CE-501 Fluid Mechanics - I - Dec 2024 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aWhat is meant by stability of a floating body? Explain the stability of a floating body with reference to its meta centric height.
   How to answer

   • Define stability of floating body: ability to return to equilibrium after disturbance
   • Explain stable, unstable and neutral equilibrium
   • Define metacentre, metacentric height GM = I/V - BG
   • Condition: GM positive stable, negative unstable with diagram
2. 7 Marks
   bDefine and distinguish between the following set of fluid properties:

   1. i)Specific weight and mass density
   2. ii)Cohesion and adhesion
   3. iii)Surface tension and capillarity
   How to answer

   • Define specific weight gamma = rho*g and mass density rho with units
   • Distinguish: weight per volume vs mass per volume
   • Define cohesion vs adhesion with examples
   • Define surface tension vs capillarity with formulas
3. 7 Marks
   aA solid cylinder 2m in diameter and 2m high is floating in water with its axis vertical. If the specific gravity of the material of cylinder is 0.65, find its meta-centric height. State also whether the equilibrium is stable or unstable.
   How to answer

   • Compute volume, weight and depth of immersion from specific gravity 0.65
   • Compute moment of inertia I = pi*D^4/64 and displaced volume V
   • Compute BM = I/V and BG from centre positions
   • Compute GM = BM - BG and state stable if positive
4. 7 Marks
   bDifferentiate the following:

   1. i)Steady and unsteady flow
   2. ii)Uniform and non uniform flow
   3. iii)Ideal flow and real flow
   How to answer

   • Define steady vs unsteady with time dependence example
   • Define uniform vs non-uniform with space dependence example
   • Define ideal vs real flow with viscosity and compressibility
   • Tabulate differences
5. 7 Marks
   aShow that the following stream function represents an irrotational flow. Find the velocity potential. $$\psi = 6x - 4y + 7xy + 9$$
   How to answer

   • Compute u = -dpsi/dy and v = dpsi/dx from given psi
   • Check irrotational condition: vorticity = dv/dx - du/dy = 0
   • Use dphi = u dx + v dy and integrate to get phi
   • State velocity potential function
6. 7 Marks
   bDescribe Stream lines, equipotential lines and flow net with neat sketch. Prove that equipotential lines and stream lines intersect each other orthogonally.
   How to answer

   • Define streamlines psi=constant and equipotential lines phi=constant
   • Sketch flow net with orthogonal squares
   • Show slopes m1 and m2 satisfy m1*m2 = -1 using u,v relations
   • Conclude orthogonal intersection
7. 7 Marks
   aA venturimeter is used to measure liquid flow rate of 7500 litres per minute. The difference in pressure across the venturimeter is equivalent to 8 m of the flowing liquid. The pipe diameter is 19 cm. Calculate the throat diameter of the venturimeter. Assume the coefficient of discharge for the venturimeter as 0.96.
   How to answer

   • Convert discharge 7500 lpm to m3/s and head 8 m of liquid
   • Apply venturimeter formula Q = Cd*A1*A2*sqrt(2gh)/sqrt(A1^2-A2^2)
   • Solve for throat area A2 with D1 = 19 cm
   • Compute throat diameter d2
8. 7 Marks
   bDefine and explain kinetic energy correction factor and momentum correction factor for laminar and turbulent flow.
   How to answer

   • Define kinetic energy correction factor alpha and momentum factor beta
   • Give expressions integral forms
   • State values: alpha=2, beta=1.33 for laminar; alpha~1.05, beta~1.02 for turbulent
   • Explain use in Bernoulli and momentum equations
9. 7 Marks
   aHow velocity of flow at any point in a pipe or a channel can be measured with a pitot Tube? Explain.
   How to answer

   • Describe Pitot tube construction: L-shaped tube with stagnation hole
   • Explain stagnation vs static pressure measurement
   • Apply Bernoulli: V = sqrt(2*(p0-p)/rho)
   • Explain application in pipe and open channel with diagram
10. 7 Marks
    bWhat is the critical velocity of flow in a circular pipe? What are the lower critical velocity and higher critical velocity?
    How to answer

    • Define critical velocity via Reynolds number Re ~2000
    • Define lower critical velocity: laminar to turbulent transition
    • Define higher critical velocity: turbulent to laminar reverse
    • Give formula Vc = Re_c*mu/(rho*D)
11. 7 Marks
    aTwo fixed parallel plates kept 8 cm apart have laminar flow of oil between them with a maximum velocity 1.5 m/sec. Taking dynamic viscosity of oil to be $\mu = 2.0$ Ns/m². The average velocity is two third of the maximum velocity. Compute:

    1. i)The discharge per meter width
    2. ii)The shear stress at the plates
    3. iii)The pressure difference between two points 25 m apart.
    How to answer

    • Compute average velocity = 2/3 * Umax = 1.0 m/s
    • Compute discharge per m width q = Vavg * B where B = spacing
    • Compute shear stress at wall from parabolic profile
    • Compute pressure drop dp/dx from mu and velocity relation for 25 m length
12. 7 Marks
    bDerive an expression for mean velocity for laminar flow through a pipe.
    How to answer

    • Consider force balance on fluid cylinder in pipe
    • Derive parabolic velocity distribution u = (1/4mu)(-dp/dx)(R^2-r^2)
    • Integrate over cross-section to get discharge Q
    • Obtain mean velocity V = (R^2/8mu)(-dp/dx)
13. 7 Marks
    aExplain the different types of hydraulic similarities that must exist between a prototype and its model.
    How to answer

    • Define geometric, kinematic and dynamic similarity
    • Explain length, velocity and force ratios
    • Give examples: Reynolds, Froude models
    • State conditions for complete similarity
14. 7 Marks
    bThe pressure drop $\Delta P$ in a pipe of diameter D, length L, due to turbulent flow depends on mass density $\rho$ and viscosity $\mu$ of the flowing fluid, mean velocity of flow V and average height K of roughness projections on the pipe surface. Obtain a dimensionless expression for $\Delta P$ by Buckingham's $\pi$ theorem. Hence show that $h_f = 4fLV^2/2dg$.
    How to answer

    • List variables DeltaP, D, L, rho, mu, V, K with dimensions
    • Select repeating variables rho, V, D and form pi terms
    • Obtain pi1 = DeltaP/(rho V^2), pi2 = mu/(rho V D), pi3 = L/D, pi4 = K/D
    • Rearrange to Darcy-Weisbach form hf = 4fLV^2/2gd
15. 14 Marks
    Write short notes on the following (any four):

    1. i)Momentum theorem
    2. ii)Stagnation point
    3. iii)Stokes law
    4. iv)Limitations of Bernoulli's equation
    5. v)Bulk modulus of elasticity
    6. vi)Froude Number
    How to answer

    • Write definition, formula and significance for each chosen topic
    • Give example or application for each
    • Add neat sketch or expression where relevant
    • Conclude with uses in fluid mechanics