GATE Mechanical Engineering (ME) 2019 Shift 2 Solved Paper

Question : 55 of 65

Marks: +1, -0

The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of 0.1with the windows and the roof closed. With the windows and the roof open, the drag coefficientbecomes 0.8. The car travels at 44 km/h with the windows and roof closed. For the sameamount of power needed to overcome the aerodynamic drag, the speed of the car with thewindows and roof open (round off to two decimal places), is ________km/h (the density of airand frontal area may be assumed to be constant).

Your Answer:

Validate

Solution:

The power needed to overcome the aerodynamic drag is given by

F_{d} × V

Where,

F_{d}

is the drag force given by

F_{d}=1 / 2 C_{d} ρ A V^{2}

For the power to remain same in both the cases of windows closed and open, then

(F_{d} × V)_{\;\text "windows closed "\;}=(F_{d} × V)_{\;\text "windows open "\;}

Or,

(1 / 2 C_{d} ρ A V^{3})_{\;\text "windows closed "\;}=(1 / 2 C_{d} ρ A V^{3})_{\text "windows open "\;}

Or,

0.1 × 44^{3}=0.8 × V^{3}

{V}=22 {km} {/} {h}

Go to Question:

Prev Question

Next Question