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Sma2110:Applied Mathematics Ii Question Paper
Sma2110:Applied Mathematics Ii
Course:Bachelor Of Computer Science
Institution: Meru University Of Science And Technology question papers
Exam Year:2013
QUESTION ONE (30 MARKS)
(a) Define the following dimensionless numbers: (i) Reynold’s nmer (2 Marks) (ii) er’s number (2 Marks) (iii) rode’s nmer (2 Marks) (b) In a geometrically similar model of spillway the discharge per meter length is
sm /
6 1 3
. If one scale of the model is
36 1
, find the discharge per metre run of the
prototype. (4 Marks)
(c) (i) State the factors the critical value of
v ux
at which boundary layer charges from
laminar to turbulent depends on. (3 Marks)
(ii) Differentiate between momentum thickness and kinetic thickness e d
.(3Marks)
(iii) The velocity distribution in the boundary layer is given by
d
dd
,
2 1
2 3
2 2yy
v u being boundary layer thickness. Calculate the ratio of displacement thickness to
boundary layer thickness
d d *
and the ratio of momentum thickness to boundary layer
2
thickness
d q
. (6 Marks)
(d) (i) explain the meaning of the term seepage flow. (2 Marks) (ii) State the six parameters that affect seepage velocity. (6 Marks)
QUESTION TWO (20MARKS)
(a) (i) Explain what you understand by boundary layer thickness and displacement thickness. (2 Marks) (ii) Determine the relationship between the two for a boundary layer which is laminar throughout, assuming that the flow obeys the law, shear stress = ?? ???? , where is the viscosity which leads to the velocity profile - = - ?? 2, where U is the free stream velocity. u is the velocity at a distance y above the plate and k is a constant. (6 Marks) (b) In the boundary layer over the face of a hill spillway, the velocity distribution was
observed to have the following form
22.0
d y
v u
The free stream at certain section was
observed to be 30m/s and a boundary layer thickness of 60mm was estimated from the discharge passing over the spillway was 63/ per metre length of the spillway. Calculate: (i) The displacement thickness. (4 Marks) (ii) The energy thickness (4 Marks) (iii) The loss of energy up to the section under consideration. (4 Marks)
QUESTION THREE (20 MARKS)
(a) (i) Briefly discuss properties of a porous media. (4 Marks) (ii) State Dace’s eaton or o o ater through soil. (2 Marks) (iii) Water at a rate of 0.0006 litre/sec is flowing through a sandy specimen of 8cm height and 45cm2 cross-sectional area under a constant head of 7cm. Determine the co-efficient of permeability. (5 Marks)
(b) (i) A shaft of 100mm diameter rotates at 60 r.p.m in a 200mm long bearing. Taking that the two surfaces are uniformly separated by a distance of 0.5mm and taking linear velocity distribution in the lubricating oil having dynamic viscosity of 0.04 poise, find the power absorbed in bearing. (5 Marks)
(ii) Describe four methods of preventing the separation of boundary layer. (4 Marks)
3
QUESTION FOUR (20 MARKS)
(a) For the following velocity profiles, determine whether the flow has separated or on the verge of separation or will attach with the surface.
(i)
2
2 1
2 3 dd yy
V u
(3 Marks)
(ii)
32 2 dd yy
v u
(3 Marks)
(iii) dd yy v u 2 (3 Marks)
(b) (i) Briefly describe the situations in which the following model laws are applicable. - enod’s mode a (1 Mark) - er’s mode a (1 Mark) - rode’s mode a (1 Mark)
(ii) A ship 300m long moves in sea water whose density is 1030kg/m3. A 1:100 model of this ship is to be tested in a wind tunnel. The velocity of air in the wind tunnel around the model is 30m/s and the resistance of the model is 60N. Determine (i) The velocity of ship in sea-water. (4 Marks) (ii) The resistance of the ship in semi-water. (4 Marks) (Take the density of air as 1.24 kg/m3. Kinnetic viscocity of semi-water and air as 0.012 stokes and 0.018 stokes respectively)
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