(i) 320 14.42
(ii) 2 1.414
(iii) 1000 90
(iv) 14.14 0.6324
(v) 0.04 0.00253
4. A thermal conductivity comparator uses a standard reference material (SRM) of thermal conductivity
45 ± 2% W/m oC. Two thermocouples placed 22 ± 0.25mm apart indicate a temperature difference of
2.5 ± 0.2 oC. The material of unknown thermal conductivity is in series with the SRM and indicates a
temperature difference of 7.3 ± 0.2 oC across a length of 20 ± 0.25 mm. Determine the thermal conductivity
of the sample and its uncertainty. (5 marks)
Scheme:
Q = KA (ΔTA/LA) = KB (ΔTB/LB) (1 mark)
Thus KB = 14 W/m K (2 marks)

And Uncertainty in KB = 1.24 W/m K = 8.85% (2 marks)
5. Explain Wien’s displacement law and the operation of a vanishing filament optical pyrometer on basis of
that, using neat schematics. (5 marks)
Scheme:
Wien’s Displacement Law

Black body radiation curve for different temperatures,
peaks at a wavelength inversely proportional
to the temperature. (2 marks)
Explanation of working and schematic of

optical pyrometer (3 marks)
6. Derive an equation to show temperature measuring device as a first order system and explain which
parameters affects its time constant. (5 marks)
Scheme:
Consider a temperature probe as a system subject to transient temperature.

ρ – density of the probe material (kg/m3)
V – volume of the probe material (m3)
A – surface area of the probe (m2)
C – specific heat of the probe material (J/kg.K)
h – heat transfer coefficient between probe and the fluid (W/m2.K)
The probe is assumed to be thermally ‘lumped’ (at uniform temperature T for any given time t). Let T 0 be
the initial temperature of the probe and T∞ be the fluid temperature.
By energy conservation,
Rate of change of energy stored in the probe = Rate of heat transfer between probe and the fluid (1
mark)
That is,
𝑑𝑇
−𝜌𝑉𝐶 = ℎ𝐴(𝑇 − 𝑇∞ ) -------------------------(1)
𝑑𝑡
𝑑𝑇 ℎ𝐴 ℎ𝐴
+ 𝜌𝑉𝐶 𝑇 = 𝜌𝑉𝐶 𝑇∞ -----------------------------(2)
𝑑𝑡
𝜌𝑉𝐶
has the unit of time and is called as the time constant τ of the first order system (Note: Study the
ℎ𝐴
effect of parameters on time constant) . It involves thermal and geometric properties. Equation (2) can now
be written as
𝑑𝑇 𝑇 𝑇∞
+𝜏= ----------------------------(3)
𝑑𝑡 𝜏
4 marks for the above steps with explanation for time constant
7. A rotating concentric cylinder viscometer is run at an angular speed of 1800±5 rpm. The geometric data is
specified as r1 = 37±0.02 mm, r2 = 38±0.02 mm, L = 100±0.5 mm and thickness of fluid layer at the bottom,
a = 1±0.01 mm. What is the torque experienced by the stationary cylinder? Estimate uncertainty in torque
measured if the fluid in the viscometer has viscosity of 0.0331 kg/ms. (5 marks)
Scheme:
1800
𝜔 = 1800𝑟𝑝𝑚 = × 2𝜋 = 188.5 𝑟𝑎𝑑/𝑠
60
Nominal value of Torque - 2 marks
2𝑟2 𝐿 𝑟12
𝑇𝑇𝑜𝑡𝑎𝑙 = 𝑇𝑖 + 𝑇𝑎 = 𝜇𝜋𝜔𝑟12 [ + ] = 0.222 𝑁. 𝑚
𝑏 2𝑎
Uncertainty equation and proper substitution – 1 mark
Uncertainty in Torque = ±0.005 Nm or 2.25% - 2 marks
8. List some of the crucial steps before identifying and finalizing upon, the measuring instruments to be used
in any experiment. (5 marks)
Scheme:
1. Objectives
2. List of specific results needed
3. Methodology for overall experiment
4. Parameters needed to calculate the results
5. Quantities to be measured for obtaining above parameters
6. Range of measured quantities
7. Method for individual measurements
8. Apparatus preliminary design
9. Design an experimental flow loop (listing the equipment and measuring devices needed) to estimate the
local forced convective heat transfer coefficient at seven locations in an internal fluid flow through a pipe.
Explain the method of calculating local heat transfer coefficient listing the parameters to be considered
and the values that need to be measured. Justify the range and choice of your measuring devices with
proper reasons. Draw a neat schematic to depict the entire set-up. (Present your answer in form of a table
wherever necessary, for easy evaluation) (10 marks)
Scheme:
1. List of parameters required – 2 marks
2. Selecting the range of operating parameters – 1 mark
3. Selecting the measuring devices with range – 2 marks
4. Justification of the chosen devices – 3 marks
5. Calculation method and possible ways to minimise errors – 1 mark
6. Schematic of the loop – 1 mark

ME305 EndSemKEY 22112017

Uploaded by

Copyright:

Available Formats

ME305 EndSemKEY 22112017

Uploaded by

Document Information

Original Description:

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

ME305 EndSemKEY 22112017

Uploaded by

Copyright:

Available Formats

NATIONAL INSTITUTE OF TECHNOLOGY, WARANGAL

(An Institution of National Importance)

Date: 22.11.2017 Max. Marks: 50

1. Explain Accuracy, Precision, Calibration, Least count and Sensitivity. (5 marks)

2marks for the above steps

Q = KA (ΔTA/LA) = KB (ΔTB/LB) (1 mark)

Thus KB = 14 W/m K (2 marks)

Wien’s Displacement Law

Explanation of working and schematic of

Consider a temperature probe as a system subject to transient temperature.

Uncertainty equation and proper substitution – 1 mark

Uncertainty in Torque = ±0.005 Nm or 2.25% - 2 marks

You might also like