CE-604-A Fluid Mechanics II - Jun 2026 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
   aExplain separation of boundary layer. What is the effect of pressure gradient on boundary layer separation?
   How to answer

   • Define boundary layer separation and separation point (zero wall shear).
   • Explain adverse pressure gradient causing reverse flow.
   • Effect of favourable, zero and adverse pressure gradient.
   • Methods to control/delay separation with diagram.
2. 7 Marks
   bDerive an expression for velocity distribution in terms of average velocity for rough pipes.
   How to answer

   • Start from logarithmic velocity distribution for rough pipes.
   • Integrate over cross-section to get average velocity.
   • Eliminate shear velocity to relate local velocity to average velocity.
   • Final expression for $(u - V_{avg})$ in terms of $y/R$.
3. 7 Marks
   aA laminar flow is taking place in a pipe of diameter of $200\text{ mm}$. The maximum velocity is $1.5\text{ m/s}$. Find the mean velocity and the radius at which this occurs. Also calculate the velocity at $4\text{ cm}$ from the wall of the pipe.
   How to answer

   • Use $V_{mean}=U_{max}/2$ for laminar pipe flow.
   • Radius for mean velocity at $r = R/\sqrt{2}$ from centre.
   • Parabolic profile $u = U_{max}[1-(r/R)^2]$.
   • Compute velocity 4 cm from wall (r = 6 cm).
4. 7 Marks
   bWrite short notes on the following:

   1. I)Hardy cross method.
   2. II)Hydraulic and Energy gradient lines.
   How to answer

   • Hardy Cross method: iterative correction for pipe networks.
   • Hydraulic Gradient Line (HGL) definition and features.
   • Energy Gradient Line (EGL) definition and relation to HGL.
   • Diagram showing HGL and EGL.
5. 7 Marks
   aExplain most economical circular section for condition of maximum velocity
   How to answer

   • Condition for most economical circular section for maximum velocity.
   • Use Chezy/Manning with geometric relations for partial flow.
   • Derive depth ratio $d/D \approx 0.81$ for maximum velocity.
   • State corresponding hydraulic mean depth.
6. 7 Marks
   bA concrete lined circular channel of $3.6\text{ m}$ diameter as a bed slope of $1:700$. Determine the maximum flow rate. Take $C = 50$.
   How to answer

   • Use Chezy formula $Q = A C \sqrt{RS}$.
   • Apply maximum flow condition for circular channel ($d/D$).
   • Compute area and wetted perimeter at that depth.
   • Calculate maximum discharge value.
7. 7 Marks
   aDetermine the Chezy's and Manning's formulae.
   How to answer

   • Derive Chezy formula $V = C\sqrt{RS}$ from force balance.
   • Relate Chezy C to Manning n.
   • State Manning formula $V = (1/n)R^{2/3}S^{1/2}$.
   • Assumptions and units.
8. 7 Marks
   bWrite short notes on the following

   1. I)Saint Vegnet equation
   2. II)venturi flume.
   How to answer

   • Saint-Venant equation: continuity and momentum for unsteady open channel.
   • Assumptions of shallow water equations.
   • Venturi flume: principle and discharge measurement.
   • Formula and diagram for venturi flume.
9. 7 Marks
   aDescribe the dynamic equation for rapidly varied flow
   How to answer

   • Define rapidly varied flow and examples (hydraulic jump).
   • Consider control volume and momentum/energy.
   • Derive dynamic equation $dy/dx$ form.
   • Assumptions and interpretation.
10. 7 Marks
    bA sluice gate discharges water into horizontal rectangular channel with a velocity of $10\text{m/s}$ and depth of flow $1\text{m}$. Determine the depth of flow of water after jump and calculate the loss of energy in total head.
    How to answer

    • Compute Froude number $Fr_1 = V_1/\sqrt{gy_1}$.
    • Use sequent depth formula $y_2 = (y_1/2)(-1+\sqrt{1+8Fr_1^2})$.
    • Compute specific energies $E_1, E_2$.
    • Energy loss $\Delta E = E_1-E_2 = (y_2-y_1)^3/(4y_1y_2)$.
11. 7 Marks
    aA circular plate of diameter $80\text{mm}$ is moved in a stationary air of density $1.2\text{ kg/m}^3$ with a velocity of $45\text{ km/hr}$. If the coefficient of drag and lift are $0.2$ and $0.8$ respectively. Determine the drag force, the lift force, the resultant force and the power required to keep the plate in motion.
    How to answer

    • Convert velocity to m/s and compute area $A=\pi D^2/4$.
    • Drag $F_D = C_D A \rho V^2/2$ and Lift $F_L = C_L A \rho V^2/2$.
    • Resultant $F_R = \sqrt{F_D^2+F_L^2}$.
    • Power $P = F_D \times V$.
12. 7 Marks
    bWrite about Magnus effect.
    How to answer

    • Define Magnus effect for spinning body in flow.
    • Explain pressure difference due to circulation.
    • Give examples (spinning ball, cylinder).
    • Diagram of streamlines and lift direction.
13. 7 Marks
    aA jet of water from a nozzle is deflected through $60^\circ$ from its original direction by a curve plate which it enters tangentially without shock with a velocity of $30\text{ m/s}$ and leaves with a mean velocity of $25\text{ m/s}$. If the discharge from the nozzle is $0.8\text{ kg/s}$. Calculate the magnitude and direction of the resultant force on the vane, if the vane is stationary.
    How to answer

    • Resolve inlet and outlet momentum in x and y.
    • Force components $F_x = \dot m(V_{1x}-V_{2x})$, $F_y = \dot m(0-V_{2y})$.
    • Resultant $F = \sqrt{F_x^2+F_y^2}$ and angle $\tan\theta = F_y/F_x$.
    • Note mass flow rate $0.8\text{ kg/s}$ as printed.
14. 7 Marks
    bWhich type of turbine requires Draft tube? Derive the expression for draft tube efficiency.
    How to answer

    • State reaction turbines (Francis, Kaplan) need draft tube.
    • Apply Bernoulli between runner exit and tailrace.
    • Derive efficiency $\eta_d$ in terms of velocity heads.
    • Explain gain in effective head.
15. 14 Marks
    Prove that the Manometric head of a centrifugal pump running at a speed $N$ and giving a discharge $Q$ may be written as $$Hmano=AN^2+BNQ+CN^2$$ Where A, B and C are constants.
    How to answer

    • Start from outlet velocity triangles and Euler head.
    • Express tangential velocity $V_{w2} \propto N$ and flow velocity $V_f \propto Q$.
    • Substitute in $H_{mano} = (u_2V_{w2})/g$ minus losses.
    • Collect terms as $AN^2+BNQ+CQ^2$ (printed as $CN^2$) with constants A,B,C.