KVPY Sample Paper KVPY Stream-SX Model Paper-16

In a wind tunnel used to test drag force on car using their models a 20 cm high car model is used for testing a car 550 cm high. Let you want to calculate drag force on car, when it is moving at \[15\,m{{s}^{-1}}\] in still air. Wind speed in the tunnel must be kept around

A) \[4\,km{{s}^{-\,1}}\]

B) \[4\,km{{h}^{-\,1}}\]

C) \[0.4\,km{{s}^{-\,1}}\]

D) \[0.4\,km\,{{h}^{-\,1}}\]

Correct Answer: C

Solution :

To keep situations similar, we must keep reynolds number of flow same in both cases.

\[\Rightarrow \] \[{{N}_{R}}={{\left( \frac{\rho vD}{\eta } \right)}_{\text{model}}}={{\left( \frac{\rho vD}{\eta } \right)}_{\text{car}}}\]

\[\Rightarrow \] \[{{v}_{m}}{{D}_{m}}={{v}_{c}}{{D}_{c}}\]

\[\Rightarrow \] \[{{v}_{m}}={{v}_{c}}\cdot \frac{{{D}_{c}}}{{{D}_{m}}}=15\times \left( \frac{550}{20} \right)=0.4\frac{km}{s}\]