List of practice Questions

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?

Consider the contour integral \( \oint_C \frac{dz}{z^4 + z^3 - 2z^2} \), along the curve \( |z| = 3 \) oriented in the counterclockwise direction. If Res[f, z\(_0\)] denotes the residue of f(z) at the point z\(_0\), then which of the following are TRUE?

A submerged cylinder of diameter 1 m is rotating clockwise at 100 rpm, in a flow with a free stream velocity of 10 m/s. Assuming ideal flow, the number of stagnation points on the cylinder is