A ship of 5000 tonne displacement has two empty rectangular double bottom tanks with dimensions:
Tank A: length 12 m, width 16 m, and height 2 m
Tank B: length 16 m, width 12 m, and height 2 m
The length of each tank is oriented along the length of the ship. It is required to ballast the ship with 192 m\(^3\) of seawater of density 1025 kg/m\(^3\). Which one of the following scenarios will minimize the free surface effect?
Tank A: length 12 m, width 16 m, and height 2 m
Tank B: length 16 m, width 12 m, and height 2 m
The length of each tank is oriented along the length of the ship. It is required to ballast the ship with 192 m\(^3\) of seawater of density 1025 kg/m\(^3\). Which one of the following scenarios will minimize the free surface effect?
Show Hint
- 100% of the given ballast water is filled in Tank A.
- 100% of the given ballast water is filled in Tank B.
- 50% of the given ballast water is filled in Tank A and the remaining in Tank B.
- 40% of the given ballast water is filled in Tank A and the remaining in Tank B
The Correct Option is B
Solution and Explanation
Step 1: Understanding free surface effect.
The free surface effect depends on the second moment of area (moment of inertia) of the tank's free surface. \[ I = \frac{b^3 l}{12} \] where \( b \) is the breadth of the tank (transverse dimension), and \( l \) is the length.
Step 2: Compare Tank A and Tank B.
Tank A: \( b = 16 \, {m} \), \( l = 12 \, {m} \) \[ I_A = \frac{16^3 \cdot 12}{12} = 4096 \] Tank B: \( b = 12 \, {m} \), \( l = 16 \, {m} \) \[ I_B = \frac{12^3 \cdot 16}{12} = 2304 \] Step 3: Select the tank with smaller free surface moment.
Since \( I_B<I_A \), Tank B contributes less to the free surface effect. Hence, filling 100% of the ballast water in Tank B is the best option.
Top Questions on Ship Dynamics
A ship of 3300 tonne displacement is undergoing an inclining experiment in seawater of density 1025 kg/m\(^3\). A mass of 6 tonne is displaced transversely by 12 m as shown in the figure. This results in a 0.12 m deflection of a 11 m long pendulum suspended from the centerline. The transverse metacenter of the ship is located at 7.25 m above the keel.
The distance of the center of gravity from the keel is ________ m (rounded off to two decimal places).
A multi-cell midship section of a ship with \( B = 40 \, {m} \) and \( D = 20 \, {m} \) is shown in the figure. The shear-flows are given as \( q_1 = q_2 = q_3 = 0.9376 \, {MN/m} \). The applied twisting moment on the midship section is ___________ MN·m (rounded off to two decimal places).
Consider a case where the load \( Q \) for a ship structure has only statistical uncertainties. The probability density function of the load \( p_Q(x) \) is shown in the figure. The characteristic limit value of the load \( Q_L \) is 1.5 and the factor of safety is 1. Which of the following probability of exceedance value(s) of the load will lead to a safe design?
- The dynamics of a 90 m long ship are governed by the non-dimensional Nomoto equation. The magnitude of Nomoto gain \( |K'| = \frac{72}{35\pi} \) and that of Nomoto time constant \( |T'| = \frac{288}{35\pi} \). The steady turning radius of the ship for a 35° turning circle maneuver is ________ m (answer in integer).
- A ship of length 100 m and displacement 5000 tonne floats even-keel at 6.5 m in fresh water of density 1000 kg/m\(^3\). The ship’s hydrostatic properties are:
MCT per cm is 10 tonne-m, TPC in seawater is 6.25,
LCB is 2 m forward of amidship,
LCF is 2 m forward of amidship.
The ship has moved to seawater of density 1025 kg/m\(^3\) without change in the displacement. The new forward and aft draughts are ________ respectively.
Questions Asked in GATE NM exam
- If \( P e^x = Q e^{-x} \) for all real values of \( x \), which one of the following statements is true?
Bird : Nest :: Bee : __________
Select the correct option to complete the analogy.- Consider the function \( f(x) = |x| - 1 \). Which of the following statements is/are true in the interval \([-10, 10]\)?
- GATE NM - 2025
- Continuity and differentiability
A closed system is undergoing a reversible process 1–P–2 from state 1 to 2, as shown in the figure, where X and Y are thermodynamic properties. An irreversible process 2–Q–1 brings the system back from 2 to 1. The net change in entropy of the system and surroundings during the above-mentioned cycle are _______ respectively.
- GATE NM - 2025
- Thermodynamics
Consider a weightless, frictionless piston with a 2 kg mass placed on it as shown in the figure. At equilibrium in position 1, the cylinder contains 0.1 kg of air. The piston cross-sectional area is 0.01 m2. The ambient pressure in the surroundings outside the piston-cylinder arrangement is 0 bar (absolute). When the mass above the piston is removed instantaneously, it moves up and hits the stop at position 2, which is 0.1 m above the initial position.
Assuming \( g = 9.81 \, {m/s}^2 \), the thermodynamic work done by the system during this process is ________ J (answer in integer).
- GATE NM - 2025
- Thermodynamics