List of top Fluid Mechanics and Marine Hydrodynamics Questions asked in GATE Naval Architecture and Marine Engineering

An ocean wave is propagating from deep to shallow water. The wave is approaching the coast at \( 45^\circ \) counterclockwise from the shore normal with an initial phase speed of \( 12.5 \, {m/s} \). After entering the shallow water, the wave direction becomes \( 30^\circ \) counterclockwise from the shore normal. The phase speed of the wave at the shallow water is ________ m/s (rounded off to one decimal place).

A negligibly thin horizontal plate PQ has a length 3 m and width 1 m. It is being pulled along its length at a speed of 1 m/s in between two static parallel plates as shown in the figure. The gap of 6 cm between the plates is filled with a Newtonian fluid of dynamic viscosity \( \mu = 0.2 \, {N-s/m}^2 \). The thin plate is located at 3 cm from the top surface. The velocity distribution between the thin plate and the static plates is linear.

The steady force required to pull the plate is __________ N (answer in integer).

Air flows with a velocity of \( 2 \, {m/s} \) over a flat stationary surface parallel to its length of \( 0.5 \, {m} \). Kinematic viscosity of air \( \nu \) is \( 1.5 \times 10^{-5} \, {m}^2/{s} \). Using Blasius solution, the boundary layer thickness at the trailing edge of the surface is ________ mm (rounded off to two decimal places).

Match the non-dimensional numbers in Column 1 with the corresponding definitions in Column 2:

Choose the correct statement(s) from the following with respect to a ship-generated Kelvin wave pattern in deep water.
For a freely floating body in water, which of the following degrees of freedom has/have inherent restoring force?
According to linear water wave theory, at a point on the free surface of a regular wave, the phase difference between the free surface elevation and the horizontal water particle acceleration is ________.
Which one of the following wave energy spectra is formulated for two peaks?
In a laminar boundary layer, the ratio of boundary layer thickness (\( \delta \)) to the corresponding displacement thickness (\( \delta^* \)) lies between ________.
The ratio of the magnitudes of vorticity to rate of rotation in a fluid flow is ________.
Identify the range of Reynolds number (Re) for a creeping flow.
The sum of the static pressure and dynamic pressure at a point in a fluid flow is called the ________.
The stream function of a two-dimensional flow field is given as \( \psi = 2xy + 2y + 2x \). The coordinates of two points \( P \) and \( Q \) in the flow field are \( (1, 2) \) and \( (2, 5) \) respectively. The magnitude of flow discharge between the streamlines passing through \( P \) and \( Q \) is ________ (answer in integer).
Consider a rectangular barge of length \( L = 100\, {m} \), breadth \( 25\, {m} \), and draught \( 10\, {m} \). The barge has the following non-dimensional hydrodynamic derivatives: \[ Y_v' = -1000 \times 10^{-5}, \quad N_r' = -800 \times 10^{-5}, \quad N_v' = -200 \times 10^{-5}, \quad Y_r' = 100 \times 10^{-5} \] The stability criterion \( C' \) is given by: \[ C' = Y_v'(N_r' - m' x_G') - (Y_r' - m') N_v' \] where \( m' = \frac{m}{\frac{1}{2} \rho L^3} \), \( m \) is the mass of the barge, \( \rho \) is the density of seawater, and \( x_G \) is the distance of the center of gravity from the origin. Which one of the following is correct regarding the controls-fixed straight-line stability?