ME-404 Fluid Mechanics - 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
   aExplain the following.

   1. i)Newtonian Fluid
   2. ii)Non Newtonian Fluid
   3. iii)Vapour Pressure
   How to answer

   • Define Newtonian fluid with linear shear stress-strain relation
   • Define non-Newtonian fluid with non-linear behaviour and examples
   • Define vapour pressure and its significance in cavitation
2. 7 Marks
   bTwo discs of 20 cm diameter are placed 1 mm apart and the gap is filled with an oil of viscosity 0.8 kg/m.s. Determine the power required to rotate the upper disc at 600 rpm while holding the lower one stationary.
   How to answer

   • Shear stress due to viscosity $\tau = \mu du/dy$
   • Integrate torque $dT = r \cdot \tau dA$ over disc radius
   • Power $P = T \cdot \omega$ with $\omega = 2\pi N/60$
   • Substitute $D=0.2 m, h=1 mm, \mu=0.8 kg/m.s, N=600 rpm$
3. 7 Marks
   aA steady, incompressible, two-dimensional velocity field is given by $u = x + 2y + 2.0$; $v = 2x - y - 3.5$. Determine the location of the stagnation point, if it exists.
   How to answer

   • Set $u=0$ and $v=0$ for stagnation point
   • Solve linear equations $x+2y+2.0=0$, $2x-y-3.5=0$
   • Obtain $x, y$ coordinates
   • Check existence and uniqueness
4. 7 Marks
   bExplain the terms rotation, vorticity and circulation, velocity potential, stream function, stream line and path line.
   How to answer

   • Define rotation, vorticity and circulation with formulas
   • Define velocity potential and stream function
   • Define streamline vs pathline with equations
   • Give examples and physical meaning
5. 7 Marks
   aTwo points A and B are located in a long 20 cm diameter pipe. When a downstream valve is completely closed the difference in pressure between B and A, $(P_B - P_A) = 100$ kPa. When the valve is open and a discharge of 70 L/s of water is flowing, $(P_A - P_B) = 50$ kPa. Calculate the head loss between A and B.
   How to answer

   • Use hydrostatic pressure difference with valve closed to get elevation difference
   • Apply Bernoulli with head loss between A and B for flowing case
   • Relate $(P_B-P_A)$ static to $\Delta z$
   • Compute $h_L$ from $(P_A-P_B)$, velocity and $\Delta z$
6. 7 Marks
   bExplain the concept of hydrostatic Paradox.
   How to answer

   • State hydrostatic paradox with vessels of different shape
   • Pressure depends only on height, not volume/weight
   • Explain with $P=\rho g h$ and force demonstration
   • Give example and conclusion
7. 7 Marks
   aProve that in case of forced vortex flow the curve acquired by fluid would be parabola.
   How to answer

   • Consider rotating fluid with angular velocity $\omega$
   • Equilibrium of pressure, centrifugal and gravity forces
   • Derive $dz/dr = \omega^2 r/g$
   • Integrate to get $z = \omega^2 r^2/2g + C$ - parabola
8. 7 Marks
   bWrite short notes on Hydraulic, gradient line, total energy line, Major and minor losses in case of flow through pipes.
   How to answer

   • Define hydraulic gradient line and total energy line
   • Give equations for HGL and TEL
   • Define major losses (friction) and minor losses
   • List formulas for bends, entrance, exit etc.
9. 7 Marks
   aWhat do you mean by boundary layer separation? What is the effect of pressure gradient on boundary layer separation?
   How to answer

   • Define boundary layer separation and separation point
   • Explain adverse pressure gradient effect
   • Describe backflow and wake formation
   • Methods to control separation
10. 7 Marks
    bWrite short notes on Stagnation Properties.
    How to answer

    • Define stagnation point and stagnation properties
    • Give $P_0, T_0, \rho_0$ relations for compressible flow
    • Explain isentropic relations
    • Mention applications in Pitot tube, nozzles
11. 7 Marks
    aA lawn sprinkler has two jets of 1.5 cm diameter on a rotating arm which can describe a circle of 60 cm diameter Fig. If the rotating speed is 210 rpm and the discharge is 3.0 L/s. Calculate the torque due to friction at the axis of rotation.

    

    How to answer

    • Compute jet velocity from discharge and diameter
    • Apply moment of momentum for rotating sprinkler
    • Find ideal torque without friction
    • Subtract actual effect to get frictional torque at axis
12. 7 Marks
    bDifferentiate shear thinning and shear thickening fluids with graphical representation.
    How to answer

    • Define shear thinning (pseudoplastic) and shear thickening (dilatant)
    • Draw shear stress vs shear rate and viscosity vs shear rate graphs
    • Give examples of each fluid
    • Compare flow behaviour index n<1 vs n>1
13. 7 Marks
    aA 20 cm diameter pipe has a $90^{\circ}$ bend (to the right) in the horizontal plane. When a discharge of 150 L/s of oil (RD = 0.8) is sent in this pipe, the pressure at the beginning of the bend is found to be 0.5 m of oil. Estimate the resultant force exerted by the oil on the bend.
    How to answer

    • Calculate velocity from $Q$ and pipe area
    • Apply momentum equation in x and y for 90-degree bend
    • Include pressure force at inlet $P=\rho g h$
    • Compute resultant force magnitude and direction
14. 7 Marks
    bWhy relative position of center of gravity and center of buoyancy cannot decide the stability of floating bodies?
    How to answer

    • Define centre of gravity, centre of buoyancy and metacentre
    • Explain metacentric height governs stability
    • Show cases where G above B can still be stable
    • Conclude relative G-B position alone insufficient
15. 7 Marks
    aA smooth flat plate 1.5 m wide and 2 m long is subjected to flow of water along its length at a uniform velocity of 2 m/s. Find ($\rho = 998$ kg/m$^3$, $\nu = 10^{-6}$ m$^2$/s).

    1. i)the extent of the laminar boundary layer on the plate
    2. ii)the thickness of the boundary layer at the edge of the laminar boundary layer and at the trailing edge
    3. iii)the shear stress at the trailing edge
    How to answer

    • Compute Reynolds number $Re_x = Ux/\nu$ and critical $Re_{crit}=5\times10^5$
    • Find laminar length $x_{crit}$
    • Compute $\delta = 5x/\sqrt{Re_x}$ at $x_{crit}$ and at $L=2m$
    • Compute wall shear $\tau_0 = 0.332 \rho U^2/\sqrt{Re_x}$ at trailing edge
16. 4 Marks
    bWrite the expression of Navier stokes equation and explain the uses of this equation.
    How to answer

    • Write Navier-Stokes vector and component form
    • Explain pressure, viscous and body force terms
    • Mention incompressible Newtonian assumptions
    • List uses: pipe flow, boundary layer, CFD, aerodynamics
17. 3 Marks
    cHow concept of control volume is more important than the concept of system in fluid mechanics.
    How to answer

    • Define system vs control volume
    • Explain Lagrangian vs Eulerian approach
    • Advantages for mass, momentum, energy analysis in fluid machines
    • Give examples of nozzles, turbines