CE-501 Fluid Mechanics - I - 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
   aWhat is manometer? What are the different types of manometer?
   How to answer

   • Definition of manometer as pressure measuring device
   • Classification into open, differential, inverted U-tube etc.
   • Simple manometers: piezometer, U-tube, single column
   • Differential and inverted types with sketches
2. 7 Marks
   bDifferentiate the following:

   1. i)Absolute and gauge pressure
   2. ii)Dynamic viscosity and kinematic viscosity
   3. iii)Cohesion and adhesion
   How to answer

   • Define absolute vs gauge pressure with datum
   • Define dynamic viscosity vs kinematic viscosity with formula $\nu=\mu/\rho$
   • Define cohesion vs adhesion with examples
   • Tabular comparison
3. 7 Marks
   aA differential manometer is connected at the two points A and B of two pipes. The pipe A contains a liquid of sp. gr. 1.5 while pipe B contains a liquid of sp. gr. 0.9. The pressures at A and B are $1\text{ kgf/cm}^2$ and $1.8\text{ kgf/cm}^2$ respectively. Find the difference in mercury level in the differential manometer (h).

   

   How to answer

   • Write manometer equation between A and B along datum X-X
   • Convert $kgf/cm^2$ to m of water/liquid heads
   • Include 3 m, 2.0 m legs and mercury specific gravity 13.6
   • Solve for mercury difference $h$
4. 7 Marks
   bDefine the distinguish the following:

   1. i)streamlines and streak lines
   2. ii)rotational and irrotational flow
   How to answer

   • Define streamline vs streakline with equations
   • Steady vs unsteady behaviour and example
   • Define rotational vs irrotational via vorticity
   • Give examples
5. 7 Marks
   aIf $\phi = 3xy$, find $x$ and $y$ components of velocity at $(1, 3)$ and $(3, 3)$. Determining discharge passing between streamlines passing through these points.
   How to answer

   • Use $u=-\partial\phi/\partial x$, $v=-\partial\phi/\partial y$ for $\phi=3xy$
   • Compute u,v at (1,3) and (3,3)
   • Discharge $dq = d\phi$ between streamlines
   • Evaluate $\Delta q = \phi_2-\phi_1$
6. 7 Marks
   bWhat is a flow net? Briefly discuss any one method of drawing a flow net.
   How to answer

   • Definition of flow net: streamlines and equipotentials
   • Properties of squares
   • One method: graphical / electrical analogy / numerical
   • Steps and use for seepage discharge
7. 7 Marks
   aThe actual velocity of a liquid issuing through a $7\text{ cm}$ diameter orifice fitted in a open tank is $6\text{ m/s}$ under a head of $3\text{ m}$. If the discharge measured in a collecting tank is $0.020\text{ m}^3/\text{s}$, calculate the coefficient of velocity, coefficient of contraction and the theoretical discharge through the orifice.
   How to answer

   • Compute theoretical velocity $V_{th}=\sqrt{2gH}$
   • Compute $C_v = V/V_{th}$
   • Compute $Q_{th}=A V_{th}$ and $C_d=Q/Q_{th}$
   • Compute $C_c = C_d/C_v$
8. 7 Marks
   bCompare and contrast the discharge of venturimeter, flow nozzle and orifice meter as primary element for flow measurement.
   How to answer

   • Working principle of each primary element
   • Discharge formula with $C_d$ and head loss
   • Comparison of accuracy, loss, cost
   • Suitability for different flows
9. 7 Marks
   aWrite the Bernoulli's equation and explain the terms in it. What are the assumptions made in deriving Bernoulli's equation?
   How to answer

   • State Bernoulli $p/\rho g + V^2/2g + z = H$
   • Explain pressure, velocity and datum heads
   • List assumptions: steady, incompressible, inviscid, along streamline
   • Derivation outline from Euler
10. 7 Marks
    bDifferentiate the following:

    1. i)laminar flow and turbulent flow
    2. ii)smooth surface and rough surface
    How to answer

    • Velocity profile and Reynolds number criteria
    • Shear stress and mixing differences
    • Smooth vs rough based on roughness Reynolds
    • Examples and friction factor behaviour
11. 7 Marks
    aWhat is the significance of Reynold's number? Oil flows in a pipe $80\text{ mm}$ bore diameter with a mean velocity of $0.4\text{ m/s}$. The density is $890\text{ kg/m}^3$ and the viscosity is $0.075\text{ Ns/m}^2$. Show that the flow is laminar and hence deduce the pressure loss per metre length.
    How to answer

    • Define Reynolds number $Re=\rho V D/\mu$
    • Compute Re ~ 379 and confirm <2000 laminar
    • Use Hagen-Poiseuille $\Delta p = 32\mu V L/D^2$
    • Compute pressure loss per metre
12. 7 Marks
    bWhat is meant by geometric, kinematic and dynamic similarities? Are these similarities truly attainable or not?
    How to answer

    • Define geometric, kinematic, dynamic similarity
    • Scale ratios for length, velocity, force
    • Conditions for complete similarity
    • Why full similarity rarely attainable
13. 7 Marks
    aThe resistance $R$ experienced by a partially submerged body depends upon the velocity $v$, length of the body $l$, viscosity of the fluid $\mu$, density of the fluid and $p$ and gravitational acceleration $g$. Using Buckingham's pi theorem, determine an expression for $R$.
    How to answer

    • List variables $R,v,l,\mu,\rho,g$ with dimensions
    • Choose repeating variables $l,v,\rho$
    • Form two pi terms $\mu/\rho v l$, $lg/v^2$
    • Write $R=\rho l^2 v^2 f(Re,Fr)$
14. 7 Marks
    bHow do you derive Darcy Weisbach equation?
    How to answer

    • Consider steady flow in pipe with friction
    • Apply Bernoulli with head loss $h_f$
    • Equate wall shear to pressure force
    • Arrive at $h_f = f L V^2/2gD$
15. 14 Marks
    Write short notes on the following (any four):

    1. i)Buckingham's $\Pi$ Theorem
    2. ii)Stokes law
    3. iii)Pitot tube
    4. iv)Stream function
    5. v)Buoyant force
    6. vi)Friction factor
    How to answer

    • Any four: statement/definition and formula
    • Working principle with neat sketch
    • Key assumptions and applications
    • Example or significance