Question

The drag force, Fd, imposed by the surrounding air on a

vehicle moving with velocity V is given by
Fd 5 CdA12
rV2
where Cd is a constant called the drag coefficient, A is the
projected frontal area of the vehicle, and r is the air density.
Determine the power, in hp, required to overcome aerodynamic
drag for an automobile moving at (a) 25 miles per hour,
(b) 70 miles per hour. Assume Cd 5 0.28, A 5 25 ft2, and r 5
0.075 lb/ft2.

Answer 1

a) 23.551 hp

b) 516.89 hp

Step-by-step explanation:

given:

`F_(d) =(1)/(2) C_(d) A_(p) V^(2) \\V_(a)=25 m/hr-->25*(5280)/(3600) =36.67ft/s\\V_(b)=70 m/hr-->70*(5280)/(3600) =102.67ft/s\\\\C_(d)=.28\\A=25 ft^2\\p=.075lb/ft^2`

required:

the power in hp

solution:

`(F_(d))_(a) =(1)/(2) C_(d) A_(p) V_(a) ^(2)`.............(1)

by substituting in the equation (1)

=353.27 lbf

`(F_(d))_(b) =(1)/(2) C_(d) A_(p) V_(b) ^(2)`..........(2)

by substituting in the equation (2)

= 2769.29 lbf

power is defined by

P=F.V

`P_(a)=`353.27*36.67

=12954.411 lbf.ft/s

=12954.411*.001818

=23.551 hp

`P_(a)=`2769.29*102.67

= 284323 lbf.ft/s

= 284323*.001818

= 516.89 hp