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NCSU
MAE308
22. Assuming frictionless, incompressible, onedimensional flow of water through the
horizontal tee connection sketched below, estimate values of the x and y components of the
force exerted by the tee on the water.
The flowrate in Section 3 is 10 m
3
/s.
The velocity and
pressure in Section 1 are 6 m/s and 200 kPaG, respectively.
Each pipe has an inside
diameter of 1 m.
Section (1)
Section (2)
Section (3)
x
y
z
Horizontal z
1
= z
2
= z
3
73
.
12
)
1
(
4
π
10
A
Q
v
2
3
3
3
=
=
=
m/s
Conservation of Mass
Q
1
+ Q
2
= Q
3
→v
1
A
1
+ v
2
A
2
= v
3
A
3
v
2
=v
3
v
1
=12.736=6.73 m/s
BE for fluid particle flowing from (1) to (3)
13
f
13
s
3
2
3
3
1
2
1
1
w
w
gz
v
2
1
ρ
p
gz
v
2
1
ρ
p
+
+
+
+
=
+
+
137037
)
73
.
12
6
(
2
999
200000
)
v
v
(
2
ρ
p
p
2
2
2
3
2
1
1
3
=

+
=

+
=
PaG
BE for fluid particle flowing from (2) to (3)
23
f
23
s
3
2
3
3
2
2
2
2
w
w
gz
v
2
1
ρ
p
gz
v
2
1
ρ
p
+
+
+
+
=
+
+
Note that the work terms in each BE are different.
195358
)
73
.
6
73
.
12
(
2
999
137037
)
v
v
(
2
ρ
p
p
2
2
2
2
2
3
3
2
=

+
=

+
=
PaG
Conservation of Momentum
∑
∫ ∫
=
cs
n
dA
v
ρ
F
v
(1): v
x
=v
1
, v
y
=0, v
n
=v
1
(2): v
x
=0, v
y
=v
2
, v
n
=v
2
(3): v
x
=0, v
y
=v
3
, v
n
=+v
3
xmomentum
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This note was uploaded on 08/01/2008 for the course MAE 308 taught by Professor Danby during the Fall '08 term at N.C. State.
 Fall '08
 DANBY

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