T
est B

FLUID
MECHANICS
（如
3
，
㘠
简单计算可出填空题）
1
Explain the
continuum
concept of a fluid?
(10 points)
2
Explain the concepts of pathline and streamline?
(10 points)
3
A U

tube manometer similar to that in Fig.2.14 is used to measure the gauge pressure
of a
fluid P of density
ρ
=800
kgm

3
. If the density of the liquid Q is 13.6
×
10
3
kgm

3
, what will be
the gauge pressure at A if
h
1
=0.
5
m
and
D is 0.
9
m
above BC?
(5 points)
4
A closed tank (Fig 3.10), rectangular in plan with vertical sides,
is
1
.
8
m deep
an
d contains
water to a depth of 1.2m. Air is pumped into the space above the water until the air pressure is
35kN
m

2
. If the length of one wall of the tank is 3m, determine the resultant force on this wall and
the height of the centre of pressure above the
base.
(10 points)
5
A pipe bend tapers from a diameter of
d
1
of 500 mm at inlet (see Fig. 5.7) to a diameter of
d
2
of 250 mm at the outlet and turns the flow through an angle
θ
of 45
o
. Measurements of pressure
at inlet and outlet show that the pressure
p
1
at inlet is 40 kNm

2
and the pressure
p
2
at outlet is 23
kNm

2
. If the pipe is conveying oil which has a density
ρ
of 850 kgm

3
, calculate the magnitude
of the resultant force
on the bend when the oil is flowing at the rate of
0.
45
m
3
s

1
. The bend is in a
horizontal
plane.
(10 points)
6
A pipe inclined at 45
o
to the horizontal (Fig.6.12) converges over a length
l
of 2 m from a
diameter
d
1
of 200 mm to a diameter
d
2
of 100 mm
at the upper end. Oil of relative density 0.9
flows through the pipe at a mean velocity
v
1
at the lower end of
2
ms

1
.
Find the pressure
difference across the 2 m length ignoring any loss of energy.
(
5
points)
7
Calculate the loss of head due to friction
and the power required to maintain flow in a
horizontal circular pipe of 40 mm diameter and 750 m long when water (coefficient of dynamic
visco
s
ity 1.14
×
10

3
Nsm

2
) flows at a rate of
30
.0 litres min

1
. Assume that for the pipe the
absolute roughness is 0.
00008m.
(10 points)
8
Water discharges from a reservoir A (Fig. 14.2) through a 100 m
m
pipe 15 m long which rises
to its highest point at B,
1.5m above
the free surface of the reservoir,
and discharge
s
direct to the
atmosphere at C, 4 m below the free surface at A. The length of pipe
l
1
from A to B is 5 m and the
length of pipe
l
2
from B to C is 10 m. Both the entrance and exit of the pipe are sharp and the
val
u
e of
f
is 0.08. Calculate the pressure in
the pipe at B.
(10 points)
9
An open channel has a cross section in the form of a
trapezium
with a bottom width B of 4 m
and side slopes of 1 vertical to 1.5 horizontal
. Assuming
that
the roughness coefficient
n
is 0.025,
the bed slope is 1 in
1
800
and th
e depth of the water is 1.2 m,
please
find the volume rate of flow
by using the Manning formula.
(10 points)
10 Points from experiment
(10 points)
11 Points from class presentation
(10 points)
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