CE-604-A Fluid Mechanics-II - Jun 2025 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
   aFind the displacement thickness, the momentum thickness, and Energy thickness for the velocity distribution in the boundary layer is given by: $$\frac{u}{U} = \frac{y}{\delta}$$
   How to answer

   • Define displacement thickness integral
   • Define momentum thickness integral
   • Define energy thickness integral
   • Substitute u/U = y/delta and integrate 0 to delta to get delta*/delta, theta/delta, delta**/delta
2. 7 Marks
   bDerive an expression for velocity distribution in terms of average velocity for rough pipes.
   How to answer

   • State logarithmic velocity distribution / Karman-Prandtl equation for rough pipes
   • Introduce average velocity by integration over cross-section
   • Eliminate friction velocity / shear stress term
   • Obtain u in terms of V_avg and radial position / y/R
3. 7 Marks
   aExplain most economical circular section for condition of maximum discharge.
   How to answer

   • Define most economical section for circular channel
   • Condition for maximum discharge: dQ/dy=0 at constant A or slope
   • Derive depth and hydraulic mean depth relations (theta ~ 308 deg)
   • State y ~ 0.95D and m conditions
4. 7 Marks
   bFind the slope of the bed of a rectangular channel of width 5m when depth of water is 2m and rate of flow is given as $20\text{ m}^3/\text{s}$. Take Chezy's constant, $C = 50$.
   How to answer

   • Compute area A = B*y and wetted perimeter P
   • Compute hydraulic mean depth m = A/P
   • Apply Chezy formula Q = A*C*sqrt(m*i)
   • Solve for bed slope i
5. 7 Marks
   aWhat is specific energy curve? Derive expression for critical depth.
   How to answer

   • Define specific energy E = y + V^2/2g
   • Explain specific energy curve E vs y for constant q
   • Condition dE/dy=0 for minimum energy
   • Derive critical depth yc = (q^2/g)^(1/3)
6. 7 Marks
   bA sluice gate discharges water into horizontal rectangular channel with a velocity of 10 m/s and depth of flow 1m. Determine the depth of flow of water after jump and calculate the loss of energy in total head.
   How to answer

   • Compute upstream Froude number Fr1 = V1/sqrt(g*y1)
   • Apply conjugate depth formula y2 = (y1/2)(-1+sqrt(1+8Fr1^2))
   • Compute specific energies E1, E2
   • Energy loss = E1 - E2
7. 7 Marks
   aExplain drag forces on a sphere.
   How to answer

   • Define drag and its components: friction and pressure drag
   • Explain flow around sphere with boundary layer separation
   • Discuss variation of Cd with Reynolds number
   • Mention Stokes law at low Re
8. 7 Marks
   bA kite $0.8\text{ m} \times 0.8\text{ m}$ weighing 3.924 N assumes an angle of $12^\circ$ to the horizontal. The string attached to the kite makes an angle of $45^\circ$ to the horizontal. The pull on the string is 24.525 N when the wind is flowing at a speed of 30 km/hour. Calculate the corresponding co-efficient of drag and co-efficient of lift. Density of air is given as $1.25\text{ kg/m}^3$.
   How to answer

   • Resolve string tension into horizontal and vertical components
   • Equate drag to horizontal component and lift to weight + vertical component
   • Compute wind velocity in m/s and dynamic pressure
   • Calculate Cd = FD/(0.5 rho A V^2) and CL = FL/(0.5 rho A V^2)
9. 7 Marks
   aIllustrate the derivation for the Minimum speed for starting a centrifugal pump.
   How to answer

   • Define priming and head developed by impeller
   • Condition for starting: manometric head > static head
   • Derive Hm = (u2^2 - u1^2)/2g or N expression
   • Obtain minimum speed Nmin formula
10. 7 Marks
    bA Francis turbine working under a head of 30 m has a wheel diameter of 1.2 m at the entrance and 0.6 m at the exit. The vane angle at the entrance is $90^\circ$ and guide blade angle is $15^\circ$. The water at the exit leaves the vanes without any tangential velocity and the velocity of flow in the runner is constant. Neglecting the effect of draft tube and losses in the guide and runner passages, determine the speed of wheel in r.p.m. and vane angle at the exit.
    How to answer

    • Draw inlet and outlet velocity triangles with given angles
    • Use Vw1 from guide vane angle and Euler head He = Vw1*u1/g
    • Equate Euler head to net head H to find u1 and N
    • Find outlet triangle with Vf constant and Vw2=0 to get vane angle
11. 7 Marks
    aDerive the expression of hydraulic efficiency of Pelton turbine.
    How to answer

    • Define Pelton turbine work from inlet/outlet buckets
    • Write Euler head and discharge relations
    • Define hydraulic efficiency = power/head power
    • Simplify to eta_h = 2(V1-u)(1-cos beta)u / V1^2
12. 7 Marks
    bIllustrate the separation of boundary layer and the methods to prevent it.
    How to answer

    • Define boundary layer separation and adverse pressure gradient
    • Explain effects: wake, drag increase
    • List prevention methods: suction, blowing, streamlined shape, guide vanes
    • Sketch flow with separation point
13. 7 Marks
    aDetermine the Chezy's and Manning's formulae.
    How to answer

    • Derive Chezy formula V = C sqrt(m i) from shear stress
    • Relate Manning n with Chezy C
    • State Manning formula V = (1/n) m^(2/3) i^(1/2)
    • Mention units and application
14. 7 Marks
    bDerive an expression for depth of hydraulic jump in terms of the upstream Froude number.
    How to answer

    • Apply momentum equation between sections before and after jump
    • Introduce Froude number Fr1
    • Solve quadratic for y2/y1 ratio
    • Obtain y2 = (y1/2)(-1+sqrt(1+8Fr1^2))
15. 14 Marks
    Write short notes on any four:

    1. a)Water hammer
    2. b)Hydraulic gradient line
    3. c)Pipes in series
    4. d)Magnus effect
    5. e)Draft tube
    How to answer

    • Select any four topics from list
    • Give definition and cause for each
    • Write relevant formula / diagram where applicable
    • Mention practical significance