# Bengal Engineering and Science University 2006 B.E Civil Engineering Fluid Mechanics-II - Question Paper

the ques. paper is with the attachment in pdf format.

Ex/BESUS/AM-402/06 B.E. (CE) Part-II 4th Semester Examination, 2006

Time : 3 hours Full Marks : 100

Use separate answerscrivt for each half.

Answer SIX questions, taking THREE from each half.

The questions are of equal value.

Programmable Calculator is not allowed in Examination Hall.

Oil of dynamic viscosity 1.53 poise and specific gravity 0.82 flows through

1. a)

3 km long and 25 cm diameter pipe. What is the Critical Velocity for the pipe? If the actual flow rate through the pipe is 65 liters/s, find the head loss and power loss in the pipe due to the viscous friction.

Two reservoirs are connected by a 4 km long and 60 cm diameter pipe. The steady difference of water levels in the reservoirs is 20m. At a distance of 1 km from the upper reservoirs, a small pipe is connected to the main pipe line, such that water may be drawn off (tapped). Find the discharge to the lower reservoir, if (i) no water is tapped through the small pipe, (ii) 250 liters/s of water is tapped through the small pipe. Take f = 0.02 and neglect minor losses.

b)

2. Two reservoirs having steady water surface level difference of 10m, are connected by a pipe line ABCD. The first part of the pipe line AB is 10cm in diameter, 40m long and has f = 0.03. The second part BD is 15cm in diameter, 60m long and f = 0.025. The part BD has a fully open gate valve (k = 4) fitted at C, the mid span of BD. Two parts AB and BD are connected in series. All changes in flow area at entrance A, exit D and expansion at D are abrupt. Find the flow rate entering in to the lower reservoir.

Evaluate different losses in the tabular form. Plot the hydraulic and energy grade lines on a neat proportionate diagram, indicating the values at salient points on the lines.

The water surface elevations in reservoirs A and B are given as Z_{A} = 14m and Z_{B} = 25m respectively and the discharges through pipe 3 is given as Q_{3} = 0.02 m^{1}/s. Find the discharges through pipes 1 and 2, with their flow direction and the water surface elevation in the reservoir C. Take f = 0.04 for all pipes and neglect minor losses. Assume that the water surface elevations in all the reservoir remain steady.

4. A pipe network having four junctions A, B, C and D, comprises of five pipes AB, BC, CD, DA and BD, whose diameters, lengths and friction factors are given as follows :

Pipe |
AB |
BC |
CD |
DA |
BD |

diameter (m) |
0.3 |
0.4 |
0.4 |
0.5 |
0.3 |

Length (m) |
1000 |
1600 |
1200 |
1200 |
800 |

f |
0.024 |
0.02 |
0.02 |
0.02 |
0.024 |

If inflows into junctions A and B are 10m^{3}/s and 2m^{3}/s, respectively, and out flow from each of junctions C and D is 6m^{3}/s, estimate the flow through each pipe with their directions. Neglect minor losses.

5. a) An aircraft weighing 120 kN has a total wing area of 20m . It flies at a velocity of 360 km/hr at a steady level in still air. Find the lift coefficient, the total drag force on the wings, taking 0.06 and the power required to keep the aircraft flying with this velocity.

b) In case of a solid sphere falling through a fluid medium, starting with Stokes law, derive an expression for its terminal velocity.

c) A 10mm diameter steel ball (sp. wt.75 kN/m^{3}) falls through glycerine (sp. wt. 8 kN/m^{3}) with a terminal velocity of 0.21 m/s. Find the drag force induced on the solid spherical steel ball and the coefficient of drag.

SECOND HALF

6. (a) In a three-dimensional incompressible flow, two orthogonal velocity components are given as -

u - x, v = 2y.

Find the simplest form of the third mutually orthogonal velocity component and the corresponding equation of the streamline passing through the point (2,2,2).

(b) Verify that existence of velocity potential function for a flow field automatically ensures that the flow is

irrotational. The velocity potential function in a two-dimensional flow field is <j> = y^{2} -x^{2}. Describe the flow and sketch the flow net (showing at least three streamlines and three equipotential lines) in the first quadrant of coordinate plane.

7. (a) In a two dimensional flow the streamlines are concentric circles with origin of coordinates as centre

and velocity at a point is directly proportional to the distance of the point from the origin and is directed perpendicular to the line joining the point to the origin. Find the stream function and show that the vorticity is constant.

(b) The velocity along the centre line of the Hagen-Poiseuille flow in a 10 cm diameter pipe is 1.8 m/s. If the specific gravity and the viscosity of the liquid are 0.8 and 0.072 Ns/m^{2}, respectively, calculate: (i) the volumetric flow rate, (ii) shearing stress in fluid near pipe wall, (iii) local skin friction coefficient and (iv) the head loss over a length of 15 metres of the pipe.

8. (a) Starting from Navier-Stokes equations, or otherwise, verify that for plane Poiseuille flow the variation

of shear stress across the flow may be expressed as

where x is measured in the direction of flow, z is measured normal to the plates and other notations have their usual meanings.

(b) Lubricating oil of sp. gr. 0.80 and viscosity 60 centipoises flows between two fixed plates held 8 cm apart. If the flow rate between the plates is 120 litres/second per metre width, determine (i) velocity at a distance of 1 cm from the lower plate, (ii) viscous shear stress exerted by oil on the upper plate, (iii) the gradient of piezometric head along the flow direction and (iv) the required slope of the plates to maintain uniform pressure throughout the flow domain.

9. (a) What is boundary layer? Calculate the displacement thickness and momentum thickness, as

fractions of boundary layer thickness, for the laminar boundary layer velocity profile given, with conventional notations, by -

8 8

(b) The velocity profile, in laminar boundary layer over a flat plate at zero angle of incidence, is estimated 2 y y^{2}

as u/U =--. Using integral momentum relation or otherwise, obtain expressions for boundary

s.

S S

layer thickness, shear stress on the plate and skin friction coefficient at varying distances from the leading edge.

10. (a) The stream function for a two-dimensional irrotational vortex motion (in a horizontal plane) of an ideal fluid is given by y/ = In (x^{2} + .y^{2}). Taking values of pressure and velocity at point (5,5) as reference values, obtain expressions for dimensionless velocity distribution and dimensionless pressure distribution along x-axis (i.e., y = 0). Plot, approximately to scale, the above dimensionless pressure distribution in the range 3 s x < 7.

(b) A thin smooth rectangular plate, 0.40 m x 1 m, is placed in atmospheric air streaming at 72 km per hour parallel to plate and along the direction of its longer dimension. Assuming that transition of boundary layer from laminar to turbulent occurs at Reynolds number of 3x10^{5}, estimate the thickness of the boundary layer at the rear of the plate. For air take density as 1.2 kg/m^{3} and dynamic viscosity as 18x10~^{6} Ns/m^{2}.

Three reservoirs A, B and C are connected by three pipes 1, 2 and 3 respectively, which have a common junction. The lengths and diameters of pipes 1, 2 and 3 are respectively 1] = 600m, dj = 30cm, 1_{2} = 1000m, d_{2} =30cm, 1_{3} =1300m, d_{3} = 20cm.

Attachment: |

Earning: Approval pending. |