Question

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.

Answer 1

Hope it helps.

Prototype is the actual structure while model is the clone of it with same ratio of dimension or force and velocity. In this way we have geometry similarity which says, there should be similarity in dimensions. Now we have some examples which have same geometric similarity and reynold number but they aren't kinematically similar.

1- Aircraft's or spacecraft's model are designe with similar dimension for test purpose and the velocity condition set to be similar as provided by atmosphere of earth and space respectively. So, the reynold number would be the same. But while travelling through the actual air, the direction of velocity and acceleration might change due to weather condition which surely change the ratio of kinematc similarity.

2- Model car tested in wind tunnel would be the example of this situation. In which the dimension designed similar as prototype and velocity inside the wind tunnel also kept similar as actual practice which makes reynold number same. Actual condition of wind for prototyle can change the acceleration and hence kinematic similarity can't hold in it.

3- Hydraulic turbine on a dam moving with the constant velocity, should have similar model dimensionally. And velocity of water for model could have designed similar as prototype's surrounding. But water speed can change with rainfall and any other obstacles present in the water or design, which will make them kinematically dissimilar.