Fluid Mechanics-I (CE-501) - Important Questions

Define surface tension and explain/derive the excess pressure inside a liquid droplet, soap bubble and liquid jet

Numerical problem using a (inverted) differential manometer to find pressure difference or manometer fluid level between two points.

What is a manometer and what are its different types?

Find the density of a metallic body which floats at the interface of mercury of specific gravity 13.6 and water such that 40% of its volume is sub-merged in mercury and 60% in water.

Differentiate between absolute and gauge pressure, dynamic and kinematic viscosity, and cohesion and adhesion

Determine total pressure and centre of pressure on a vertically immersed isosceles triangular plate with base at free surface.

Explain stability of a floating body in terms of metacentric height and differentiate stable, unstable and neutral equilibrium.

State Newton's law of viscosity, define viscosity and kinematic viscosity, explain its importance and variation with temperature for liquids and gases.

Define absolute, gauge, vacuum and atmospheric pressures and state the relations between them.

Define the following fluid properties: Density, weight density, specific volume and specific gravity of a fluid.

Define and distinguish between the following set of fluid properties:

Determine dynamic viscosity for a plate sliding on an inclined plane lubricated by an oil film.

Explain and distinguish the different types of fluid flow: steady vs unsteady, uniform vs non-uniform, and rotational vs irrotational flow.

Given velocity potential $\phi(x,y)$, find velocity components and stream function / discharge between streamlines.

Given velocity components $U(x,y), V(x,y)$, obtain the stream function $\Psi$.

Define and distinguish streamlines vs streak lines and rotational vs irrotational flow.

What is a flow net and explain a method of drawing a flow net?

Given stream function $\Psi(x,y)$ for 2-D flow, check if flow is irrotational/rotational and find the velocity potential function.

Describe stream lines, equipotential lines and flow net with sketch and prove that stream lines and equipotential lines intersect orthogonally.

Differentiate the following:

Explain velocity potential function and stream function.

Define the equation of continuity and derive the three-dimensional continuity equation.

Describe in brief the velocity potential function, stream function and flow net.

Given velocity components $U(x,y,z,t), V(x,y,z,t), W(x,y,z,t)$, find the velocity and acceleration of a fluid particle at a given point and time.

Compare venturimeter vs orifice meter (and flow nozzle) as primary flow-measurement elements.

Numerically apply the venturimeter discharge formula to find throat diameter or differential manometer reading from flow rate.

State Bernoulli's theorem for steady flow of an incompressible fluid and derive Bernoulli's equation from first principles.

Prove that the kinetic energy correction factor is 2 for viscous (laminar) flow through a circular pipe.

Calculate orifice coefficients $C_v$, $C_c$ and theoretical discharge from measured velocity, head and actual discharge.

Write Bernoulli's equation, explain the terms in it, and state the assumptions made in its derivation.

Explain with a neat sketch the working of a Pitot / pitot-static tube for measuring velocity of flow at a point in a pipe or channel.

Write short notes on momentum theorem, stagnation point, Stokes law, limitations of Bernoulli's equation, bulk modulus of elasticity and Froude number.

Define and explain the kinetic energy correction factor and momentum correction factor for laminar and turbulent flow.

Define the momentum equation and state its applications.

A $45^{\circ}$ reducing bend is connected in a pipe line, the diameters at the inlet and outlet of the bend being $600\,mm$ and $300\,mm$ respectively. Find the force exerted by water on the bend if the intensity of pressure at inlet to bend is $8.829\,N/cm^{2}$ and rate of flow of water is $600\,litres/s$.

Derive the expression for rate of flow through a venturimeter.

Derive the laminar velocity distribution $u(y)$ between two fixed parallel plates, and hence obtain the shear stress distribution, volume flow rate, and mean velocity showing that $u_{mean} = \frac{2}{3}u_{max}$.

For laminar flow in a circular pipe with parabolic velocity profile, relate maximum, mean and local velocity and find discharge and the radius where velocity equals mean velocity.

Explain significance of Reynolds number and verify laminar flow to determine pressure loss per unit length.

Derive Hagen-Poiseuille equation and expression for mean velocity for laminar flow through a circular pipe.

What is the critical velocity of flow in a circular pipe? What are the lower critical velocity and higher critical velocity?

Numerical on laminar flow between fixed parallel plates: given plate spacing, maximum velocity (with $u_{mean}=2/3\,u_{max}$) and viscosity, compute discharge per unit width, wall shear stress, and pressure drop over a given length.

Derive the Darcy-Weisbach equation for loss of head due to friction in pipe flow.

Using Buckingham's pi theorem, obtain a dimensionless expression for turbulent pipe pressure drop $\Delta P$ as a function of diameter, length, velocity, density, viscosity and wall roughness.

Explain geometric, kinematic and dynamic (hydraulic) similarities between a prototype and its model and whether they are truly attainable.

For turbulent pipe flow, determine discharge from centre-line velocity and velocity at a given distance from centre.

Explain Prandtl mixing length theory and derive the expression for turbulent shear stress.

Using Buckingham's pi theorem, derive the expression for resistance $R$ of a partially submerged body as a function of velocity, length, viscosity, density and gravity.

Determine the discharge (and velocities) through pipes in series connecting two reservoirs given pipe lengths, diameters, water level difference and friction coefficients, with/without minor losses and TEL/HGL.

Explain what is meant by dimensional analysis and describe the uses of Buckingham's pi theorem.

Write short notes on any three:

Write short notes on the following (any four):

Differentiate the following: