Question

Q1 (a) For each statement, choose whether the statement is true or false and discuss your answer briefly. (1) Kinematic similarity is a necessary and sufficient condition for dynamic similarity. (ii) Geometric similarity is a necessary condition for dynamic similarity. (iii) Geometric similarity is a necessary condition for kinematic similarity. (iv) Dynamic similarity is a necessary condition for kinematic similarity (8 marks) (b) Explain with THREE (3) examples of prototypes and their corresponding models flow that have geometric similarity, but not kinematic similarity, even though the Reynolds numbers match. (9 marks) (c) Write the primary dimensions of each of the following variables: (1) moment of inertia I; (ii) modulus of elasticity E, also called Young's modulus; (iii) strain (iv) stress (v) Finally, show that the relationship between stress and strain (Hooke's law) is a dimensionally homogeneous equation. (Refer Table Q1(c)) (8 marks)

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Answer 1

alo a) Condition TRUE TRUE ;) Kinematic similarity is a necessary and sufficient condition for dynamic Sintarity TRUE Hi Geometric fimilarity is a necessary for dynamic similarity ili, Geometric fimilarity is a necessary condition for Kinematic finilarity įv, Dynamic similarity is a necessary condition for kinematic similarity - FALSE Explanation geometric similarity & (similarity in shape) To satisfy the condition, the ratio's of the corres- ponding lengths in the model and its prototype must be same. Kinematic similarity & (similarity of motion) Stres reanline pattem in model must be some as that in its prototype. The ratios of kinematic qualities representing flow cherecterising as time, relocity acceleration and discharge must be some at all corresponding points, Dynamic similarity & (similarity of forces) corresponding forces have the same ratio throughout the flow flaid.

For either For compleate similarity to exist between the model and its prototype it is necessary that it must be geonetrically, kinematically, and dynamically similar. * For either dynamic or kinematic fimilarity to exist geometric similarity is a requisite. * If two flow rate fields are dynamically Similar they are necessarily, kinematically and geometrically similar. prer TIR F c) poimary dimensions of 1, moment of Inertia -Mo Lu To Cunits = 1) I modulous of Slasticity 'E = M['T2 (unitsa No cil, Strain MOTO (Nounits) 19 Stress METZ Camits NA Hook's law Stress directly proposanal to strain Stress a strain V Stress = Ex strain whese 'E is the limit of proportanality

Stress 2 Strain, Relation between stress and strin is a dimensionally homogenibus equation. stress Strain. b) model and prototype or creen prototype is a full size machine Model is the tool for studying the behaviour of a prototype. It may be larger, smaller fame size of the prototype. Renoldly model law (Re) prototype Pomiman Spuple Mon Mp & Volv - (Remodel MY Renolds can similarity similarity is used where ever viscous forces are important. Suchas eg a completely submerged bodies, Airplanes, torpedo ete. WE

ega completely enelased flow Flow through pipes, flow past plates, fluid drag and lift on body shapes such as Cars, trains, Para Chutes ett. > Settling of particles and creeping flow a flow meters such as venturi meter, of orifice meter etc. Flow machines such as propellers, pumps and turbines. SINARAGAR y Fans, blowers,