The Cessna Citation executive jet weighs 67 kN and has a win

The Cessna Citation executive jet weighs 67 kN and has a wing area of 32 m2. Using a lift coefficient of 0.21 and a drag coefficient of 0.015. Plot both (a) the cruise speed in m.p.h. and (b) the power required in kW to maintain cruise velocity as a function of the altitude up to 10 km. Note: for simplicity you may model atmospheric density in this range using the linear interpolation: = ah + 0, where a=-78.3×106 kg/m4, 0=1.22 kg/m3 is the density of dry air at sea-level, and h is the altitude in meters.. Can someone help me with this problem

Solution

Input

Weight (W) = 67 kN
Wing area (S) = 82 m2

Lift Coefficient (CL) = 0.21

Drag coefficient (CD) = 0.015

Facts

Thrust = Drag

Lift = Weight

Flight altitude (h) = 10km

@10km = 78.3×106kg/m4 x 10000 = 78.3×102kg/m3

= 1.22 + 0.783 =

(a) The cruise speed

W = L = CL x ½ x x V2 x S

V= SQRT ( W / (½ x x S x Cl))

V = SQRT ( (67000/9.81) /   (½ x 2.003 x 32 x 0.21)

V= 31.86 meter per second = 71.27 mph

Cruising speed = 71.27 mph

(b) The power required

Power = D V

D = CD x ½ x x V2 x S

Power = 0.015x ½ x 2.003 x 31.86 x 31.86 x 32 x 31.86

          = 15546 W

Power required = 15.546 kW

Answer

Cruising speed = 71.27 mph

Power required = 15.546 kW