FLUID MECHANICS – II (C)

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Reg. No. : .....................................
Name : ..........................................
Fourth Semester B.Tech. Degree Examination, December 2009
(2003 Scheme)
03.405 : FLUID MECHANICS – II (C)
Time : 3 Hours Max. Marks : 100
Note: Answers shall be brief and illustrated with sketches wherever necessary.
Answer all questions.
PART – A
1. Water flows in a channel of the shape of isosceles triangle of bedwidth ‘b’ and
sides making an angle 45° with the bed. Determine the relationship between depth
of flow ‘y’ and bed width ‘b’ for the maximum velocity condition. Use Manning’s
equation and assume ‘y’ less than b/2.
2. Explain the difference between alternate depth and sequent depth of flow in an
open channel.
3. For a constant specific energy of 0.8 N.m/N, calculate the maximum discharge that
may occur in a rectangular channel 4.0 m wide.
4. Illustrate the gradually varied flow profiles S 3 and M 2 type giving the salient points.
5. Determine the displacement thickness, momentum thickness and shape factor in
terms of the nominal boundary layer thickness '� ',
for the velocity profile in the
boundary layer on a flat plate expressed by u / u o � ( y / �)
, where ‘u’ is velocity
at a height ‘y’ above the surface, and ‘uo ’ the free stream velocity.
6. State the differential equation for gradually varied flow, indicating the assumptions
clearly.
7. A jet of water coming from a nozzle with a velocity of 24 m/s, and it impinges
normally on a flat plate moving away from it at 12 m/s. If the cross-sectional area of
the jet is 0.02 m 2 , determine the force developed on the plate.
8. What is meant by multistage pumps ? State the purposes and procedures used in
multistaging. (8×5=40 Marks)
1/
m
P.T.O.

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PART – B
Module – I
9. a) A concrete lined circular channel of diameter 2.0 m has a bed slope of 1 in 600.
Work out the flow rate of the most economical section for the maximum velocity
criteria. Assume roughness co-efficient of channel as 0.016. 8
b) A 5.0 m wide rectangular channel carries a discharge of 20 m3 /s at a depth of
flow of 2.0 m. Determine :
i) width to which the channel section should be contracted so that the depth in
contracted section is critical
ii) depth at the contracted section if the width there is 4.0 m
iii) depth of flow in the upstream and in the contracted section if the width of the
channel is reduced to 2.5 m. 12
OR
10. a) A trapezoidal channel having a bottom width of 10 m, and a side slope of 2H:1V
has got a conveyance factor of 948.7 m 3 /s when uniform flow occurs in the
channel. Find the normal discharge passing through the channel. Also find the
normal depth of flow. Take the bed slope of channel as 1 in 1000 and roughness
of channel as 0.013. 10
b) State the condition for the formation of a hydraulic jump in open channel flow.
A hydraulic jump occurs in a rectangular channel and the depths of flow before
and after the jump one 0.5 m and 2.0 m respectively. Calculate the critical depth
of flow. Also calculate the Froude’s number before the jump and energy loss in
the jump. 10
Module – II
11. a) The resistance R experienced by a partially submerged body depends upon the
velocity ‘v’, length of the body ‘l’, viscosity of fluid (� ), density of fluid, '�'
and acceleration due to gravity ‘g’. Show that the dimensionless expression for
R is a function of the Reynolds number and Frodue’s number of flow. 10
b) Illustrate with the help of a figure, the phenomena of Boundary layer separation,
stating clearly pressure gradient and velocity gradient effects. 5

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c) The velocity profiles for a boundary layer in terms of the nominal boundary
layer thickness '� ' is given below. Check whether there is a possibility of
separation of boundary layer. State reasons for the answer :
i) u/u 0 =
2( y / �)
� ( y / �)
4 3
ii) u/u 0 = 2(
y / �)
� ( y / �)
� 2(
y / �)
2
where ‘u’ represents the velocity at a height ‘y’ above the surface and u 0 the
free stream velocity. 5
OR
�5
12. a) Oil of kinematic viscosity 4.
6 � 10 m / s is used in a flow situation where the
prototype is influenced by both viscous and gravity force effects. If the model
scale ratio is 1:6, what should be the kinematic viscosity of the fluid to be used
in the model so as to achieve dynamic similarity ? 8
2
b) State Buckingham � -theorem and explain how it can be used for deriving the
functional relationship between variables in a fluid flow problem. 6
c) A flat plate 2.0 m long � 5.0 m wide is placed in an air stream having a velocity
of 90 km/hour. The drag co-efficients for laminar and turbulent boundary layers
are given by
C � 1.
33 Re (laminar)
D
0.
455
CD �
(log Re )
10
l
l
2.
58
(turbulent)
Where Re l is the Reynolds number. Compute the skin friction drag over the
entire length of the plate and find the thickness of the boundary layer at a distance
of 1.5 m from the leading edge ? 6

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Module – III
13. a) In a Pelton wheel, the bucket deflects the jet by 165° and the relative velocity is
reduced by 10% due to frictional loss in the bucket. If the speed ratio of the
wheel is 0.45, find the hydraulic efficiency of the wheel. The bucket circle diameter
of the wheel is 0.9 m and there is one jet having a co-efficient of velocity 0.97.
Take the mechanical efficiency of the wheel as 90%. If the wheel develops
1750 kW under a head of 560 m, calculate the speed of the wheel and the
diameter of nozzle. 10
b) The diameter and stroke length of a single acting reciprocating pump are 10 cm
and 20 cm respectively. The pump is fed by a suction pipe 6 cm. in diameter
and 5 m long, the suction lift being 3.5 m. What is the maximum speed at which
the pump can be run without separation in the suction pipe ? Given that separation
occurs when pressure in the pump falls below 2.4 m of water (absolute) and the
manometer reads 760 mm. of mercury. 10
OR
14. a) A two stage centrifugal pump has an impeller of 40 cm in diameter and 20 cm
wide. The blade angle at the outlet is 40° and the area occupied by the thickness
of vanes may be assumed as 8.5% of the outlet area. If the pump delivers
216 m 3 /hour, when running at 910 r.p.m, calculate the power required to drive
the pump, the manometric head and specific speed of pump. Assume mechanical
efficiency as 85% and manometric efficiency as 75%. 10
b) Briefly explain the phenomena of cavitation in turbines and its effects. 5
c) A turbine develops 2300 kW under a net head of 5.65 m with an overall efficiency
of 85%. The draft tube of the turbine has a diameter of 2.75 m at its inlet and has
an efficiency of 75%. In order to avoid cavitation, the pressure head at the entry
to the draft tube must not drop more than 4.4 m below atmosphere. Calculate
the maximum height at which the runner may be set above the tail race level. 5
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