FMM IT-3 key.docx

7/27/2019 FMM IT-3 key.docx

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PART A

1. Define dimensional analysis and write its uses. -------------- (2)

Dimensional analysis is a mathematical technique which makes use of the study ofdimensions as an aid to solution of several engineering problems. It plays animportant role in research work. It helps in testing the dimensional homogeneity of any equation of fluid motion. It helps in deriving equations expressed in terms of non-dimensional parameters.

2.Define dimensional homogeneity. -------------- (2)

An equation is said to be dimensionally homogeneous if the dimensions of the termson its LHS are same as the dimensions of the terms on its RHS.

3.Define model and prototype-------------- (2)

The small scale replica of an actual structure or the machine is known as its

Model, while the actual structure or machine is called as its Prototype. Mostlymodels are much smaller than the corresponding prototype.

4. Write the advantages of model analysis. B -------------- (2)

Model test are quite economical and convenient.

Alterations can be continued until most suitable design is obtained.

Modification of prototype based on the model results.

The information about the performance of prototype can beobtained well in advance.

5. Mention the various forces considered in fluid flow.Inertia force, Viscous force, Gravity force,Pressure force, Surface Tension force, Elasticity force.

6. Define model law or similarity law. -------------- (2)

The condition for existence of completely dynamic similarity between a model

and its prototype are denoted by equation obtained from dimensionless numbers.

The laws on which the models are designed for dynamic similarity are called Model

laws or Laws of Similarity

7.Define geometric similarity. -------------- (2)

It exists between the model and prototype if the ratio of corresponding lengths,dimensions in the model and the prototype are equal. Such a ratio is known as

Scale Ratio.


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8. Define Eulers number and Webers number. -------------- (2)

9. Define undistorted and distorted model. -------------- (2)An undistorted model is that which is geometrically similar to its prototype, i.e.

the scale ratio for corresponding linear dimensions of the model and its prototypeare same.

Distorted models are those in which one or more terms of the model arenot identical with their counterparts in the prototype.

10.Name some dimensionless parameters. -------------- (2)

Reynolds number, Machs number, Eulers number, Froudes number, Webers number

PART B:

11) (a) Determine the dimensions of the quantities given below (i) Angular velocity, angular

acceleration (ii) Dynamic viscosity (iii) Kinematic viscosity (iv) Specific weight -----(8)

(ii)

iii

iv


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11) (b) State Buckinghams -theorem . ------------------ (8)

12 ) Explain the procedure for solving problems by Buckinghams theorem by considering the

following problem . The resisting force R of a supersonic plane during flight can be

considered as dependent upon the length of the aircraft l, velocity v, air viscosity , air

density and bulk modulus of air K. Express the functional relationship between these

variables and the resisting force. ----------- (4+4+4+4)


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13) Using Buckinghams -theorem, show that the discharge Q consumed by an oil ring is

given by Q= Nd3

[

,

,

]where d is the internal diameter of the ring, N

is rotational speed, is density, is viscosity, is surface tension and w is the specific

weight of oil.--------------------- (4+4+4+4)


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14) Derive on the basis of dimensional analysis suitable parameters to present the thrust

developed by a propeller. Assume that the thrust P depends upon the angular

velocity, speed of advance V, diameter D, dynamic viscosity , mass density,

elasticity of the fluid medium which can be denoted by the speed of sound in the

medium C. ------------(4+4+4+4)


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15) (a)Explain Rayleighs method of dimensional analysis. (4)


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(b) Find the expressions for the drag force on smooth sphere of diameter D, moving with a

uniform velocity V in a fluid of density and dynamic viscosity . (4)

(c) Water is flowing through a pipe of diameter 30 cm at a velocity 4 m/s. Find the velocity of

oil flowing in another pipe of diameter 10 cm, if the condition of dynamic similarity issatisfied between the two pipes. The viscosity of water and oil is given as 0.01 poise and

0.025 poise. The sp.gr of oil is 0.8. (8)


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