List of top Fluid Mechanics and Marine Hydrodynamics Questions

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?