CE-501 Fluid Mechanics - I - 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
   aDefine the following fluid properties: Density, weight density, specific volume and specific gravity of a fluid.
   How to answer

   • Define density as mass per unit volume with formula and units
   • Define weight density / specific weight with formula
   • Define specific volume and specific gravity with relations
   • Give typical values / examples for water
2. 7 Marks
   bAn oil film of thickness $1.5\,mm$ is used for lubrication between a square plate of size $0.9\,m \times 0.9\,m$ and an inclined plane having an angle of inclination $20^{\circ}$. The weight of the square plate is $392.4\,N$ and it slides down the plane with a uniform velocity of $0.2\,m/s$. Find the dynamic viscosity of the oil.
   How to answer

   • Resolve plate weight component along 20 degree incline
   • Apply Newton's law of viscosity tau = mu*du/dy
   • Equate shear force on plate area to driving component
   • Solve for mu and state units
3. 7 Marks
   aDefine viscosity and kinematic viscosity and explain the variation of viscosity with respect to temperature.
   How to answer

   • Define dynamic viscosity mu and kinematic viscosity nu = mu/rho
   • State units of both
   • Explain viscosity decreases with temperature for liquids
   • Explain viscosity increases with temperature for gases with reason
4. 7 Marks
   bA $15\,cm$ diameter vertical cylinder rotates concentrically inside another cylinder of diameter $15.10\,cm$. Both the cylinder is $25 cm$ high. The space between the cylinder is filled with a liquid whose viscosity is unknown if a torque of $12\,N/m$ is required to rotate the inner cylinder at $120\,rpm$. Determine the viscosity of fluid.
   How to answer

   • Compute clearance and tangential velocity from 120 rpm
   • Apply Newton's viscosity for concentric cylinders torque formula
   • Substitute torque 12 N/m, height 25 cm, diameters
   • Solve for viscosity and give units
5. 7 Marks
   aDefine absolute, vacuum and gauge pressures.
   How to answer

   • Define absolute pressure with reference to absolute vacuum
   • Define gauge pressure with reference to atmosphere
   • Define vacuum pressure as negative gauge
   • Give relation P_abs = P_atm +/- P_gauge
6. 7 Marks
   bExplain about U-tube differential manometer and inverted U-tube differential manometer?
   How to answer

   • Describe construction of U-tube differential manometer
   • Explain working for measuring pressure difference
   • Describe inverted U-tube for light fluids / gases
   • Mention manometric equation and applications
7. 7 Marks
   aExplain about velocity potential function and stream function.
   How to answer

   • Define velocity potential function phi and condition for existence
   • Define stream function psi and its properties
   • Give relations u, v in terms of phi and psi
   • Explain equipotential and streamlines orthogonality
8. 7 Marks
   bDefine the equation of continuity. Obtain the expression for continuity equation in three dimensions?
   How to answer

   • State law of conservation of mass for fluid element
   • Derive 3D continuity equation partial rho/partial t + div(rho V)=0
   • Simplify for steady incompressible flow
   • Give Cartesian form du/dx+dv/dy+dw/dz=0
9. 7 Marks
   aDefine momentum equation and its applications.
   How to answer

   • State momentum principle from Newton's second law
   • Write impulse-momentum equation in vector form
   • List applications: pipe bends, jets, vanes, hydraulic machines
   • Mention assumptions
10. 7 Marks
    bA $45^{\circ}$ reducing bend is connected in a pipe line, the diameters at the inlet and outlet of the bend being $600\,mm$ and $300\,mm$ respectively. Find the force exerted by water on the bend if the intensity of pressure at inlet to bend is $8.829\,N/cm^{2}$ and rate of flow of water is $600\,litres/s$.
    How to answer

    • Calculate inlet/outlet areas and velocities from Q=600 litres/s
    • Apply continuity and Bernoulli to get outlet pressure
    • Apply momentum equations in x and y for 45 degree bend
    • Compute resultant force exerted by water on bend
11. 14 Marks
    The difference in water surface levels in two tanks, which are connected by three pipes in series of lengths $300\,m$, $170\,m$, and $210\,m$ and of diameters $300\,mm$, $200\,mm$ and $400\,mm$ respectively is $12\,m$. Determine the rate of flow of water if co-efficient of friction are $0.005$, $0.0052$ and $0.0048$ respectively. Considering:

    1. i)Minor losses
    2. ii)neglecting minor losses.
    How to answer

    • Write energy equation between tanks with major + minor losses
    • Express head loss in each pipe using friction coefficients
    • Solve for discharge considering minor losses
    • Solve for discharge neglecting minor losses and compare
12. 7 Marks
    aDetermine the expression for rate of flow through the venturi meter?
    How to answer

    • Apply Bernoulli between inlet and throat with continuity
    • Introduce Cd and manometer head difference
    • Derive Q = Cd*A1*A2*sqrt(2gh)/sqrt(A1^2-A2^2)
    • State assumptions of horizontal venturimeter
13. 7 Marks
    bA horizontal venturi meter with inlet diameter $20\,cm$ and throat diameter $10\,cm$ is used to measure the flow of oil of sp.gr. $0.8$. The discharge of oil through venturi meter is $60\,lit/s$. Find the reading of oil-mercury differential manometer. Take $Cd = 0.98$.
    How to answer

    • Compute inlet and throat areas and theoretical discharge formula
    • Use given Q and Cd to find differential head h
    • Convert head to oil-mercury manometer reading using specific gravities
    • Report manometer deflection
14. 7 Marks
    aExplain in brief about the different types of kinematics of flow
    How to answer

    • Define steady/unsteady, uniform/non-uniform flow
    • Explain laminar/turbulent, compressible/incompressible
    • Explain rotational/irrotational, 1D/2D/3D flow
    • Give examples of each type
15. 7 Marks
    bWhat do you understand by the dimension analysis and describe in brief about the uses of Buckingham-pi theorem.
    How to answer

    • Define dimensional analysis and its purpose
    • State Buckingham-pi theorem and formation of pi terms
    • Explain procedure with variables m, n, repeating variables
    • List uses: model testing, empirical relations, checking equations