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Previous year question hub

Similarity and Buckingham Pi Theorem - Dimensional Analysis - Engineering Sciences Previous Year Questions

Practice Similarity and Buckingham Pi Theorem - Dimensional Analysis - Engineering Sciences previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

20Papers
20Years
40Questions
1Topics

Similarity and Buckingham Pi Theorem question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Similarity and Buckingham Pi Theorem. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Easy 20 50%
Medium 18 45%
Hard 2 5%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

MCQ 26 65%
Numerical Answer Type (NAT) 13 32.5%
MSQ 1 2.5%

Subject weightage

Top subjects by unique question coverage.

Engineering Sciences
40 Qs

Most asked topics

Top topics across the included previous year papers.

Dimensional Analysis
40 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Similarity and Buckingham Pi Theorem
40 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

Engineering Sciences (XE) 2026
1 Qs
Engineering Sciences (XE) 2025
1 Qs
Engineering Sciences (XE) 2024
1 Qs
Engineering Sciences (XE) 2023
2 Qs
Engineering Sciences (XE) 2022
4 Qs
Engineering Sciences (XE) 2021
1 Qs
Engineering Sciences (XE) 2020
2 Qs
Engineering Sciences (XE) 2019
3 Qs
Engineering Sciences (XE) 2018
2 Qs
Engineering Sciences (XE) 2017
2 Qs
Engineering Sciences (XE) 2016
2 Qs
Engineering Sciences (XE) 2015
1 Qs
Engineering Sciences (XE) 2014
3 Qs
Engineering Sciences (XE) 2013
2 Qs
Engineering Sciences (XE) 2012
2 Qs
Engineering Sciences (XE) 2011
2 Qs
Engineering Sciences (XE) 2010
1 Qs
Engineering Sciences (XE) 2009
2 Qs
Engineering Sciences (XE) 2008
4 Qs
Engineering Sciences (XE) 2007
2 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
Engineering Sciences (XE) 202620261View paper
Engineering Sciences (XE) 202520251View paper
Engineering Sciences (XE) 202420241View paper
Engineering Sciences (XE) 202320232View paper
Engineering Sciences (XE) 202220224View paper
Engineering Sciences (XE) 202120211View paper
Engineering Sciences (XE) 202020202View paper
Engineering Sciences (XE) 201920193View paper
Engineering Sciences (XE) 201820182View paper
Engineering Sciences (XE) 201720172View paper
Engineering Sciences (XE) 201620162View paper
Engineering Sciences (XE) 201520151View paper
Engineering Sciences (XE) 201420143View paper
Engineering Sciences (XE) 201320132View paper
Engineering Sciences (XE) 201220122View paper
Engineering Sciences (XE) 201120112View paper
Engineering Sciences (XE) 201020101View paper
Engineering Sciences (XE) 200920092View paper
Engineering Sciences (XE) 200820084View paper
Engineering Sciences (XE) 200720072View paper

All Similarity and Buckingham Pi Theorem previous year questions

Practice every matching question in batches of 20, with every available option.

1
2007 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2007
The non-dimensional number obtained from specific heat (\(c_p\)), thermal conductivity (\(k\)) and viscosity (\(\mu\)) is
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2
2007 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2007
A model of characteristic length 20 cm is built to study the flow of water (\( \nu = 10^{-6} \, \text{m}^2/\text{s} \)) in an open channel of 5 m characteristic length. What should be the kinematic viscosity of the fluid used in the model?
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3
2008 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2008

Which of the following statements is true for two kinematically similar flows?

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4
2008 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2008

The non-dimensional numbers shown in column 1 relate the inertial force with another force shown in column 2. Match the dimensionless number with the corresponding force.

Column 1Column 2
R: Reynolds numberP: Pressure
F: Froude numberG: Gravity
E: Euler numberS: Surface tension
W: Weber numberV: Viscous
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5
2008 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2008

A 4 m wide canal is modelled using a 1 m wide dynamically similar model in the laboratory. A wooden block was observed to travel between two points in the model in 8 seconds. How long will it take to travel between the corresponding points in the actual canal?

