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*8053* (Pages : 4) 8053<br />
Reg. No. : .....................................<br />
Name : ..........................................<br />
Fourth Semester B.Tech. Degree Examination, December 2009<br />
(2003 Scheme)<br />
03.405 : <strong>FLUID</strong> <strong>MECHANICS</strong> <strong>–</strong> <strong>II</strong> (C)<br />
Time : 3 Hours Max. Marks : 100<br />
Note: Answers shall be brief and illustrated with sketches wherever necessary.<br />
Answer all questions.<br />
PART <strong>–</strong> A<br />
1. Water flows in a channel of the shape of isosceles triangle of bedwidth ‘b’ and<br />
sides making an angle 45° with the bed. Determine the relationship between depth<br />
of flow ‘y’ and bed width ‘b’ for the maximum velocity condition. Use Manning’s<br />
equation and assume ‘y’ less than b/2.<br />
2. Explain the difference between alternate depth and sequent depth of flow in an<br />
open channel.<br />
3. For a constant specific energy of 0.8 N.m/N, calculate the maximum discharge that<br />
may occur in a rectangular channel 4.0 m wide.<br />
4. Illustrate the gradually varied flow profiles S 3 and M 2 type giving the salient points.<br />
5. Determine the displacement thickness, momentum thickness and shape factor in<br />
terms of the nominal boundary layer thickness '� ',<br />
for the velocity profile in the<br />
boundary layer on a flat plate expressed by u / u o � ( y / �)<br />
, where ‘u’ is velocity<br />
at a height ‘y’ above the surface, and ‘uo ’ the free stream velocity.<br />
6. State the differential equation for gradually varied flow, indicating the assumptions<br />
clearly.<br />
7. A jet of water coming from a nozzle with a velocity of 24 m/s, and it impinges<br />
normally on a flat plate moving away from it at 12 m/s. If the cross-sectional area of<br />
the jet is 0.02 m 2 , determine the force developed on the plate.<br />
8. What is meant by multistage pumps ? State the purposes and procedures used in<br />
multistaging. (8×5=40 Marks)<br />
1/<br />
m<br />
P.T.O.
8053 -2- *8053*<br />
PART <strong>–</strong> B<br />
Module <strong>–</strong> I<br />
9. a) A concrete lined circular channel of diameter 2.0 m has a bed slope of 1 in 600.<br />
Work out the flow rate of the most economical section for the maximum velocity<br />
criteria. Assume roughness co-efficient of channel as 0.016. 8<br />
b) A 5.0 m wide rectangular channel carries a discharge of 20 m3 /s at a depth of<br />
flow of 2.0 m. Determine :<br />
i) width to which the channel section should be contracted so that the depth in<br />
contracted section is critical<br />
ii) depth at the contracted section if the width there is 4.0 m<br />
iii) depth of flow in the upstream and in the contracted section if the width of the<br />
channel is reduced to 2.5 m. 12<br />
OR<br />
10. a) A trapezoidal channel having a bottom width of 10 m, and a side slope of 2H:1V<br />
has got a conveyance factor of 948.7 m 3 /s when uniform flow occurs in the<br />
channel. Find the normal discharge passing through the channel. Also find the<br />
normal depth of flow. Take the bed slope of channel as 1 in 1000 and roughness<br />
of channel as 0.013. 10<br />
b) State the condition for the formation of a hydraulic jump in open channel flow.<br />
A hydraulic jump occurs in a rectangular channel and the depths of flow before<br />
and after the jump one 0.5 m and 2.0 m respectively. Calculate the critical depth<br />
of flow. Also calculate the Froude’s number before the jump and energy loss in<br />
the jump. 10<br />
Module <strong>–</strong> <strong>II</strong><br />
11. a) The resistance R experienced by a partially submerged body depends upon the<br />
velocity ‘v’, length of the body ‘l’, viscosity of fluid (� ), density of fluid, '�'<br />
and acceleration due to gravity ‘g’. Show that the dimensionless expression for<br />
