CE-604-A Fluid Mechanics-II - May 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
   aEnunciate Newton's law of viscosity. Explain importance of viscosity in fluid motion. What is effect of temperature on viscosity of water and that of air?
   How to answer

   • State Newton's law: shear stress proportional to velocity gradient, tau = mu*du/dy
   • Define dynamic and kinematic viscosity
   • Explain role of viscosity in resistance, shear, boundary layer and losses
   • Effect of temperature: liquids decrease, gases increase with reason
2. 7 Marks
   bFor laminar flow of an oil having dynamic viscosity $u = 1.766$ Pa.s in a $0.4$m diameter pipe, the velocity distribution is parabolic with a maximum point velocity of $4$ m/s at the center of the pipe. Calculate the shear stresses at the pipe wall and within the fluid $40$ mm from the pipe wall.
   How to answer

   • Assume parabolic profile u = Umax*(1 - (r/R)^2)
   • Compute velocity gradient du/dr
   • Apply tau = mu*du/dr at r=R for wall
   • Evaluate at 40 mm from wall i.e. r = R-0.04 m
3. 7 Marks
   aWrite a note on the historical development of fluid mechanics.
   How to answer

   • Outline ancient to modern contributors
   • Developments in hydrostatics, hydraulics and theoretical fluid mechanics
   • Mention Prandtl boundary layer, Reynolds, Bernoulli, Euler etc.
4. 7 Marks
   bDiscuss the concept that "a fluid continues to deform so long it is acted upon by a shear force".
   How to answer

   • Define fluid vs solid response to shear
   • Explain continuous deformation under shear
   • Give example of shear in fluid layer
5. 7 Marks
   aExplain briefly a pilot tube with neat sketch diagram and also discuss its measurement of velocity.
   How to answer

   • Describe Pitot tube construction with neat sketch
   • Explain stagnation vs static pressure principle
   • Give velocity formula V = sqrt(2*(p0-p)/rho)
6. 7 Marks
   bFind the smallest diameter of a manometer tube such that error due to capillary action in the measured gauge pressure of $100$ N/m$^2$ is less than $5$ percent. The manometric liquid is water.
   How to answer

   • Relate capillary rise to tube diameter: h_c = 4*sigma*cos(theta)/(rho*g*d)
   • Set allowable error 5% of 100 N/m2 pressure head
   • Solve for smallest diameter satisfying error limit
7. 7 Marks
   aDerive Euler's equation of motion along a stream line and hence derive the Bernoulli's theorem.
   How to answer

   • Consider forces on fluid element along streamline
   • Apply Newton's second law to derive Euler's equation
   • Integrate for steady incompressible flow to get Bernoulli equation
   • State assumptions and final form p/rho*g + V^2/2g + z = constant
8. 7 Marks
   bExplain the working of reciprocating pump.
   How to answer

   • Describe cylinder, piston, suction and delivery valves
   • Explain suction and delivery strokes
   • Mention function of air vessel if applicable
9. 7 Marks
   aExplain the total energy line (energy gradient line) and the hydraulic gradient line for fluid flow through a piping system.
   How to answer

   • Define total energy line and hydraulic gradient line
   • Explain components: datum, pressure and velocity heads
   • Describe relative positions and losses in piping system
10. 7 Marks
    bCalculate the friction drag on a plate $15$ cm wide and $45$ cm long placed longitudinally in a stream of oil (specific gravity $0.925$ and kinematic viscosity $0.9$ stokes) flowing with a free stream velocity of $6$ meter per second. Also find the thickness of the boundary layer and shear stress at the trailing edge.
    How to answer

    • Compute Reynolds number to check laminar/turbulent regime
    • Apply Blasius friction drag formula for plate
    • Compute boundary layer thickness at trailing edge and wall shear
11. 7 Marks
    aA wooden block floats in water with $5$ cm height projecting above the water surface. The block is next launched in glycerin (relative density $= 1.35$) and projects $7.5$ cm above the surface of glycerin. Make calculations for the height of block and its relative density.
    How to answer

    • Apply Archimedes principle for water and glycerin cases
    • Form two equations in block height H and density
    • Solve for H and relative density
12. 7 Marks
    bState and prove the Pascal's law and give some examples where this principle is applied.
    How to answer

    • State Pascal's law: pressure equally transmitted in confined fluid
    • Prove using small fluid element equilibrium
    • Give examples: hydraulic press, jack, brakes
13. 7 Marks
    aThe velocity potential for a two-dimensional flow is, $\phi = x (2y - 1)$ Determine the velocity at the point $P(4, 5)$. Also obtain the value of stream function at this point $P$.
    How to answer

    • Compute u = -dphi/dx, v = -dphi/dy
    • Evaluate at P(4,5) for magnitude and direction
    • Integrate to get stream function psi
14. 7 Marks
    bWhat is pressure head? How pressure can be expressed in terms of height of a liquid column?
    How to answer

    • Define pressure head p/rho*g
    • Explain conversion of pressure to liquid column height
    • Give example with manometer
15. 7 Marks
    aDifferentiate between the Eulerian and Lagrangian method of representing, fluid motion.
    How to answer

    • Define Eulerian: fixed point observation
    • Define Lagrangian: following fluid particle
    • Compare advantages, applications
16. 7 Marks
    bState the principle of pressure measurement by manometer. Explain the difference between a simple and a differential manometer.
    How to answer

    • State hydrostatic principle p = rho*g*h
    • Explain simple manometer types
    • Contrast with differential manometer for pressure difference