USN I I I I I I I I I I I 2002 SCHEMEFourth Semester B.E. Degree
Examination, June-July 2009
F luid Mechanics
ME45
Time: 3 hrs. Max. Marks:IOONote: 1. Answer any FIVE ull
questions.2. Assume any missing data suitably.
a. Define surface tension. Sketch a liquid droplet on a solid
surface wheni) Adhesion is more then cohesionii) Cohesion is more
then adhesionShow the angle of contact on the sketches.A glass tube
of small diameter is dipped tn a mercury container vertically.
Sketch themercury surface inside and outside the tube indicattng
the angle of contact clearly. Obtain anexpression for capillary ~ i
s e / d e p r c s s i o n that would take place in this tube in
terms ofdensityof iquid, surface tension, angle ofcontact and local
accelerationdue to gravity. (10 Marks)b. A cylindrical shaft of90
mm diameter rotates about a vertical axis inside a fixed
cylindricaltubo of length 0.5 m and 95 mm internal diameter. I f he
space between tube and the shaft isfilled by a lubricant of
viscosity 0.2 Pa.s, determine the power required to overcome
viscousresistance when the shaft is rotated at a speed of240rpm.
(10 Marks)2 B. Explain clearly how the magnirudc and dtrection of
resultant hydrostatic force on a curvedsurface is determined (10
M.arks)b. A hydrometer shown in Fig.Q2(b) is to be used to
determine relative d e n . i i e s of dtfferentliquids. I t has a
mass of20g. The external stem diameter is 5 rnm. Find the distance
betweenthe markings corresponding to lhe following relative
densities
i) 1.0 and 0.95; ii) 1.0Md 1.05. (10 :.Urtu)
Flg.Q.2(b).3 a. Define metacentric height C?fa floating body. Ob
tain an expression for metacentric height ofa floating body in
terms of second mnment of area of its plan at water surface,
submergedvolume and distance between centre of gravity and centre
of buoyancy of the floating body.(10M rks)b. If the pipe shown in
Fig.Q.3(b) contains water and there is no flow, calculate the value
ofmanometer reading h. l f manometer reading b 50 mm when water is
tlowlllg through thepipe, calculate the pressure difference J>A-
P6 111 kl'a. (10 Morks)
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.l'ig.Q.3(b).I of2
i\farks)
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ME454 a. State the continuity principle. Derive three
dimensional continuity equations in di!Ierentialform for a general
fluid flow situation. Simplify it to two dimensional
ste3dy,mcompressible flow and one dimensional unste U as y o.
Calculate the displacementthickness, and \he momcnlwn. thickness 6.
(10 Marks)b. Define mach nwnber."*Sbow that speed of propagation of
a pressure disturbance in acompressible fluid dp . For cine d i m e
n s i o ~ a l steady compressible flow of gases, writedpdown the
continuity equation-and equation ofmotion and shOw that = ~ ~ 1 t _
1):A U (10 Marks)
