Engineering Sciences
GATE XE topic:dimensional-analysis PYQs
Build your understanding with focused practice from past exam papers.
Questions 11–17 of 17. Imported answers require independent review unless marked reviewed.
Question 17
Open questionXE-BNAT2 marksNeeds review
A sphere model of 10 cm diameter is tested in water flowing at 2 m/s. The drag force is measured as 5 N. Prototype of 1.5 m in diameter is tested in air with dynamic similarity conditions. (Density of water is 1000 kg/m
, density of air is 1.2 kg/m
, viscosity of water is 0.001 Ns/m
and viscosity of air is 1.78 x 10
Ns/m
).Drag force experienced by the prototype is ______ N (rounded off to two decimal places).
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Open questionXE-BMCQ1 markNeeds review
The power input
to a centrifugal pump is a function of the volume flow rate
, impeller diameter
, rotational speed
, fluid density
, dynamic viscosity
, and surface roughness
. To carry out a dimensional analysis using Buckingham’s
theorem, which one of the following sets can be taken as the set of repeating variables?Your answerChoose one option.
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Open questionXE-BNAT2 marksNeeds review
In a steady incompressible flow of a fluid past a smooth stationary sphere, the drag force
depends on the flow velocity
, diameter
, and the dynamic viscosity
and density
of the fluid. Experiments are conducted on the same sphere at the same flow velocity using two different fluids. The density of the second fluid is two times that of the first fluid. The dynamic viscosity of the second fluid is
times that of the first fluid. If the non-dimensional force
remains the same in both the experiments, the value of
is ______.Log in to check the answer
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Open questionXE-BMCQ1 markNeeds review
The influence of Froude number is most significant in
Your answerChoose one option.
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Open questionXE-BNAT2 marksNeeds review
Capillary waves are generated in the sea. The speed of propagation (C) of these waves is known to be a function of density (ρ), wave length (λ), and surface tension (σ). Assume, ρ and λ to be constant. If the surface tension is doubled, in the functional form of the relevant non-dimensional group, the percentage increase in propagation speed (C) is ______ .
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Open questionXE-BMCQ2 marksNeeds review
The volumetric flow rate (
) of a triangular notch is a function of the upstream liquid surface elevation (
) measured from the bottom of the notch, acceleration due to gravity (
), notch angle (
) and the approach velocity (
). Which one of the following is the correct expression for
?Your answerChoose one option.
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Open questionXE-BNAT2 marksNeeds review
Model tests are to be carried out to study the flow through a large prototype valve of 0.6 m diameter at a flow rate of 10 m³/s. The same working fluid is used for both the model and the prototype. A complete geometric similarity is maintained between the model and the prototype. If the valve diameter of the model is 80 mm, its required flow rate (in m³/s, rounded off to the first decimal place) would be ________.
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