-
1. Water is pumped at a
constant velocity 1m/s from large reservoir
resting on the floor to the open top of an
absorption tower. The point of
discharge is 4 meter above the floor, and the
friction losses from the reservoir
to
the tower amount to 30 J/kg. At what height in the
reservoir must the water level be kept if the pump
can
develop only60 J/kg?
U
2
2
P
2
U
1
2
P
1
w=Z
2
g+
?
h
f
?
?
(Z
1
g+
?
)
2
?
2
?
U
1
=0
?
1
?
?
2
?
1
?
0
W=60j/kg
h
f
?
30/
kg
U
2
=1m/s
?
2
?
(60
?
30
?
0.5)
/
g
?
3m
?
Z
?
Z
2
?
Z
1
?
4
?
3
?
1m
2.
The
fluid
(density
1200
kg/m
3
)
is
pumped
at
a
constant
rate
20
m
3
/h
from
the
large
reservoir
to
the
evaporator.
The
pressure
above
the
reservoir
maintains
atmosphere
pressure
and
the
pressure
of
the
evaporator keeps 200 mmHg (vacuum). The
distance between the level of liquid in the
reservoir and the exit
of evaporator is
15 meter and frictional loss in the pipe is 120
J/kg not including the exit of evaporator, what
is the pump effective work and power if
the diameter of pipe is 60 mm?
U
?
U
?
W
?
2
?
Z
2
g+
2
?
h
f
?
2
?
2
200
x1.013x10
5
?
< br>?
2.67x10
4
N
/
m
2
?
1
?
0
P
2
?
?
760
?
?
1200Kg
/
< br>m
3
U
< br>1
?
0
< br>h
f
?
120J
/
kg
V
< br>20
U
2
?
?
?
1
.97m
< br>/
s
2
A
3600*
π
/
4
*
0
.
06
Z
1
?
0
Z
2
< br>?
15
?
Z
1
g+
2.67x10
4
1
.97
2
W
?
?
?
15x9.81
?
?
120
?
246.88J
/
< br>kg
1200
2
N
?
W
?
Q
?
246.88x1200x20/3600=1646
W
3. Water comes
out of the pipe (
Φ
108x4 mm),
as shown in Fig. The friction loss of the pipeline
which does
not cover the loss at the
exit of pipe can be calculated by the following
equation:
?
1
2
1
2
h
f
=6.5U
2
where U is the velocity in the pipe,
find
a. water velocity at
section A-A'.
b. water flow rate, in
m
3
/h.
?
1
?
?
Z
1
g+
U
?
U
?
2
?
Z
2
g+
2
?
h
f
2
?
2
2
1
2
U
1
?
0
?
1
?
?
2
Z
1
?
6m
Z
2
?
0
2
U
2
?
6.5U
2
h<
/p>
f
?
6.5U
6x9.81
?
2
.
2
x3600
?
82m
3
/
h
U
?
2.9m
/
s
V=UA=2.9
π
/
4x01
4. Water passes through
the variable pipe. The velocity in the small pipe
is 2.5 m/s. The vertical glass tubes
are inserted respectively at the
section A and B to measure the pressure (see fig.)
If the friction loss between
two
section is 15 J/kg, what is the water column
difference between two glass tubes? By the way,
draw the
relative liquid column height
of two tubes in the Fig.
U<
/p>
a
A
a
?
U
b
A
b
U
b
?
2.5*(33/
47)
2
?
1
.23m/s
?
a
U
a
2
?
b
U
b
2
?
Z
a
g+
?
?
Z
b
g+
< br>?
h
f
< br>Z
a
=Z
b
?
2
?
2
?
a
?
b<
/p>
U
b
2
U
a
2
?
?
?
?
h
f
?
1
.23
2
/
2
?
2.5
2
/
2
?
15
?
12.63
?
?
2
< br>2
12.63
?
1
.29x10
?
3
m
P
a
?
P
b
?
?
R
?
g
?
R=
3
9.8x10
5.
A
centrifugal pump takes brine (density 1180
kg/m
3
, viscosity 1.2 cp)
from the bottom of a supply tank
and
delivers
it
into
another
tank.
The
line
between
the
tanks
is
300
m
of
25
mm
diameter
pipe
(inner
diameter). The flow
rate is 2 m
3
/h. In this
line, there are two gate valves, four elbows
(90
o
) and one return
bend, what is the friction loss if the
roughness of pipe is 0.025 mm?
l
U
2
U
2
?
h
f
?
h
fst
?
h
flocal
?
4f
?
?
k
d
2
2
?
?
1180kg
/
m
3
l
?
300m,
d=0.025m
v
?
2m
3
/
h <
/p>
?
=1.2cp=1.2x10
-3
Pa.s
k=0.025mm
k/d=0.025/25=0.001
k
c
=0.4
k
l
=1
k
r
=2x0.07=0.14
k
el
?
4x0.
75
?
3 k
re
?
1
.5-2.2
u
?
v/
A
?
2/(3600x
?
/
4x0.025
2
)
?
1
.13m/
s
u
?
d
Re
?
?
2.78x10
4
f
?
0
.063
?
?
h
f
?
4x0.0063x300<
/p>
/
0.025x1
.13
2
/
2+
(0.4+1+2x0.07+4x0.7+1.5)x1.13
2
/2
=197.86J/kg
6.
The orifice meter (diameter of orifice
0.0001 m) is installed for measuring the flow
rate. The indicating
liquid of orifice
is mercury if U shape pressure gauge reading is
0.6 meter and orifice coefficient can be taken
as 0.61, what is the flow rate of
water?
u
o
?
c
o
2gR(
?
