List of practice Questions

A tsunami that originated off the Indonesian coast has propagated towards the east-coast of India. It enters the continental shelf at 150 km away from the coast of Chennai. If the average water depth is 80 m from the coast to the continental shelf and 20 minutes is the tsunami period, the time taken by the tsunami to reach the coast of Chennai on entering the continental shelf is .................... hours (round off to two decimal places)

A buoy of virtual mass 30 kg oscillates in a fluid medium as a single degree of freedom system. If the total damping in the system is set as 188.5 N-s/m, such that the oscillation just ceases to occur, then the natural period of the system is .................... s (round off to one decimal place)

For a marine screw propeller, the open water characteristics at J = 0.6 are \(K_T = 0.1336\) and \(10K_Q = 0.2010\). The open water propeller efficiency \(\eta_o\), is .................... (round off to two decimal places)

Saturated liquid water (m = 1 kg) initially at 0.101 MPa and 100 °C is heated at constant pressure until the temperature increases to 500 °C. Assume a constant \(C_p\) of steam = 1.9 kJ/kg-K, and enthalpy of vaporization, \(h_{fg}\) = 2257 kJ/kg at 0.101 MPa. The change in entropy of the water is .................... kJ/K (round off to two decimal places)

The stress field, \(\sigma_x = 4x^3 + 3x^2y + 5xy^2\) \(\sigma_y = -x^3 + 6x^2y - 7xy^2\) \(\tau_{xy} = -5x^2y - 3xy^2\) would satisfy the strain compatibility condition if

If y(x) is the solution of the differential equation \[ (1+x^2)y'' - 2xy' = 0 \] satisfying y(0) = 0 and y'(0) = 3, then y(1) equals ....................

For a ship of length L = 100 m, the distance between the bow and stern pressure system is 0.942L. Assume g = 10 m/s². The ship velocity corresponding to the prismatic hump of the wave making resistance curve is .................... m/s (round off to one decimal place)

For a given time varying load applied on a single degree of freedom system, the dynamic response amplitude is always less than the static response amplitude if

An insulated nozzle has an inlet cross-sectional area of 314 cm². Air flows through the nozzle with an inlet temperature of 300 K at a steady rate of 1.256 m³/s. The velocity at the exit is greater than that at the inlet by 210 m/s. Assume a constant \(C_p = 1.004\) kJ/kg-K. The temperature (in K) of air at the exit of the nozzle lies between

The heave natural frequencies of a Jacket structure, FPSO and a semi-submersible are \(\omega_J\), \(\omega_F\) and \(\omega_S\) respectively. Each one of them has a pay load capacity of 10000 tonnes. Which of the following is TRUE?

A vertical frictionless piston-cylinder arrangement contains air of mass 1 kg. During a process, 50 J of heat is transferred from outside to the system such that the piston is raised slowly by 0.1 m from its initial equilibrium position. The mass of the piston is 1 kg, and the diameter is 0.1 m. Assume that g = 9.81 m/s², and Patm = 100 kPa. The change in internal energy of the air in J (round off to two decimal places) lies between
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For a 2D ideal flow, let \(\varphi\) be the velocity potential and \(\psi\) be the stream function. Which one of the following is TRUE?

The velocity vector of a 2D flow field is given by \(\vec{V} = 2y^2 \hat{i} + x^2t \hat{j}\).
The acceleration is
Note: There's a typo in the OCR of the question (î twice) and options. The solution assumes the standard form V = uî + vĵ.

Water is flowing with a free stream velocity of 0.25 m/s around a submerged flat plate of 2 m length (in the direction of flow) and 1 m width. The local shear stress at a distance \(x\) from the leading edge of the plate is given by \[ \tau = \frac{0.332\rho u^2}{\sqrt{Re_x}} \] where \(\rho = 1000\) kg/m³ is the density of the water, \(u\) is the free stream velocity and \(Re_x\) is the Reynolds number at \(x\). Assume that the flow is laminar, and the kinematic viscosity of water is \(10^{-6}\) m²/s. The drag force (in Newton) acting on one side of the plate lies between

A ship of length 125 m has a design speed of 25 knots (1 knot = 0.5144 m/s). A 5.0 m long geometrically similar model with wetted surface area of 4 m\(^2\) has a coefficient of residuary resistance of \(1.346 \times 10^{-3}\) at the corresponding speed. The ship's residuary resistance in kN (in sea water of density 1025 kg/m\(^3\)), and the model speed in knots (round off to the nearest integer) respectively are

A solid cantilever shaft of diameter 0.1 m and length 2 m is subjected to a torque of 10 kN-m at the free end (shear modulus is 82 GPa). The maximum induced shear stress is .................... N/mm\(^2\) (round off to the nearest integer).

The value of the surface integral \( \iint_S (x^2 \,dydz + y^2 \,dzdx + z^2 \,dxdy) \) over the surface of the cube given by \( 0 \le x \le 2, 0 \le y \le 2, 0 \le z \le 2 \), is

An oil tanker of breadth 20 m and having a displacement of 24000 tonnes in sea water (density of sea water = 1025 kg/m\(^3\)) is carrying oil of relative density 0.8 in 9 longitudinally distributed tanks which are all half-filled. Each longitudinal tank is 12 m long and 16 m wide. The apparent change in vertical center of gravity, due to the presence of oil in the tanks is .................... m (round off to one decimal place)

For a regular sinusoidal wave propagating in deep water having wave height of 3.5 m and wave period of 9 s, the wave steepness is .................... (round off to three decimal places)

A ship of length 180 m has a displacement of 14400 tonnes and is floating on an even keel in sea water of density 1025 kg/m\(^3\). The trim changes by 0.18 m when a weight of 120 tonnes that is already onboard, is shifted 24 m forward. The longitudinal metacentric height is .................... m.

A piezometer and a pitot tube measure the static and the total pressure of a fluid in a pipe flow respectively. The piezometer reads 100 kPa and the pitot tube shows 200 kPa. The density of the fluid is 1000 kg/m\(^3\). The velocity of the flow is .................... m/s (round off to one decimal place)

A Carnot heat engine operates between two reservoirs of temperatures 900 \(^{\circ}\)C (T\(_H\)) and 30 \(^{\circ}\)C (T\(_L\)). If the heat transferred during one cycle to the engine from T\(_H\) is 150 kJ, then the energy rejected to T\(_L\) is .................... kJ (round off to the nearest integer)

A stationary ship has longitudinal symmetry. The surge, sway and heave motions are represented by indices 1-2-3, respectively and roll, pitch and yaw motions are represented by indices 4-5-6, respectively. Which of the following are TRUE about the added mass (\(A_{ij}\))?

The failure modes that may be observed in a riveted joint to fasten two plate members, subjected to shear load are

Let X be any random variable and \( Y = -2X + 3 \). If E[Y] = 1 and E[Y\(^2\)] = 9, then which of the following are TRUE?