R is a function of the Reynolds number and Frodue’s number of flow. 10<br />
b) Illustrate with the help of a figure, the phenomena of Boundary layer separation,<br />
stating clearly pressure gradient and velocity gradient effects. 5
*8053* -3- 8053<br />
c) The velocity profiles for a boundary layer in terms of the nominal boundary<br />
layer thickness '� ' is given below. Check whether there is a possibility of<br />
separation of boundary layer. State reasons for the answer :<br />
i) u/u 0 =<br />
2( y / �)<br />
� ( y / �)<br />
4 3<br />
ii) u/u 0 = 2(<br />
y / �)<br />
� ( y / �)<br />
� 2(<br />
y / �)<br />
2<br />
where ‘u’ represents the velocity at a height ‘y’ above the surface and u 0 the<br />
free stream velocity. 5<br />
OR<br />
�5<br />
12. a) Oil of kinematic viscosity 4.<br />
6 � 10 m / s is used in a flow situation where the<br />
prototype is influenced by both viscous and gravity force effects. If the model<br />
scale ratio is 1:6, what should be the kinematic viscosity of the fluid to be used<br />
in the model so as to achieve dynamic similarity ? 8<br />
2<br />
b) State Buckingham � -theorem and explain how it can be used for deriving the<br />
functional relationship between variables in a fluid flow problem. 6<br />
c) A flat plate 2.0 m long � 5.0 m wide is placed in an air stream having a velocity<br />
of 90 km/hour. The drag co-efficients for laminar and turbulent boundary layers<br />
are given by<br />
C � 1.<br />
33 Re (laminar)<br />
D<br />
0.<br />
455<br />
CD �<br />
(log Re )<br />
10<br />
l<br />
l<br />
2.<br />
58<br />
(turbulent)<br />
Where Re l is the Reynolds number. Compute the skin friction drag over the<br />
entire length of the plate and find the thickness of the boundary layer at a distance<br />
of 1.5 m from the leading edge ? 6
8053 -4- *8053*<br />
Module <strong>–</strong> <strong>II</strong>I<br />
13. a) In a Pelton wheel, the bucket deflects the jet by 165° and the relative velocity is<br />
reduced by 10% due to frictional loss in the bucket. If the speed ratio of the<br />
wheel is 0.45, find the hydraulic efficiency of the wheel. The bucket circle diameter<br />
of the wheel is 0.9 m and there is one jet having a co-efficient of velocity 0.97.<br />
Take the mechanical efficiency of the wheel as 90%. If the wheel develops<br />
1750 kW under a head of 560 m, calculate the speed of the wheel and the<br />
diameter of nozzle. 10<br />
b) The diameter and stroke length of a single acting reciprocating pump are 10 cm<br />
and 20 cm respectively. The pump is fed by a suction pipe 6 cm. in diameter<br />
and 5 m long, the suction lift being 3.5 m. What is the maximum speed at which<br />
the pump can be run without separation in the suction pipe ? Given that separation<br />
occurs when pressure in the pump falls below 2.4 m of water (absolute) and the<br />
manometer reads 760 mm. of mercury. 10<br />
OR<br />
14. a) A two stage centrifugal pump has an impeller of 40 cm in diameter and 20 cm<br />
wide. The blade angle at the outlet is 40° and the area occupied by the thickness<br />
of vanes may be assumed as 8.5% of the outlet area. If the pump delivers<br />
216 m 3 /hour, when running at 910 r.p.m, calculate the power required to drive<br />
the pump, the manometric head and specific speed of pump. Assume mechanical<br />
efficiency as 85% and manometric efficiency as 75%. 10<br />
b) Briefly explain the phenomena of cavitation in turbines and its effects. 5<br />
c) A turbine develops 2300 kW under a net head of 5.65 m with an overall efficiency<br />
of 85%. The draft tube of the turbine has a diameter of 2.75 m at its inlet and has<br />
an efficiency of 75%. In order to avoid cavitation, the pressure head at the entry<br />
to the draft tube must not drop more than 4.4 m below atmosphere. Calculate<br />
the maximum height at which the runner may be set above the tail race level. 5<br />
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