0
?
?
)
< br>?
2gx0.6x(13600
< br>?
1000)
1000
V
0
?
u
o
s
0
?
0.61x
?
/
4x0
.0001
2
x
?
5.8x10
?
8
m
3
/
s
7.
Water flows through a pipe with a
diameter di 100 mm as shown in figure.
a. when the valve is closed, R is 600
mm and h equals 1500 mm. While the valve opens
partially, R=400 mm
and
h=1400
mm,
f=0.00625
(Finning
factor)
and
k
c
=0.5
(contraction
coefficient),
what
is
the
flow
rate
of
water, in m
3
/h?
b. If the valve opens fully, what is
the pressure of section 2-2', in N/m
2
? The equivalent length of the valve is
1.5 m and the Fanning factor f keeps
the same?(
?
H2O
=10
00kg/m
3
,
?
Hg
=13600kg/m
3
)
(1) the valve opens
partially ,for selection
1-1
’
and
2-2
’
, we have
u
1
2
?
1
u
2
2
?
2
gZ
1
?
?
?
gZ
2
?
?
?
h
f1-2
2
?
2
?
?
1
?
0
?
2
?
g(<
/p>
?
Hg
R
?
?
H
2
o
h)
?
39630N/
m
2
u
1
?
0
Z
2
=0 h
f1-2
l
u
2
u
2
?
4f
+k
c
?
2.13u
d
2
2
We can get Z1 from the valve closed
h=1.5m R=0.6m Z
1
?
?
Hg
gR/
< br>?
H
2
O
?
h
?
6.66m
< br>
9.81x6.66
?
u
2
/
2
?
2.13u
2
?
396
30/1000
u=3.13m/s V
h
?<
/p>
3600x
?
/
4x0.1
2
x3.13
?
88.5m
3
/
h
(2) when the valve opens
fully, for section 1-1
’
and
3-3
’
, we have
u<
/p>
3
2
?
3
u
1
2
?
1
gZ
1
?
?
?
gZ
3
?
?
?
h
f1-3
2
?
2
?
Z
3
?
0
Z
1
?
6.66m
u
1
=0
l
?
l
e
u
2
3.
?
1
.5
?
k
c
)
?
(4x0.00625x
< br>+0.5)
?
4.81u
2
h
f1-3
?
(4f
d
2
0.01
2
2
9.81x6.66
?
u
/
2
?
4.81u
u
?
3.51m
/
s
For section
1-1
’
and
2-2
’
u
1
2
?
1
u<
/p>
2
2
?
2
gZ
1
?
?
?
gZ
2
?
?
?
h
f1-2
2
?
2
?
?
1
?
0
Z
1
?
6.66
Z
2
?
0
u
1
?
0 u
2
?
3.51
l
u
2
?
(4x0.00625x15/
0.1
?
0.5)3.51
2
/
2
?
26.2J
/
kg
h
f1-2
?
(4f
?
k
c
)
d
< br>2
?
9.81x6.66
?
3.15
2
/
2<
/p>
?
26.2
?
2
?
N
?
2
?
32970
2
m
8.
The rotameter
is installed to measure the water flow rate, as
shown in figure. If the total length including
equivalent length of pipeline A is 10 m
and the reading of rotameter is 2.72 m
3
/h, what is the flow rate for
pipeline B? (f
A
=0.0075, f
B
=0.0045)
For parallel pipe line
?
h
fA<
/p>
?
?
h
fB
V
total
?
V
A
+V
B
?
(l+le)
u
A
2
2.72<
/p>
2
?
h
fA
?
4f
A
?
4x0.0075x10
/
0.053/
2(
)
d
A
2
3600x
?
/<
/p>
4x0.053
2
?
0.333J
/
kg
?
(l+le)
u
B
2
?
h
fB
?
4f
B
?
4x0.0045x2
/
0.3/
2xu
B
2
?
0.333
d
B
2
u
B
?
2.36m
/
s V
B
=u
B
A
B
?
2.
36x
?
/
4x0.23
2
?
600m
3
/h
10. A flat furnace wall is constructed
of 120 mm layer of sil-o-cel brick, with a
thermal
conductivity
0.08
w/(m
o
C), backed by a 150 mm of common brick,
of conductivity 0.8 w/(m
o
C), the temperature of inner face
of the wall is 1400
o
, and that of the outer face is
200
o
C.
a. What
is the heat loss through the wall in w per square
meter.
b.
To
reduce
the
heat
loss
to
600
w/m
2
by
adding
a
layer
of
cork
with
k
0.2
w/(m
o
C)
on
the
outside
of
common brick, how many
meters of cork are requied?
Q
?
?
t
1400
?
200
a.
?
?
?
711N
/
m
2
1
< br>1
L
?
R
?
0.08
0.8
0.12
0.15
b.
600=(1400-200)/(0.12/0.08+0.15/0.8+x/0.2)
x=0.0625m
13. Air at the normal pressure passes
through the pipe (d
i
20 mm) and is heated from
20
o
C to 100
o
C. What
is the film heat
transfer coefficient between the air and pipe wall
if the average velocity of air is 10 m/s? The
properties of air at 60
o
C are as follows:
density
1.06 kg/m
3
, viscosity 0.02
cp, conductivity 0.0289 w/(m
o
C), and heat capacity 1 kJ/kg-K
u
?
d
10x0.02x1
.06
Re=
?
?
1
.06x10
4
?
10
4<
/p>
?
3
?
0.02x10
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