PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY

#### Concept explainers

Question
100%
Chapter 2, Problem 1P
To determine

## The power required to overcome the aerodynamics drag.

The power required to overcome the aerodynamics drag is 57.19hp

### Explanation of Solution

Given:

Drag Coefficient of sports car, CD = 0.30

Front area of the car, A=21ft2

Speed of the car, V = 110mi/h

Density, ρ = 0.002378slugs/ft2

Formula Used:

The power required to overcome the aerodynamic drag is

P = F × V

Where,

Force =

Velocity = V

Calculation:

The required power is calculated by power equation

P = F × V ..................... (1)

We know that

Force applied on caris given by

F = 12ρACDV2 ...................... (2)

Where,

Density = ρ

Front Area of the Car = A

Drag coefficient = CD

Rearranging the equation (1) as

P = F × V

P = (12 ρACD×V2) ×(V)

P = (12 ρACD)×V3   .................. (3)

To calculate power in (lb-ft/r), we have to convert the velocity from mi/h to ft / sec

V = 110 mi/h = 110×52803600ft/s

As -

1mi/h = 5280 ft3600 sec

Put the given values in equation (3)

P = (12  ρACD)×V3P = (12×0.002378×21×0.3)×( 110×5280 3600)3

P = 31455.364 lb-ft/s .......................... (4)

But we want the power in hp -

We know that - 1 lb-ft/s  = 1550hp

So, the calculated power of equation (4) is converted into hp as

P = 31455.364550hpP = 57.19 hp

Conclusion:

Thus, the power required to overcome the aerodynamics drag is 57.19hp

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