DIMENSIONAL ANALYSIS PROBLEM Hi, the answer below says, \"By observation v and I

Question

DIMENSIONAL ANALYSIS PROBLEM Hi, the answer below says, "By observation v and I are repeated'. How do I know this, THANKS QUESTION A hydrofoil moves over water with a speed of 0.8 m/s. In order to predict the drag, D, a 1/20 scale model is built. (a) The drag is known to depend on the length of the hydrofoil, , its velocity, v, the density of the water, p, and the acceleration due to gravity, g. Use the Buckingham Pi method to show that gl pv2l2 ANSWER 5 parameters, 3 dimensions 2 principle and 3 repeated variables. [1] By observation v and 1 repeated. Choose D and g to be principle (OR p and g)

Explanation / Answer

There are certain consideration to choose the repeating variables. The number of repeating variables are equal to the number of fundamental dimensions of the problem.

Considerations to choose repeating variables :-

1. As far as possible, the dependent variable should not be selected as repeating variable.

2. The repeating variable is chosen in such a way that one variable contains geometric property, other variable contain flow property and third variable contains fluid property .

Variables with Geometric property are - Length , Diameter, Height etc

Variables with flow property are - Velocity and acceleration

Variables with fluid property are - Viscosity, Density

3. The repeating variables selected should not form a dimensionless group.

4. The repeating variables together must have the same number of fundamental dimensions.

5. No two repeating variables should have the same dimensions.

The choice of repeating variables may be like

Length, density, velocity

Diameter, velocity, density.

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