Consider the possibility of using two rotating cylinders to replace the conventional wings on an airplane for lift. consider an airplane flying at 150 km/hr through the standard atmosphere at 2,000 m. each "wing cylinder" has a 1.0-m radius. the surface velocity of each cylinder is 20 km/hr. find the length ℓ of each wing to develop a total lift of 40 kn. assume potential flow and neglect end effects. hints: = 2 r v see example 6.6

27.35m

Explanation:

For the calculation of the Support Force we rely on the formula for obtaining the force in a cylinder of a certain length l,

Here each term is,

= Lift force

= density of air

= vortex strength

For this last equation, its mathematical representation is given by,

Here each term is,

a= 1m, radios of cylinder

, the velocity of cylinder surface.

In order to find the density of the area at 2000m we will refer to the table of Standard Atmosphere of the United States, that is

Replacing the values,

Clearing l and solving for it we have,

In this way we can conclude that the length of the cylinder must be 27.35m

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

the answer would be c