An aircraft carrier contains primarily steel (density 8000 kg/m^3) and air (dens

Question

An aircraft carrier contains primarily steel (density 8000 kg/m^3) and air (density 1.29 kg/m^3). a. What maximum percentage of the carrier's interior can be steel, and what minimum percentage must be air, in order for the carrier to float? b. Water for the nuclear reactor onboard the carrier is supplied with water through a pipe with an initial radius of 0.50m, and a final radius of 0.10m. If the final speed of the water is 12.0 m/s and the pipe receives water from a pump located 20m below the coolant tank, what must be the initial water pressure that the pump provides? The outflow end of the pipe is open to the air.

Explanation / Answer

(A) Fnet = Weight - Fb = 0

suppose volume of steel is V1 and of air is V2.

(8000V1+ 1.29V2)g - (V1 + V2)(1000)g = 0

7000V1 = 998.71 V2

V2 = 7 V1

V1 + V2 = V1 + 7V1 = 8 V2

% of steel = 100/8 = 12.5 %

% of air = (7/8) x 100 = 87.5 %

(b) v2 = 12 m/s

A1^2 v1 = A2^2 v2^2

v1 = (0.10/0.50)^2 (12) = 0.48 m/s

Applying bernoulli's equation,

P + rho g h + rho v^2 /2 = constant

P1 + (1000 x 9.8 x 0 ) + (1000 x 0.48^2 /2) = (101325) + (1000 x 9.8 x 20) + (1000 x 12^2 / 2)

P1 = 101325 + 196000 + 71884.8

P1 = 369000 Pa

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