Chapter: Dimensional Analysis and Similarities
1.

Dimensional analysis is used to

A. Test the dimensional homogeneity of any equation of fluid motion
B. Derive rational formulae for a flow phenomenon
C. Derive equations expressed in terms of non– dimensional parameters
D. All of the above.
Answer» D. All of the above.
2.

Which of the following is an advantage of dimensional analysis?

A. It expresses the functional relationship between the variables in dimensionless terms
B. In hydraulic model studies it reduces the number of variables involved in a physical phenomenon, generally by three
C. By the use of dimensional analysis design curves can be developed from experimental data or direct solution of the problem
D. All of the above.
Answer» D. All of the above.
3.

dimensionally homogeneous equation is applicable to

A. C.G.S. system only
B. F.P.S. system only
C. M.K.S. and SI systems
D. All systems of units.
Answer» D. All systems of units.
4.

In which of the following methods of dimensional analysis, a functional relationship of some variables is expressed in the form of an exponential equation, which must be dimensionally homogeneous?

A. Buckingham’s π-method
B. Rayleigh’s method
C. Bridgman’s method
D. Matrix–tensor method.
Answer» B. Rayleigh’s method
5.

In dimensional analysis the Buckingham’s π–theorem is widely used and expresses the resulting equation in terms of

A. The repeating variables
B. Geometric, kinematic and dynamic variables
C. (n – m) dimensionless parameters
D. n dimensionless parameters.
Answer» C. (n – m) dimensionless parameters
6.

To apply Buckingham’s π–theorem, m repeating variables are selected from amongst the n variables influencing the phenomenon. The repeating variables are selected such that they

A. Belong to kinematic and dynamic category of variables
B. Must always contain the dependent variables
C. In combination contain each of the m fundamental dimensions involved in the problem.
D. None of the above.
Answer» C. In combination contain each of the m fundamental dimensions involved in the problem.
7.

In order that results obtained in model studies correctly represent the behaviour of the prototype, which of the following similarities must be ensured between the model and the prototype?

A. Geometric similarity
B. Kinematic similarity
C. Dynamic similarity
D. All of the above.
Answer» D. All of the above.
8.

Dynamic similarity between the model and prototype is the

A. Similarity of motion
B. Similarity of lengths
C. Similarity of forces
D. None of the above.
Answer» C. Similarity of forces
9.

...... is equal to the product of shear stress due to viscosity and surface area of flow.

A. Viscous force
B. Inertia force
C. Pressure force
D. Gravity force.
Answer» A. Viscous force
10.

Kinematic similarity between model and prototype is the

A. Similarity of discharge
B. Similarity of shape
C. Similarity of streamline pattern
D. None of the above.
Answer» C. Similarity of streamline pattern
11.

......... is the ratio of the inertia force to the viscous force.

A. Froude’s number
B. Weber’s number
C. Reynolds number
D. Mach’s number.
Answer» C. Reynolds number
12.

........ is the square root of the ratio of the inertia force to the pressure force.

A. Reynolds number
B. Mach’s number
C. Euler’s number
D. Froude’s number.
Answer» C. Euler’s number
13.

Euler number is important in which of the following flow situations?

A. Discharge through orifices, mouthpieces and sluices
B. Pressure rise due to sudden closure of valves
C. Flow through pipes
D. All of the above
Answer» D. All of the above
14.

Mach’s number is defined as the square root of the ratio of the

A. Inertia force to the pressure force
B. Inertia force to the surface tension force
C. Inertia force to the elastic force
D. None of the above.
Answer» C. Inertia force to the elastic force
15.

...... is important in compressible fluid flow problems at high velocities, such as high velocity flow in pipes or motion of high-speed projectiles and missiles.

A. Euler’s number
B. Mach’s number
C. Reynolds number
D. Froude’s number.
Answer» B. Mach’s number
16.

Distorted models are required to be prepared for which of the following?

A. Rivers
B. Dams across very wide rivers
C. Harbours
D. All of the above.
Answer» D. All of the above.
17.

The scale effect in models can be

A. Positive only
B. Negative only
C. Both positive and negative
D. None of the above.
Answer» C. Both positive and negative
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