In 1993 the radius of hurricane emily was about 350 km. the wind speed near the center ("eye") of the hurricane, whose radius was about 30 km, reached about 200 km/h. as air swirled in from the rim of the hurricane toward the eye, its angular momentum remained roughly constant. estimate
a. the wind speed at the rim of the hurricane.
b. the pressure difference at the earth's surface between the eye and the rim.
c. if the kinetic energy of the swirling air in the eye could be converted completely to gravitational potential energy, how high would the air go?
d. in fact, the air in the eye is lifted to heights of several kilometers. how can you reconcile this with your answer to part c?

a. v_r = 17.14 km/h

b. P_r - P_e = 1838.55 N/m²

c. h = 157.50 m

d. Air is compressible and does not meet the Bernoulli equation. There are more variables that change the behaviour of the air:

Explanation:

a. If angular momentum is constant: (I_r)(ω_r) = (I_e)(ω_e)

Since ω = v/r and I = mr²

Thus,

(m(r_r)²)(v_r/r_r) = (m(r_e)²)(v_e/r_e) ⇒ (v_r)(r_r) = (v_e)(r_e)

⇒ v_r = ((v_e)(r_e))/r_r

          = ((200)(30))/350

          = 17.14 km/h

b. v_e = 55.56 m/s      v_r = 4.76 m/s

   h_e  = 0                    h_r = 0 (Earth's surface)

By Bernoulli's equation:

P_r + ρg(h_r) + 1/2(ρ)((v_r)²) = P_e + ρg(h_e) + 1/2(ρ)((v_e)²)

P_r - P_e = 1/2(ρ)((v_e)²- (v_r)²) = 1/2(1.20)(55.56² - 4.76²)

                = 1835 N/m²

Since P_r - P_e > 0 ⇒P_r > P_e (pressure is higher in the rim)

c. Kinetic Energy = Gravitational Potential Energy

1/2(m)(v_e)² = mgh

⇒ h = (v_e)²/2g

      = (55.56)²/2(9.80)

      = 157.50 m

d. Air is compressible and does not meet the Bernoulli equation. There are more variables that change the behaviour of the air:

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:

80cm/s.

24cm/s.

53.3cm/s.