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6
2008 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2008
The drag force on a ship travelling in sea depends on the viscous resistance as well as the effect of surface waves. A model with complete dynamic similarity is to be constructed in the laboratory using a fluid with a kinematic viscosity which is 1/64 times that of seawater $\left(\frac{v_m}{v_p} = \frac{1}{64}\right)$. What should be the length ratio $(l_m/l_p)$? Note that the subscripts $m$ and $p$ refer to the model and the prototype respectively.
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7
2009 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2009
Under strong wind conditions, electrical cables can be subjected to wind-induced oscillations. Which one of the following non-dimensional numbers is relevant to this problem ?
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8
2009 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2009
A 1:20 model of a submarine is to be tested in a towing tank containing sea water. If the submarine velocity is 6 m/s, at what velocity should the model be towed for dynamic similarity ?
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9
2010 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2010

The length scale of a model is kept as 1 : 64. The prototype fluid is water. Viscous and gravity forces are equally dominant in the prototype. The required kinematic viscosity (m2/s) of the fluid used in the model is

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10
2011 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2011
A certain fluid flow is influenced by density (ρ), angular velocity (ω), dynamic viscosity (μ), and a characteristic length (L). A relevant non-dimensional parameter will be
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11
2011 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2011

An open channel flow is to be simulated in the laboratory. For this purpose, a 1:25 scale model is constructed. If the flow velocity in the prototype is 5 m/s, for dynamic similarity the model should have a flow velocity of

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12
2012 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2012
Air flows over a spherical storage vessel of diameter 4 m at a speed of 1 m/s. To find the drag force on the vessel, a test run is to be carried out in water using a sphere of diameter 100 mm. The density and dynamic viscosity of air are 1.2 kg/m³ and 1.8 × 10⁻⁵ Pa.s, respectively. The density and dynamic viscosity of water are 1000 kg/m³ and 10⁻³ Pa.s, respectively. The drag force on the model is 4 N under dynamically similar conditions. The drag force (in N) on the prototype is approximately
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13
2012 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2012
Given that \( V \), \( L \) and \( g \) are the characteristic velocity, characteristic length and acceleration due to gravity, respectively, the expression \( \frac{V}{\sqrt{Lg}} \) represents
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14
2013 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2013
The velocity in m/s, at which the model is towed, is
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15
2013 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2013

The resistance of the prototype, in kN, is

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16
2014 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2014
A fruit juice of viscosity \(\mu\) and density \(\rho\) is agitated using an impeller of diameter D at a speed of N revolutions per minute. The terms \(X = \frac{P}{\rho N^3 D^5}\), \(Y = \frac{D^2 N \rho}{\mu}\), \(Z = \frac{N^2 D}{g}\) represent three process related numbers, where P is power imparted by impeller and g is acceleration due to gravity. Which of the following is correct representation of these numbers?
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17
2014 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2014
It is required to carry out model studies on a boat having a characteristic length of 3.6 m and travelling at a speed of 3 m/s. Assume the acceleration due to gravity as 10 m/s\(^2\) and neglect the effects due to viscous and surface tension forces. The value of appropriate non-dimensional number is ____.
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18
2014 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2014
The model of a conduit is scaled to 1/100 of the actual size. Seawater is used in the prototype and fresh water is used in the model. Velocity in the prototype is 0.5 m/s. Density and dynamic viscosity of the seawater are 1025 kg/m³ and \(1.07 \times 10^{-3}\) kg/m-s, respectively. Density and dynamic viscosity of fresh water are 1000 kg/m³ and \(1 \times 10^{-3}\) kg/m-s, respectively. Assume the viscous forces to be dominant. The velocity to be maintained in the model to ensure dynamic similarity is ____ m/s.
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19
2015 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2015
A certain fluid flow phenomenon is described by Reynolds, Weber and Ohnesorge numbers. The Weber and Ohnesorge numbers are defined as \(We = \frac{\rho U^2 L}{\sigma}\), and \(Oh = \frac{\mu}{\sqrt{\rho \sigma L}}\) respectively, where \(\sigma\) is the surface tension, \(\rho\) is the density, \(\mu\) is the dynamic viscosity, \(U\) is the velocity and \(L\) is the characteristic dimension. If \(Re\) denotes the Reynolds number, which of the following relations is true?

Question diagram

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20
2016 · Engineering Sciences · Dimensional Analysis · Similarity and Buckingham Pi Theorem
Engineering Sciences (XE) 2016
Prototype of a dam spillway ( a structure used for controlled release of water from the dam) has characteristic length of 20m and characteristic velocity of 2 m/s. A small model is constructed by keeping Froude number same for dynamic similarity between the prototype and the model. What is the minimum length-scale ratio between prototype and the model such that the minimum Reynolds' number for the model is 100? The density of water is 1000 kg/m³ and viscosity is \( 10^{-3} \) Pa-s.
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