# Test B --FLUID MECHANICS36

Mechanics

Oct 24, 2013 (4 years and 6 months ago)

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T
est B

--
FLUID

MECHANICS
（如
3

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,