CE-501 Fluid Mechanics - I - Nov 2023 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. 8 Marks
   aDescribe in brief about the Surface tension and Pressure intensity inside a droplet, a bubble and a liquid jet.
   How to answer

   • Define surface tension and excess pressure concept
   • Droplet: single interface $p=2\sigma/d$ or $4\sigma/d$ by notation
   • Bubble: two interfaces $p=8\sigma/d$
   • Liquid jet: $p=2\sigma/d$ with cylindrical consideration
2. 6 Marks
   bIf a density of a liquid is $840\text{ kg/m}^3$ and kinematics viscosity is $1.70\text{ St}$, find its specific weight, specific gravity, specific volume and coefficient of viscosity.
   How to answer

   • Compute specific weight $w=\rho g$
   • Compute specific gravity $S=\rho/1000$
   • Compute specific volume $v=1/\rho$
   • Convert kinematic viscosity St to $m^2/s$ and $\mu=\rho \nu$
3. 5 Marks
   aDefine Pascal law and intensity of pressure.
   How to answer

   • State Pascal's law of pressure transmission
   • Define intensity of pressure $p=F/A$
   • Unit and isotropic nature
4. 9 Marks
   bDetermine the total forces and pressure distribution diagram for the surface AB, BC, CD and DA and also locate the centre of pressure for the surface BC.

   

   How to answer

   • Compute hydrostatic force $F=\rho g \bar{h} A$ for each face AB, BC, CD, DA
   • Draw triangular/trapezoidal pressure distribution diagrams
   • Locate centre of pressure for BC using $h_p$ formula / $y_p$ formula
   • Account for tube head and tank width
5. 8 Marks
   aDescribe in brief about the Potential function, Stream Function and Flow net.
   How to answer

   • Define velocity potential function and its properties
   • Define stream function and its properties
   • Define flow net, equipotential and streamlines orthogonality
6. 6 Marks
   bIf the velocity component is given by $$U = 8 + 4xy + t^2, V = -(xy + 20t), W = 5x + y$$ Find the velocity and acceleration of a particle at $(3, 2, 1)$ at $t = 1\text{ sec}$.
   How to answer

   • Substitute $x=3, y=2, z=1, t=1$ to get $U,V,W$ and resultant velocity
   • Compute local and convective acceleration components $a_x, a_y, a_z$
   • Compute magnitude of acceleration vector
7. 9 Marks
   aDerive an Equation of Bernoulli's Theorem by using Euler Equation of motion along a streamline.
   How to answer

   • Write Euler equation along streamline
   • Integrate assuming steady, incompressible, along streamline
   • Obtain $p/\rho g + V^2/2g + z = $ constant
8. 5 Marks
   bWrite the Assumption, Limitation and Modification of the Bernoulli's Theorem.
   How to answer

   • List assumptions: steady, incompressible, inviscid, along streamline
   • List limitations: viscous losses, compressibility, unsteady
   • Mention modifications: head loss, pump/turbine head
9. 4 Marks
   aExplain the difference between Venturi meter and Orifice meter.
   How to answer

   • Construction differences: converging-diverging vs orifice plate
   • Head loss and cost comparison
   • Accuracy and application range
10. 10 Marks
    bDerive the Expression for the measurement of Discharge using Orifice Meter.
    How to answer

    • Apply Bernoulli between inlet and orifice sections
    • Introduce continuity and vena-contracta coefficients
    • Obtain $Q = C_d A_0 A_1 \sqrt{2gh}/\sqrt{A_1^2-A_0^2}$ form
11. 5 Marks
    aDescribe in brief about the Weirs and Notches.
    How to answer

    • Define weirs vs notches
    • Types: rectangular, triangular, trapezoidal
    • Uses in open channel flow measurement
12. 9 Marks
    bA pump is pumping water at the rate of $7536\text{ lit/min}$. The pump inlet is $40\text{ cm}$ in diameter and the vacuum pressure over there is $15\text{ cm}$ of Mercury. The pump outlet is $20\text{ cm}$ in diameter and it is $1.2\text{ m}$ above the inlet. The pressure at the Outlet is $107.4\text{ kN/m}^2$. Estimate the power added by pump.
    How to answer

    • Convert discharge to $m^3/s$ and diameters to areas
    • Convert vacuum 15 cm Hg and outlet pressure to head
    • Apply Bernoulli with pump head between inlet and outlet
    • Compute power $P=\rho g Q H_p$
13. 9 Marks
    aDerive the expression for the Velocity Distribution and Shear stress distribution for the flow of a viscous fluid between two parallel fixed plate.
    How to answer

    • Consider steady laminar flow between fixed plates
    • Integrate Navier-Stokes / force balance to get parabolic profile
    • Derive shear stress linear variation across gap
14. 5 Marks
    bA $150\text{ mm}$ diameter pipe carries liquid in laminar regime. At a radial distance of $20\text{ mm}$ from the axis of pipe the velocity is $0.4\text{ m/sec}$ calculate:

    1. i)Max velocity
    2. ii)Mean velocity
    3. iii)Discharge of pipe in lps
    How to answer

    • Use parabolic relation $u = U_{max}(1-r^2/R^2)$ with given $u$ at $r$
    • Compute $U_{max}$ then $U_{mean}=U_{max}/2$
    • Compute $Q = A U_{mean}$ and convert to lps
15. 14 Marks
    Define the following.

    1. i)Bulk Modulus
    2. ii)Reynolds number
    3. iii)Stoke's Law
    4. iv)Stream Lines
    How to answer

    • Define bulk modulus $K = -dp/(dV/V)$
    • Define Reynolds number $Re=\rho VL/\mu$ and significance
    • State Stokes law for drag
    • Define streamlines and properties