(SEM III) THEORY EXAMINATION 2023-24 FLUID MECHANICS

This examination evaluates the student’s conceptual understanding, analytical skills, and numerical ability across all core areas of Fluid Mechanics, including pressure measurement, fluid kinematics, fluid dynamics, dimensional analysis, flow measurement devices, boundary layer theory, and fluid forces.

The paper is structured into three sections, ensuring coverage from foundational concepts to advanced engineering applications.

SECTION A – Short Conceptual Questions (14 Marks)

Seven questions × 2 marks each

This section tests the basic principles of fluid mechanics through concise definitions and direct applications.

Topics Covered:

1. Continuum Assumption

Fluid treated as continuous with no molecular discontinuity.

2. Density, Specific Weight & Weight of 1 Liter Petrol

Using specific gravity relation → computation of fluid properties.

3. Types of Fluid Flow

Steady/unsteady, uniform/non-uniform, laminar/turbulent, compressible/incompressible, rotational/irrotational.

4. Components of Compressible Flow

Density variation, Mach number, compressibility effects, pressure waves.

5. Streamline Flow

Flow in which velocity at a point remains constant with time; tangent gives flow direction.

6. Forces in Fluid Flow

Inertial, pressure, viscous, gravity, surface tension, elastic forces.

7. Model Analysis

Use of similitude, scaling, and dimensionless parameters for prototype prediction.

This section checks conceptual clarity and fundamental fluid properties.

SECTION B – Applied Numerical & Short Derivation Problems (21 Marks)

Attempt any three questions × 7 marks

This section focuses on practical calculations, theoretical derivations, and measurement techniques.

1. Single Column Manometer

Definition, construction, working, pressure measurement using differential heights and fluid columns.

2. Continuity Equation – Finding Third Velocity Component

Given velocity components:

u=x2+y2+z2,v=xy2−yz2+xyu = x^2 + y^2 + z^2,\quad v = xy^2 - yz^2 + xyu=x2+y2+z2,v=xy2−yz2+xy

Determine w such that the 3D continuity equation is satisfied:

∂u∂x+∂v∂y+∂w∂z=0\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z}=0∂x∂u​+∂y∂v​+∂z∂w​=0 

3. Sonic Velocity Calculations

Using formula:

c=Kρc = \sqrt{\frac{K}{\rho}}c=ρK​​

Calculate sound speed for:
(i) Crude oil with bulk modulus 153036 N/cm²
(ii) Mercury with bulk modulus 2648700 N/cm²

4. Venturi Meter

Neat labeled sketch, components (converging section, throat, diverging section), and derivation of flow rate:

Q=CdA22Δpρ(A12−A22)Q = C_d A_2\sqrt{\frac{2\Delta p}{\rho (A_1^2 - A_2^2)}}Q=Cd​A2​ρ(A12​−A22​)2Δp​​ 

5. Hydraulic Jump – Model & Prototype

Given scale 1:20, use Froude similarity to compute:
• Prototype jump height
• Energy dissipation (power scaling using L2V3L^2 V^3L2V3)

This section evaluates practical understanding of measurement, similarity laws, and fluid property calculations.

SECTION C – Long Descriptive & Analytical Questions (35 Marks)

One question from each group × 7 marks.

3. Hydrostatic Forces / Metacentric Height

Option A – Pressure on Vertical Circular Plate

Diameter = 1.5 m, depth = 3 m
Find:
• Total pressure: P=ρgAhˉP = \rho g A \bar{h}P=ρgAhˉ
• Centre of pressure: hcpˉ=hˉ+IGAhˉ\bar{h_{cp}} = \bar{h} + \frac{I_G}{A\bar{h}}hcp​ˉ​=hˉ+AhˉIG​​

Option B – Experimental Metacentric Height

Procedure using:
• Floating body
• Adjustable weight
• Tilting angle
• Geometry of stability
Neat sketch required.

4. Stream Function / Continuity Equation

Option A – Stream Function

Given ψ=2xy\psi = 2xyψ=2xy:
Calculate velocity components using:

u=∂ψ∂y,v=−∂ψ∂xu = \frac{\partial \psi}{\partial y},\quad v = -\frac{\partial \psi}{\partial x}u=∂y∂ψ​,v=−∂x∂ψ​

Find velocity at P(2,3) and derive the velocity potential.

Option B – Continuity Equation

Assumptions (steady, incompressible, continuous fluid) + full derivation of:

∂u∂x+∂v∂y+∂w∂z=0\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0∂x∂u​+∂y∂v​+∂z∂w​=0 

5. Orifice Meter / Sudden Expansion

Option A – Orifice Meter Discharge

Given:
• do=10 cm,D=20 cmd_o = 10\text{ cm}, D = 20\text{ cm}do​=10 cm,D=20 cm
• Pressure readings: 19.62 N/cm² & 9.81 N/cm²
• Cd=0.6C_d = 0.6Cd​=0.6
Calculate discharge using:

Q=CdA02(gΔh)1−(A0/A)2Q = C_d A_0 \sqrt{\frac{2(g\Delta h)}{1-(A_0/A)^2}}Q=Cd​A0​1−(A0​/A)22(gΔh)​​

Option B – Loss of Head Due to Sudden Expansion

Show:

hL=(v1−v2)22gh_L = \frac{(v_1-v_2)^2}{2g}hL​=2g(v1​−v2​)2​ 

6. Turbulent Flow / Laminar Boundary Layer

Option A – Velocity Distribution

Determine location where local velocity = average velocity.

Option B – Boundary Layer Thickness & Drag

Given velocity profile → compute:
• Boundary layer thickness
• Shear stress at x = 1.5 m
• Total drag on plate (2 m × 1.4 m)

7. Drag on Sphere / Buckingham π-Theorem

Option A – Drag on a Sphere

For Re < 0.2 using Stokes Law:

FD=3πμVDF_D = 3\pi \mu V DFD​=3πμVD

Option B – Fan Efficiency via π-Theorem

Given:

η=f(ρ,μ,ω,D,Q)\eta = f(\rho, \mu, \omega, D, Q)η=f(ρ,μ,ω,D,Q)

Form dimensionless groups and express η in terms of π-parameters.