Question Paper: Fluid Mechanics Question Paper - May 18 - Mechanical Engineering (Semester 4) - Mumbai University (MU)

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## Fluid Mechanics - May 18

### Mechanical Engineering (Semester 4)

Total marks: 80

Total time: 3 Hours
INSTRUCTIONS

(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Draw neat diagrams wherever necessary.

**1.a.**Explain briefly the boundary layer formation and define boundary layer thickness.

**1.b.**With neat sketch explain working and construction of a Pitot tube.

**1.c.**The following represent the velocity components. Calculate the unknown velocity component so that they satisfy the continuity equation.

$u=2 x^{2} \quad ; \quad v=2 x y z$

**1.d.**The absolute viscosity of a liquid having a specific gravity of 0.87 is 0.073 Poise. Find its kinematics viscosity in $\mathrm{m}^{2} / \mathrm{s}$ and in stokes.

**1.e.**Explain Stability of floating bodies.

**2.a.**Derive the differential form of the general mass conservation equation in Cartesian coordinate for a fluid.

**2.b.**A semicircular 12 $\mathrm{m}$ diameter tunnel is to be built under a 45 $\mathrm{m}$ deep, 240 $\mathrm{m}$ long lake. Determine the magnitude and direction of total hydrostatic force acting on the roof of the tunnel.

**3.a.**A $90^{\circ}$ vertical reducing bend has a diameter 300 $\mathrm{mm}$ at inlet and 150 $\mathrm{mm}$ at exit carries 0.6 $\mathrm{m}^{3} / \mathrm{s}$ oil of specific gravity 0.85 with a pressure of 120 $\mathrm{KN} / \mathrm{m}^{2}$ at inlet to the bend. The volume of bend is 0.15 $\mathrm{m}^{3} .$ Find the magnitude and direction of the force on the bend. Neglect the frictional losses and assume both inlet and outlet sections to be at same horizontal level.

**3.b.**Consider a two dimensional viscous incompressible flow of a Newtonian fluid between two parallel plates, separated by a distance 'b'. One of the plates is stationary and the other is moving with a uniform velocity U. There is no pressure gradient in the flow. Obtain the general equation from the general Navier-Stokes equation.

**4.a.**Using the laminar boundary layer velocity distribution: $\frac{u}{U_{\infty}}=2\left(\frac{y}{\delta}\right)-2\left(\frac{y}{\delta}\right)^{2}+\left(\frac{y}{\delta}\right)^{4}$

i) Check if boundary layer separation occurs. ii) Determine Boundary layer thickness (In terms of Re)

**4.b.**Derive Euler's equation of motion in Cartesian co-ordinate.

**5.a.**Air has a velocity of 1000 $\mathrm{km} / \mathrm{hr}$ at a pressure of 9.81 $\mathrm{KN} / \mathrm{m}^{2}$ vacuum and a temperature of $47^{\circ} \mathrm{C}$ . Compute its stagnation properties (Pressure, Temperature and Density). Take atm. pressure $98.1 \mathrm{KN} / \mathrm{m}^{2}, \mathrm{R}=287 \mathrm{J} / \mathrm{Kg}^{\circ} \mathrm{K}$ and $\Upsilon=1.4$

**5.b.**A flow has a velocity potential function as $\emptyset=x^{3}-3 \mathrm{xy}^{2} .$ Verify whether it represents a valid flow field. If it dees then determine the stream function.

**6.a.**Two reservoirs are connected by three pipes in series.

Pipe | Length | Diameter | f |
---|---|---|---|

1 | 500 m | 30 cm | 0.02 |

2 | 200 m | 10 cm | 0.025 |

3 | 100 m | 10 cm | 0.03 |

Calculate the discharge through them if the elevation difference of the levels is in the reservoirs is 10 $\mathrm{m}$ considering minor losses.

**6.b. Write short notes (any TWO)**

**6.b.i.**Moody's Diagram

**6.b.ii.**Lift force on circulating cylinder in uniform flow.

**6.b.iii.**Compressible flow through the Convergent Divergent Nozzle