Boundary Layers and Flow around Particles - Fluid Mechanics and Mechanical Operations - Chemical Engineering Previous Year Questions

1

2009 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Boundary Layers and Flow around Particles

Chemical Engineering (CH) 2009

For a mixing tank operating in the laminar regime, the power number varies with the Reynolds number (Re) as

A

\(Re^{-1/2} \)

B

\(Re^{1/2} \)

C

\(Re \)

D

\(Re^{-1} \)

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2

2010 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Boundary Layers and Flow around Particles

Chemical Engineering (CH) 2010

The diameter of a drop of liquid fuel changes with time, due to combustion, according to the relationship, \( D = D_0 \left(1 - \frac{t}{t_b}\right) \). While burning, the drop falls at its terminal velocity under Stokes’ flow regime. The distance it will travel before complete combustion, is given by

A

\(\frac{D_0^2 \Delta \rho t_b g}{18 \mu} \)

B

\(\frac{D_0^2 \Delta \rho t_b g}{36 \mu} \)

C

\(\frac{D_0^2 \Delta \rho t_b g}{54 \mu} \)

D

\(\frac{D_0^2 \Delta \rho t_b g}{108 \mu} \)

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3

2012 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Boundary Layers and Flow around Particles

Chemical Engineering (CH) 2012

For uniform laminar flow (in the \( x \)-direction) past a flat plate at high Reynolds number, the local boundary layer thickness ( \( \delta \) ) varies with the distance along the plate ( \( x \) ) as

A

\(\delta \propto x^{1/4} \)

B

\(\delta \propto x^{1/3} \)

C

\(\delta \propto x^{1/2} \)

D

\(\delta \propto x \)

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4

2016 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Boundary Layers and Flow around Particles

Chemical Engineering (CH) 2016

Consider a rigid solid sphere falling with a constant velocity in a fluid. The following data are known at the conditions of interest: viscosity of the fluid = 0.1 Pa s, acceleration due to gravity = 10 m s^-2, density of the particle = 1180 kg m^-3 and density of the fluid = 1000 kg m^-3. The diameter (in mm, rounded off to the second decimal place) of the largest sphere that settles in the Stokes’ law regime (Reynolds number ≤ 0.1), is ________

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5

2017 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Boundary Layers and Flow around Particles

Chemical Engineering (CH) 2017

The thickness of laminar boundary layer over a flat plate varies along the distance from the leading edge of the plate. As the distance increases, the boundary layer thickness

A

increases

B

decreases

C

initially increases and then decreases

D

initially decreases and then increases

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6

2017 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Boundary Layers and Flow around Particles

Chemical Engineering (CH) 2017

A gas bubble (gas density \(\rho_g = 2\) kg/m³; bubble diameter \(D = 10^{-4}\) m) is rising vertically through water (density \(\rho = 1000\) kg/m³; viscosity \(\mu = 0.001\) Pa.s). Force balance on the bubble leads to the following equation.
\[\frac{dv}{dt} = -g\frac{\rho_g - \rho}{\rho_g} - \frac{18\mu}{\rho_g D^2}v\]
where \(v\) is the velocity of the bubble at any given time \(t\). Assume that the volume of the rising bubble does not change. The value of \(g = 9.81\) m/s².
The terminal rising velocity of the bubble (in cm/s), rounded to 2 decimal places, is ______ cm/s.

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7

2017 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Boundary Layers and Flow around Particles

Chemical Engineering (CH) 2017

A propeller (diameter \( D = 15 \) m) rotates at \( N = 1 \) revolution per second (rps). To understand the flow around the propeller, a lab-scale model is made. Important parameters to study the flow are velocity of the propeller tip (\( V = \pi ND \)), diameter \( D \) and acceleration due to gravity (\( g \)). The lab-scale model is \( 1/100^{th} \) of the size of the actual propeller.
The rotation speed of the lab-scale model, to the nearest integer, should be ______ rps.

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8

2019 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Boundary Layers and Flow around Particles

Chemical Engineering (CH) 2019

For a fully-developed turbulent hydrodynamic boundary layer for flow past a flat plate, the thickness of the boundary layer increases with distance \( x \) from the leading edge of the plate, along the free-stream flow direction, as

A

\(x^{0.5} \)

B

\(x^{1.5} \)

C

\(x^{0.4} \)

D

\(x^{0.8} \)

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9

2020 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Boundary Layers and Flow around Particles

Chemical Engineering (CH) 2020

Consider an incompressible flow of a constant property fluid over a smooth, thin and wide flat plate. The free stream flows parallel to the surface of the plate along its length and its velocity is constant. Value of the Reynolds number at a distance of 2.0 m from the leading edge of the plate is 8000. The flow within the boundary layer at a distance of 1.0 m from the leading edge of the plate is

A

laminar

B

turbulent

C

transitioning from laminar to turbulent

D

inviscid

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10

2020 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Boundary Layers and Flow around Particles

Chemical Engineering (CH) 2020

Ratio of momentum diffusivity to thermal diffusivity is

A

Reynolds number

B

Prandtl number

C

Nusselt number

D

Peclet number

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11

2021 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Boundary Layers and Flow around Particles

Chemical Engineering (CH) 2021

Consider a fluid confined between two horizontal parallel plates and subjected to shear flow.

In the first experiment, the plates are separated by a distance of 1 mm. It is found that a shear stress of 2 N m^–2 has to be applied to keep the top plate moving with a velocity of 2 m s^–1, while the other plate is fixed.

In the second experiment, the plates are separated by a distance of 0.25 mm. It is found that a shear stress of 3 N m^–2 has to be applied to keep the top plate moving with a velocity of 1 m s^–1, while the other plate is fixed.

In the range of shear rates studied, the rheological character of the fluid is

A

Newtonian

B

Pseudoplastic

C

Dilatant

D

Ideal and inviscid

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12

2023 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Boundary Layers and Flow around Particles

Chemical Engineering (CH) 2023

A large tank is filled with water (density = \( 1 \text{ g.cm}^{-3} \)) upto a height of \( 5 \text{ m} \). A \( 100 \text{ μm} \) diameter solid spherical particle (density = \( 0.8 \text{ g.cm}^{-3} \)) is released at the bottom of the tank. The particle attains its terminal velocity (\( v_t \)) after traveling to a certain height in the tank. Use acceleration due to gravity as \( 10 \text{ m.s}^{-2} \) and water viscosity as \( 10^{-3} \text{ Pa.s} \). Neglect wall effects on the particle. If Stokes law is applicable, the absolute value of \( v_t \) (in \( \text{mm.s}^{-1} \)) is ______ (rounded off to two decimal places).

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13

2025 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Boundary Layers and Flow around Particles

Chemical Engineering (CH) 2025

The sum of the components of the force due to pressure and shear at the solid-fluid boundary of a solid body in the direction normal to the flow is

A

Drag

B

Friction

C

Lift

D

Buoyancy

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14

2026 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Boundary Layers and Flow around Particles

Chemical Engineering (CH) 2026

Consider a two-dimensional, steady, laminar flow of an incompressible fluid with zero pressure gradient, over a thin horizontal flat plate of length 2 m. The free stream velocity is 1 m s⁻¹. A boundary layer thickness of 1 mm is observed at a distance of 0.25 m from the leading edge of the plate. At 1 m from the leading edge, the boundary layer thickness (in mm) is ______ (rounded off to the nearest integer).

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