Fluid Mechanics I Question Paper

Fluid Mechanics I

Course:Bachelor Of Science

Institution: Kenyatta University question papers

Exam Year:2009

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
SCIENCE AND BACHELOR OF EDUCATION SCIENCE

SMA 333:
FLUID MECHANICS I

DATE: Tuesday, 29th December, 2009

TIME: 2.00 p.m. – 4.00 p.m.
------------------------------------------------------------------------------------------------------------
INSTRUCTIONS:
Answer question ONE and any TWO other questions.
Q.1
a)
Define
streamlines.
(4
marks)

b)
Derive the equivalence relations that are characteristic of a fluid particle in
motion hence explain the significance of each term.
(5 marks)

c)
For a fluid moving in a fine tube of variable section A, prove from first
?? ?
principles that the equation of continuity is A
+
(A? v)= ,0 where
?t ?s
? is the density of the fluid and v the velocity.

(8 marks)

d)
the velocity of an incompressible fluid is given by
q =[- wy,wx,0](w=cons tan t).
i)
Verify that this flow is that of an incompressible fluid.
ii)
Find the streamlines.
(4 marks)

e)
State the results that constitute Pascal’s laws of static fluids. (3 marks)
Page 1 of 2

f)
By considering the forces of a fluid acting on a tetrahedron, show that
p = p = p = .
p

(6 marks)
x
y
z

Q.2
a)
Derive Euler’s equation of motion and deduce Bernoulli’s equation for the
flow of an incompressible steady fluid.

(12 marks)
b)
Discuss the venturi tube as an application of Bernoulli’s equation.
(8 marks)

Q.3
For a sphere moving with constant velocity in a liquid which is otherwise at rest,
obtain

a)
velocity components at a point P(r,? ,?),r > .
a (6
marks)

b)
the velocity potential at the point P (r,? ,?),r > .
a
(6
marks)
c)
the
kinetic
energy
of
the
fluid. (8
marks)

Q.4
a)
For a steady viscous flow in a tube of uniform x-section, obtain the

Navier – stoke’s equation for this flow if velocity is q = w(x, y)k.

(8 marks)

b)
There is steady motion between two parallel planes which are such that the
bottom one is at rest while the top plane moves with velocity Vj. Obtain
the total flow per unit breadth across a plane perpendicular to Oy if the
planes are at a distance h apart.

(12 marks)

Q.5
a)
Derive the equation of continuity for an inviscid fluid.
(10 marks)

b)
Liquid flows through a pipe whose surface is the surface of revolution of
the curve
2
y = kx about the x-axis (-1= x = )
1 ,k a constant. If the liquid
enters at the end x = -1of the pipe with velocity v, find the time taken by a
liquid particle to traverse the entire length of the pipe from x = -1to x =1.

(10 marks)
Page 2 of 2

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