CE-604-A Fluid Mechanics-II - 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. 6 Marks
   aWhat do you understand by turbulent flow? What factors decides the type of flow in pipes?
   How to answer

   • Define turbulent flow as irregular, random, eddying motion with high Reynolds number.
   • Distinguish laminar vs turbulent with Reynolds number criterion for pipes.
   • List factors: velocity, diameter, viscosity/density, roughness, Reynolds number $Re = \rho V D/\mu$.
   • Explain critical Reynolds number ~2000-4000 for pipe flow.
2. 8 Marks
   bDetermine the difference in the elevations between the water surfaces in the two tanks which are connected by a horizontal pipe of diameter 300 mm and length 400 m. The rate of flow of water through the pipe is 300 litres/s. Consider all losses and take the value of $f = 0.008$.
   How to answer

   • Compute velocity and velocity head from $Q$ and $D$.
   • Compute friction loss $h_f = 4fL/D \cdot V^2/2g$.
   • Add entrance, exit and kinetic losses for total head difference.
   • Calculate elevation difference $H = h_{entry}+h_f+h_{exit}$.
3. 7 Marks
   aDefine and explain the following terms :

   1. i)Hydraulic gradient line
   2. ii)Total energy line
   How to answer

   • Define hydraulic gradient line as $p/\rho g + z$ line.
   • Define total energy line as $p/\rho g + V^2/2g + z$ line.
   • Explain relative positions and gap equals velocity head.
   • Sketch HGL and TEL for pipe flow with losses.
4. 7 Marks
   bDetermine the maximum discharge of water through a circular channel of diameter 1.5 m when the bed slope of the channel is 1 in 1000. Take $c = 60$.
   How to answer

   • State condition for maximum discharge: depth ~0.95D and Chezy formula.
   • Compute area and wetted perimeter for max Q condition.
   • Apply $Q = A C \sqrt{m i}$ with $i=1/1000$.
   • Calculate numerical value of $Q_{max}$.
5. 7 Marks
   aDefine the term most economical section of a channel. What are the conditions for the rectangular channel of the best section?
   How to answer

   • Define most economical section as minimum wetted perimeter for given area.
   • State condition for rectangular best section: $b = 2y$, $m = y/2$.
   • Derive from $P = b+2y$ with $A$ constant.
   • Mention maximum conveyance implications.
6. 7 Marks
   bThe specific energy for a 3 m wide channel is to be 3 kg-m/kg. What would be the maximum possible discharge?
   How to answer

   • Write specific energy $E = y_c + V_c^2/2g$ with critical condition.
   • Use $E_c = 3y_c/2$ for rectangular channel.
   • Find $y_c$ and $q_{max} = \sqrt{g y_c^3}$.
   • Compute $Q_{max}=q_{max} \times B$.
7. 7 Marks
   aWhat is the essential difference between gradually varied flow and rapidly varied flow? Illustrate with neatly drawn sketches.
   How to answer

   • Define GVF as slow change in depth over long length vs RVF as abrupt change.
   • Compare assumptions, curvature, pressure distribution.
   • Give examples: backwater curve vs hydraulic jump.
   • Provide neat sketches of both profiles.
8. 7 Marks
   bProve that the loss of energy in hydraulic jump is equal to $(d_2-d_1)^3/4d_1d_2$, where $d_1$ and $d_2$ are the conjugate depths.
   How to answer

   • Apply continuity and momentum between sections $d_1$ and $d_2$.
   • Write specific force equality and energy equations.
   • Simplify to get $E_L = (d_2-d_1)^3/(4 d_1 d_2)$.
   • Define conjugate depths $d_1, d_2$.
9. 7 Marks
   aDifferentiate between

   1. i)Stream lines body and bluff body
   2. ii)Friction drag and Pressure drag
   How to answer

   • Define streamlined body with separation at rear vs bluff body with early separation.
   • Define friction drag due to shear vs pressure drag due to pressure difference.
   • Compare drag coefficients and wake size.
   • Give examples: airfoil vs flat plate normal to flow.
10. 7 Marks
    bA circular disc 3 m in diameter is held normal to a 26.4 m/s wind of density 0.0012 gm/cc. What force is required to hold it at rest? Assume coefficient of drag of disc = 1.1.
    How to answer

    • Compute projected area $A = \pi D^2/4$.
    • Convert density $0.0012$ gm/cc to kg/m$^3$.
    • Apply drag force $F_D = C_D A \rho V^2/2$.
    • Calculate force required to hold disc at rest.
11. 7 Marks
    aDifferentiate between

    1. i)The impulse and reaction turbines
    2. ii)Radial and axial flow turbines
    How to answer

    • Compare working principle: impulse uses kinetic energy at atmospheric pressure vs reaction uses pressure + kinetic.
    • Compare radial vs axial flow path and examples Francis vs Kaplan/propeller.
    • Tabulate differences in head, discharge, casing.
    • Mention efficiency and applications.
12. 7 Marks
    bAn airfoil of chord length 2 m and of span 15 m has an angle of attack as $6^{\circ}$. The airfoil is moving with a velocity of 80 m/s in air whose density is $1.25$ kg/m$^3$. Find the weight of the airfoil and the power required to drive it. The values of co efficient of drag and lift corresponding to angle of attack are given as 0.03 and 0.5 respectively.
    How to answer

    • Compute lift $F_L = C_L A \rho V^2/2$ equals weight.
    • Compute drag $F_D = C_D A \rho V^2/2$.
    • Compute power $P = F_D \times V$.
    • Insert $A = chord \times span$, $V=80$ m/s, $\rho=1.25$ kg/m$^3$.
13. 7 Marks
    aFind an expression for the head lost due to friction in suction and delivery pipes.
    How to answer

    • Consider reciprocating pump with crank, connecting rod, piston motion.
    • Derive acceleration head $h_a = l/g \cdot A/a \cdot \omega^2 r \cos\theta$.
    • Apply separately to suction and delivery pipes with lengths and diameters.
    • State maximum at beginning/end of stroke and effect on indicator diagram.
14. 7 Marks
    bA Pelton wheel has a mean bucket speed of 35 m/s with a jet of water flowing at the rate of 1 m$^3$/s under a head of 270 m. The buckets deflect the jet through an angle of $170^{\circ}$. Calculate the power delivered to the runner and the hydraulic efficiency of the turbine. Assume coefficient of velocity as 0.98.
    How to answer

    • Compute jet velocity $V = C_v\sqrt{2gH}$ and bucket speed $u=35$ m/s.
    • Apply Pelton power $P = \rho Q (V-u)(1-\cos\beta)(u)$ with $\beta=180-170$.
    • Compute hydraulic efficiency $\eta_h = 2(V-u)(1-\cos\beta)u / V^2$.
    • Insert $Q=1$ m$^3$/s, $H=270$ m, $C_v=0.98$.
15. 14 Marks
    Write short notes on any two of the following :

    1. a)Water hammer
    2. b)Normal depth and critical depth
    3. c)Surges in open channels
    4. d)Aerofoil development
    How to answer

    • Select any two topics with definition and causes.
    • Explain governing principle with formula/sketch.
    • Give practical significance and control measures.
    • Conclude with examples in fluid systems.