FLUID MECHANICS (ME-404) - Important Questions

Explain the stability of a floating body in terms of centre of gravity, centre of buoyancy and metacentre, and why CG vs CB position alone is insufficient.

Determine the total hydrostatic pressure force and location of centre of pressure on a plane surface immersed vertically/inclined in a liquid.

Determine total hydrostatic pressure force and centre of pressure on a vertically immersed rectangular plate / vertical wall of tank.

What is the continuum hypothesis in fluid mechanics, when does it break down, and define metacentre and metacentric height with conditions for stable, unstable and neutral equilibrium of a floating body?

Determine the (average) bulk modulus of elasticity of a liquid from a given pressure increase and corresponding volume decrease or density increase.

Explain the hydrostatic paradox and the effect of shape of vessel on liquid pressure.

Explain Newtonian fluid, non-Newtonian fluid and vapour pressure.

Determine power required to rotate a disc over a viscous fluid film.

Prove that the free surface in forced vortex flow is a parabola.

Differentiate shear thinning and shear thickening fluids with graphical representation.

State Newton's law of viscosity and explain viscosity / Newtonian fluid behaviour.

Define dynamic viscosity and kinematic viscosity with units.

Describe the different types of fluid flow and distinguish between steady vs unsteady, uniform vs non-uniform, compressible vs incompressible, rotational vs irrotational, and laminar vs turbulent flow.

Given a 2D stream function $\psi$, determine the corresponding velocity potential $\Phi$.

Distinguish between Lagrangian and Eulerian methods and derive the 3-D continuity equation for steady incompressible flow.

In a two-dimensional incompressible fluid flow, the velocity components are given by $u = x^2-y^2$ and $v = -2xy$.

Define flow net and explain graphical and analytical methods of construction, with applications and limitations.

Apply the continuity equation to pipe flow to find discharge, velocity at changed / branched sections, and mass rate of flow.

Determine the location of the stagnation point for a given steady, incompressible, two-dimensional velocity field.

Explain rotation, vorticity, circulation, velocity potential, stream function, streamline and pathline.

Define and explain path line, streamline, streak line and stream tube.

Explain the physical significance of divergence ($\nabla \cdot \mathbf{V}$) and curl ($\nabla \times \mathbf{V}$) of the 3D fluid velocity vector in fluid mechanics.

Given velocity components $u$ and $v$ in 2D incompressible flow, derive the stream function, check for irrotationality, and compute velocity at a point.

Define stream function and velocity potential function and prove that streamlines and equipotential lines intersect orthogonally.

State and prove (derive) Bernoulli's theorem for flow along a streamline with assumptions

State Bernoulli's theorem and derive/prove Bernoulli's equation from Euler's equation along a streamline with assumptions, and explain modification for real viscous flows

Determine venturimeter throat area or discharge from continuity, Bernoulli and manometer reading neglecting losses or using $C_d$.

Determine the required diameter of a parachute (or its terminal velocity) from vertical equilibrium between weight and aerodynamic drag, $W = C_D \cdot \frac{1}{2}\rho A V^2$.

Calculate head loss between two points A and B from pressure difference measurements with valve closed and open.

Calculate the frictional torque at the axis of a rotating lawn sprinkler given jet diameter, arm diameter, rotational speed and discharge.

Estimate the resultant force exerted by fluid on a 90-degree horizontal pipe bend given diameter, discharge, fluid properties and inlet pressure.

How concept of control volume is more important than the concept of system in fluid mechanics.

What is a venturimeter and derive the expression for discharge / rate of flow through it

Derive Euler's equation along a streamline.

Write short notes on any three:

Find the diameter of a hemispherical parachute given weight, terminal descent velocity, drag coefficient and air density.

Derive the Hagen-Poiseuille equation for pressure drop in steady laminar flow through a horizontal circular pipe and show that the friction factor is $f = 64/Re$.

Calculate discharge through a reservoir-connecting pipeline with given diameter, length, head difference and friction factor, considering (i) major losses only and (ii) all losses including entry and exit.

Write the Navier-Stokes equation in Cartesian coordinates with physical significance of each term, and explain Hydraulic Gradient Line (HGL) and Total Energy Line (TEL).

Determine the discharge through pipes connected in series for a given head difference and the equivalent diameter of a single pipe replacing the compound system.

For laminar flow in a circular pipe with given diameter and maximum velocity, find the mean velocity, the radius at which mean velocity occurs, and the velocity at a given distance from the wall.

Write short notes on Hydraulic, gradient line, total energy line, Major and minor losses in case of flow through pipes.

State the Navier-Stokes equation and explain its uses.

Explain the flow phenomenon between two parallel plates kept at distance 2h apart.

Explain minor and major losses in pipe flow and derive Chezy's formula for head loss due to friction.

Derive the expression for velocity distribution for viscous flow through a circular pipe.

Calculate power loss / pumping power required due to friction in a circular pipe given length, diameter, discharge and friction factor.

Two pipes each $300\, \text{m}$ long are available for connecting to a reservoir from which a flow of $0.085\, \text{m}^3/\text{s}$ is required. If diameters of the two pipes are $300\, \text{mm}$ and $150\, \text{mm}$ respectively, determine the ratio of head lost when the pipes are connected in series to the head lost when connected in parallel. Neglect minor losses.

Explain boundary layer separation and the effect of pressure gradient on it.

Explain boundary layer separation and describe the methods to prevent or delay separation.

For the cubic profile $u/U = \frac{3}{2}(y/\delta)-\frac{1}{2}(y/\delta)^3$ over a flat plate, express displacement and momentum thickness in terms of $\delta$ and calculate drag force.

Define stagnation temperature, pressure and density and derive $T_0$ in terms of $T$, $M$ and $\gamma$ for isentropic flow.

Explain normal shock waves in compressible flows. Why does a shock wave only occur in supersonic flows? Briefly explain the significance of Fanno and Rayleigh lines with the help of an h-s (enthalpy-entropy) diagram.

For the boundary-layer velocity profile $\frac{u}{U} = 2\left(\frac{y}{\delta}\right) - \left(\frac{y}{\delta}\right)^2$, compute the boundary-layer thicknesses (displacement, momentum, energy thickness).

Write short notes on Stagnation Properties.

A smooth flat plate 1.5 m wide and 2 m long is subjected to flow of water along its length at a uniform velocity of 2 m/s. Find ($\rho = 998$ kg/m$^3$, $\nu = 10^{-6}$ m$^2$/s).

Evaluate the boundary layer thickness $\delta$ and skin friction coefficient $C_f$ for flow over a flat plate by using following profile.

Write the short note on the following:

Define Mach number. What is the significance of Mach number in compressible fluid flows?

Explain separation of boundary layer and the different methods of preventing boundary layer separation.