5pm, Friday September 9, 2011 - University of Sydney

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The University of Sydney

School of Aerospace, Mechanical and Mechatronic Engineering

AMME2200 THERMOFLUIDS


Fluid Mechanics

Assignment
1

Due: 5pm,

Friday

September

9
, 20
11


This assignment should require around
9

hours of work by an average student.


Place
completed assignment in the box

marked AMME2200
on level 3
(
outside
Room 339) in the
Mechanical Engineering building
.


Assignment Problems:


1
. The velocity distribution in a 1.0 cm diameter pipe is given by
u(r)=
16(1

-

r
2
/r
o
2
)


m/s, where
r
o

is

the

pipe radius. Calculate the shear stress at the centerline, at r=0.25 cm and at the wall if water at 20
o
C is

flowing. (
Ans. 0, 3.2 Pa, 6.4 Pa
)


2
. A 2 mm
diameter bubble is formed by a

stream of 10
o
C water. Determine the gauge pressure in the

bubble.
Surfa
ce tension data: see text, P 448.
(Ans.

299 Pa)



3
. A 2 m wide, 3 m high vertical rectangular gate has its top edge 2 m belo
w the water level. It is hinged

along its lower edge. What
horizontal
force, acting on the top edge, is needed to hold the gate shut? ( Ans.

88.3 kN)


4
.
A turbine which is 87% efficient accepts 2 m
3
/s of water from a 50 cm diameter
pipe. The pressure drop

is 600 kPa

and the exit velocity is small. Determine the turbine output. (Ans. 1.135 MW)


5
.
The exit area of

the nozzle in a fireman’s hose is so small that the velocity in the hose is negligible.

What is the maximum exit velocity and the maximum height the water c
an reach if the pressure in the hose

is 700 kPa? (Ans. 37.4 m
/
s, 71.4 m)


6
. A pitot
-
static

tube is used to measure the velocity of an aircraft flying at 1000 m

(see Table A24).

Calculate the velocity for a pressure reading of 2 kPa.
. (Ans. 59.9 m/s)


7
.

A 75% efficient pump delivers 0.1 m3 of water from a reservoir to a device at an ele
vation of 50 m

above the reservoir. The pressure at the 8
-
cm diameter entrance to the device is 180 kPa.
The piping loss

coefficient is 5.6. Determine the pump input power

needed. (Ans. 264 kW)


8
. Water flows at the rate of 600 l/min in a 4 cm diameter horizontal pipe
with a pressure of 690 kPa. If

the pressure after an enlargement to 6 cm diameter is measured to be 700 kPa,
calculate the head loss across

the

enlargement.

(Ans. 1.57 m)





Tutorial set 1: see overleaf




Tutorial set 1 (
not

to be handed in):

(From

Masri;
Thermodynamics and Fluids, 2010

)


These questions a
re exercises only. Completing some or all of these will assist you greatly in solving
the
assignment questions.



Answer





Answer




10
-
22


0.55 Nm



11
-
30


1053 kg/m
3



10
-
26


0.0231 Ns/m
2

10
-
28


0.565N



11
-
32


2987kg/m
3

10
-
36


0.0232 N/m



11
-
33

10
-
37


100 Pa, 4 Pa






11
-
58


10
-
39


0.075 N/m



11
-
59

10
-
40


2.4 mm, 4.1 mm


11
-
64








11
-
73


9.5 cm, 59.7 N





12
-
6


77.6%, 72.7%






12
-
7


2121 kW, 636 kW

10
-
49


0.79 Nm, 0.063 Nm


12
-
10


67.2 %

, 196 kPa










12
-
25


334 kPa

11
-
8


83.0 k
N, 8.56 m


12
-
27



11
-
12






12
-
34a


h
max

= 1/(2g)*{4m
in
/(

D
o
2
)}
2

11
-
13


9.134*10
7

N



12
-
41


6.24 cm

11
-
14


288 kN



12
-
44


0.15 m/s

11
-
21


0.38 m, 0.52 m


12
-
45









12
-
46


33.8 m/s

12
-
55


7.14*10
-
3

m
3
/s, 299 kpa

11
-
23


177 kN



12
-
56


6.12*10
-
3

m
3
/s








12
-
66


$68,900/year

12
-
76







12
-
79








12
-
82


31.2 kPa