Skip to main content

Transport Phenomena - short answer questions from AMIE exams (Winter 2019)

Answer the following (20 marks)

Explain frictional losses due to sudden expansion and contraction with necessary equations.

Head Loss Due to Sudden Contraction in Pipe

hc = 0.5 (V2/2g)

Head Loss Due to Sudden Expansion in Pipe

he = (V1 - V2)2/2

Write a short note on Creeping flow and Couette flow.

Creeping flow.  Stokes flow also named creeping flow or creeping motion, is a type of fluid flow where advective inertial forces are small compared with viscous forces. The Reynolds number is low, i.e. Re << 1. This is a typical situation in flows where the fluid velocities are very slow, and the viscosities are very large.

Couette flow.  In fluid dynamics, Couette flow is the flow of a viscous fluid in the space between two surfaces, one of which is moving tangentially relative to the other. The relative motion of the surfaces imposes shear stress on the fluid and induces flow. 

What is Reynolds's analogy?

Reynolds's analogy gives the interrelationship between fluid friction and newton’s law of viscosity.

The Reynolds analogy is given by,


Nu/RePr = St = Cf/2


where

Nu = Local Nusselt number, Re = Local Reynolds number, St = Local Stanton number, Pr = Prandtl number, C= Skin friction coefficient

Bernoulli’s theorem

The total mechanical energy of the moving fluid comprising the gravitational potential energy of elevation, the energy associated with the fluid pressure and the kinetic energy of the fluid motion, remains constant.

p + (p{v^2}/2) + \rho gh = cons\tan t

The physical significance of Reynolds and Froude's number

Froude numbers express a relationship between the free surface of a flow and the various waves and ruffles that form there, and bedforms at the sediment-water interface. Reynolds numbers deal with the bulk characteristics of flow – whether it has a laminar or turbulent structure.

What is the Mixing Length of Prandtl?

The mixing length is the distance that a fluid parcel will keep its original characteristics before dispersing them into the surrounding fluid. Here, the bar on the left side of the figure is the mixing length.


According to Prandtl, the mixing length l, is the distance between two layers in the transverse direction such that lumps of fluid particles from one layer could reach the other layer and the particles are mixed in the other layer in such a way that the momentum of the particles in the direction of x is same.

The relation between shear stress and mixing length is given by

\tau  = \rho {l^2}{\left( {\frac{{du}}{{dy}}} \right)^2}

State the similarities and differences between Newton’s law of viscosity and Fourier’s law of heat conduction

Newton's law of viscosity describes that momentum flux in any fluid is proportional to the velocity gradients while Fourier's law describes that heat flux due to conduction is proportional to temperature gradients where velocity and temperature gradients are the driving force, respectively.

Continuity equation

For a steady flow through a control volume with many inlets and outlets, the net mass flow must be zero.

AV = constant

Define kinematic viscosity and eddy viscosity

The kinematic viscosity formula is expressed as,

ν = μ/ρ

Where μ= absolute or dynamic viscosity,

ρ = density

Eddy viscosity is the proportionality factor describing the turbulent transfer of energy as a result of moving eddies, giving rise to tangential stresses. It is also referred to as turbulent viscosity and doesn’t have any physical existence.

How is the stream function defined, and why is it useful?

The stream function in a two-dimensional flow automatically satisfies the continuity equation. It is the scalar function of space and time.

The partial derivative of the stream function with respect to any direction gives the velocity component perpendicular to that direction. Hence it remains constant for a streamline.

u =  - \frac{{\partial \psi }}{{\partial y}};v = \frac{{\partial \psi }}{{\partial x}}
---

The study material for AMIE/Junior Engineer exams is available at https://amiestudycircle.com

Comments

Popular posts from this blog

Mechanics of Fluids (Solved Numerical Problems)

Numerical The surface Tension of water in contact with air at 20°C is 0.0725 N/m. The pressure inside a droplet of water is to be 0.02 N/cm² greater than the outside pressure. Calculate the diameter of the droplet of water. (7 marks) (AMIE Summer 2023) Solution Surface tension, σ = 0.0725 N/m Pressure intensity, P = 0.02 N/m 2 P = 4σ/d Hence, the Diameter of the dropd = 4 x 0.0725/200 = 1.45 mm Numerical Find the surface tension in a soap bubble of 40 mm diameter when the inside pressure is 2.5 N/m² above atmospheric pressure. (7 marks) (AMIE Summer 2023) Answer: 0.0125 N/m Numerical The pressure outside the droplet of water of diameter 0.04 mm is 10.32 N/cm² (atmospheric pressure). Calculate the pressure within the droplet if surface tension is given as 0.0725 N/m of water. (AMIE Summer 2023, 7 marks) Answer: 0.725 N/cm 2   Numerical An open lank contains water up to a depth of 2 m and above it an oil of specific gravity 0.9 for a depth of 1 m. Find the pressure intensity (i) at t...

Energy Systems (Solved Numerical Problems)

Wind at 1 standard atmospheric pressure and \({15^0}C\) has velocity of 15 m/s, calculate (i) the total power density in the wind stream (ii) the maximum obtainable power density (iii) a reasonably obtainable power density (iv) total power (v) torque and axial thrust Given: turbine diameter = 120 m, and turbine operating speed = 40 rpm at maximum efficiency. Propeller type wind turbine is considered. (AMIE Winter 2023) Solution For air, the value of gas constant is R = 0.287 kJ/kg.K 1 atm = 1.01325 x 105 Pa Air density \(\rho  = \frac{P}{{RT}} = \frac{{1.01325x{{10}^5}}}{{287}}(288) = 1.226\,kg/{m^3}\) Total Power \({P_{total}} = \rho A{V_1}^3/2\) Power density \(\begin{array}{l}\frac{{{P_{total}}}}{A} = \frac{1}{2}\rho {V_1}^3\\ = \frac{1}{2}(1.226){(15)^3}\\ = 2068.87{\mkern 1mu} W/{m^2}\end{array}\) Maximum power density \(\begin{array}{l}\frac{{{P_{\max }}}}{A} = \frac{8}{{27}}\rho A{V^3}_1\\ = \frac{8}{{27}}(1.226){(15)^3}\\ = 1226{\mkern 1mu} W/{m^2}\end{array}\) Assuming eff...

Design of Electrical Systems (Solved Numerical Problems)

Important note There is something wrong with this question paper. It seems that instead of "Design of Electrical Systems" the IEI has given problems from "Electrical Machines". You should raise a complaint to director_eea@ieindia.org in this regard. Numerical A 120 V DC shunt motor draws a current of 200A. The armature resistance is 0.02 ohms and the shunt field resistance is 30 ohms. Find back emf. If the lap wound armature has 90 slots with 4 conductors per slots, at what speed will the motor run when flux per pole is 0.04 Wb?​ (AMIE Summer 2023, 8 marks) Solution The back EMF (E b ) of a DC motor can be calculated using the formula: E b = V - I a R a   Given: V = 120 V I a = 200 A R a = 0.02 ohms Substituting the values into the formula: E b = 120 − 200 × 0.02 = 120 − 4​ = 116 V Now, let's calculate the speed (N) at which the motor will run using the given flux per pole (φ p ). The formula to calculate the speed of a DC motor is: N = 60×E b /(P×φ p ) Wh...