Final answer:
The specific power for motion at high speed for a swordfish with given parameters is approximately 0.158 kW/kg, calculated using the formula ½C₀ₓρAv³ and factoring in the drag coefficient, fluid density, cross-sectional area, and velocity.
Step-by-step explanation:
To calculate the specific power for motion at high speed, we use the formula ½C₀ₓ
hoAv³, where C₀ₓ is the drag coefficient, ρ (rho) is the density of the fluid (seawater, in this case), A is the cross-sectional area, and v is the velocity.
The swordfish has a mass of 650 kg, a cross-sectional area of 0.92 m², a drag coefficient of 0.0091, and can sustain a speed of 30 m/s.
The density of seawater is 1026 kg/m³.
To find the power, we multiply the constant ½ by the drag coefficient, seawater density, cross-sectional area, and the cube of the velocity:
Power = ½ × 0.0091 × 1026 kg/m³ × 0.92 m² × (30 m/s)³
Power = ½ × 0.0091 × 1026 × 0.92 × 27000
Power = 0.004155 × 1026 × 0.92 × 27000 ≈ 102.484 kW
To determine the specific power, we then divide the power by the mass of the swordfish:
Specific Power = 102.484 kW / 650 kg
≈ 0.158 kW/kg
Therefore, the specific power for motion at the high speed for the swordfish is approximately 0.158 kW/kg.