List of top Fluid Mechanics and Marine Hydrodynamics Questions

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

In dimensional analysis, according to Buckingham's \(\pi\)-theorem, if n is the total number of variables and m is the number of independent dimensions, then the maximum number of independent dimensionless \(\pi\)-groups will be

A steady incompressible laminar flow exists between two long parallel plates separated by \(h = 1\ \text{m}\). The bottom plate is fixed and the upper plate moves with velocity \(U = 10\ \text{m/s}\). The kinematic viscosity of the fluid is \(10^{-6}\ \text{m}^2/\text{s}\) and density is \(10^3\ \text{kg/m}^3\). No pressure gradient acts. Then the shear stress at the bottom plate is ____________ N/m\(^2\) (correct to two decimal places).

Consider a steady flow through a horizontal nozzle. The nozzle inlet area is 1 m\(^2\) and the outlet area is 0.05 m\(^2\). At the outlet, the flow discharges to atmosphere. Assuming the flow to be incompressible and frictionless, and the density of the fluid as 1 kg/m\(^3\), the gauge pressure required at the nozzle inlet to produce an outlet speed of 100 m/s is ________________ N/m\(^2\) (rounded off to nearest integer).

A rectangular barge has length (L) of 100 m, breadth (B) of 18 m and depth (D) of 10 m. It is subdivided transversely into four equal compartments of equal length with the end compartments loaded fully with oil of density = 0.9 tonne/m\(^3\). The barge floats in water having a density of 1000 kg/m\(^3\). If the hull structural weight is ignored, then the transverse metacentric height of the barge is ______________ m (correct to two decimal places).

Consider a point source in a uniform flow of velocity \(U = 4\) m/s along the positive \(x\)-axis as shown in the figure. Assume a two-dimensional steady potential flow. The potential due to the point source is given by \(\log_e(r)\), where \(r^2 = x^2 + y^2\). Then the magnitude of the distance \(d\) between the point source and the stagnation point is ________________ m (rounded off to two decimal places).

Which of the following statements are TRUE for a fluid flow over a deeply submerged body?

In a potential flow field, if the stream function \( \psi = xy^2 \), then the velocity potential \( \phi \) is:

The laminar and turbulent boundary layer thickness of a flat plate are: \[ \delta_l = \frac{5x}{Re_x^{1/2}}, \qquad \delta_t = \frac{0.37\,x}{Re_x^{1/5}} \] The fluid has kinematic viscosity \( \nu = 10^{-6}\ \text{m}^2/\text{s} \). A 100 m long plate moves at 10 m/s. The boundary layer thickness at the rear end of the plate is ____________ m (rounded to two decimals).

If a ship enters shallow water from deep water, maintaining the same speed, then which of the following are TRUE?

A truck loaded with a half-filled water tank is moving at a constant horizontal acceleration $a$. The acceleration due to gravity is $g$. At steady state, the angle $\theta$ made by the free surface with the horizontal plane is

Which one of the following combinations of elementary flows will lead to an ideal flow past a deeply submerged circular cylinder with circulation?