# Statement (I): Reynolds number must be the same for model and the prototype when both are tested as immersed in a subsonic flow. Statement (II): A mod

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Statement (I): Reynolds number must be the same for model and the prototype when both are tested as immersed in a subsonic flow.

Statement (II): A model should be geometrically similar to the prototype.
1. Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
2. Both Statement (I) and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I)
3. Statement (I) is true but Statement (II) is false
4. Statement (I) is false but Statement (II) is true (II) is true:

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Correct Answer - Option 2 : Both Statement (I) and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I)

Explanation:

The similitude is defined as the similarity between the model and its prototype in every respect, which means that the model and prototype have similar properties or model and prototype are completely similar.

A model should be similar to its prototype in 3 ways. They are as follows:

1. Geometric similarity:

The geometric similarity is said to exist between the model and the prototype. The ratio of all corresponding linear dimensions in the model and prototype are equal.

2. Kinematic similarity:

It means the similarity of motion between model and prototype. Thus kinematic similarity is said to exist between the model and the prototype if the ratios of the velocity and acceleration at the corresponding points in the model and at the corresponding points in the prototype are the same.

3. Dynamic similarity:

It means the similarity of forces between model and prototype. Thus dynamic similarity is said to exist between the model and the prototype if the ratios of the corresponding forces acting at the corresponding points are the same.

Models are designed on the basis of the ratio of the force, which is dominating in the phenomenon. The laws on which models are designed for dynamic similarity are called Model laws or laws of similarity.

Different model laws with their significance are given below in the table.

 Serial No Number Equation Significance 01 Reynolds No. $\frac{{Fi}}{{Fv}} = \frac{{\rho VL}}{\mu }$ Flow in a closed conduit. Resistance experienced by submarines, airplanes, fully immersed bodies. 02 Froude No. $\sqrt {\frac{{{F_i}}}{{{F_g}}}} = \frac{V}{{\sqrt {gL} }}$ Where a free surface is present and gravity force is predominant such as Spillway, weirs, Open Channels, waves in ocean. The flow of jet from an orifice or nozzle. Fluids of different densities flow over one another. 03 Euler No. $\sqrt {\frac{{{F_i}}}{{{F_P}}}} = \frac{V}{{\sqrt {p/\rho } }}$ In cavitation studies. Where pressure force is predominant. (Used in a closed pipe where turbulence is fully developed so that viscous forces are negligible.) 04 Mach No. $\sqrt {\frac{{{F_i}}}{{{F_e}}}} = \frac{V}{C}$ Where fluid compressibility is important. Launching of rockets, airplanes, and projectiles moving at supersonic speed. Underwater testing of torpedoes. Water-hammer problems. 05 Weber No. $\sqrt {\frac{{{F_i}}}{{{F_\sigma }}}} = \frac{V}{{\sqrt {\sigma /\rho L} }}$ In Capillary studies. Where Surface tension is predominant. The capillary rise in narrow passages. Capillary movement of water in the soil. Capillary waves in channels. Flow over weirs for small heads.

So here both the statements are correct.