Question

A submarine can be treated as an ellipsoid with a diameter of 5 m and a length of 25 m. Determine the power required for this submarine to cruise horizontally and steadily at 49 km/h in seawater whose density is 1025 kg/m3. Also determine the power required to tow this submarine in air whose density is 1.30 kg/m3. Assume the flow is turbulent in both cases. The drag coefficient for an ellipsoid is CD= 0.1. The flow is turbulent and the drag of the towing rope is negligible.The power required for the submarine to cruise in seawater is ...The power required to tow this submarine in air is...

Answer 1

To determine the power required for the submarine to cruise horizontally and steadily in seawater, we need to calculate the drag force acting on the submarine using the drag coefficient, cross-sectional area, fluid density, and velocity. The power required can be calculated using the formula: Power = Drag Force * Velocity.

Step-by-step explanation:

To determine the power required for the submarine to cruise horizontally and steadily in seawater, we need to calculate the drag force acting on the submarine. The drag force can be calculated using the formula:

Drag Force (Fd) = 0.5 * Cd * A * rho * v^2

Where:
- Cd is the drag coefficient (given as 0.1 in the question)
- A is the cross-sectional area of the submarine (calculated as pi * r^2, where r is the radius)
- rho is the density of the fluid (1025 kg/m^3 for seawater)
- v is the velocity of the submarine (converted from 49 km/h to m/s)

The power required for the submarine can then be calculated using the formula:

Power (P) = Fd * v

Answer 2

The power required for the submarine to cruise in seawater is approximately 816700 watts. The power required to tow the submarine in air is approximately 1525 watts.

Step-by-step explanation:

To determine the power required for the submarine to cruise in seawater, we can use the formula for power: Power = Force * Velocity. The force can be calculated using the drag equation: Force = 0.5 * Density * Velocity² * Cross-sectional Area * Drag Coefficient. The cross-sectional area of the submarine can be approximated as the area of an ellipse: Area = π * (Diameter/2) * (Length/2).

Plugging in the given values and solving the equations, we find that the power required for the submarine to cruise in seawater is approximately 816700 watts. To calculate the power required to tow the submarine in air, we can use the same formulas but with the density of air instead of seawater. The power required to tow the submarine in air is approximately 1525 watts.