About this previous year paper
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=CdA2ρ(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}}hcpˉ=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=CdA01−(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.