This preview shows pages 1–2. Sign up to view the full content.
Homework 2 solutions
Fluid Mechanics CE 3502 Fall, 2008
(1)
The velocity of water flow in the nozzle shown is given by the following expression:
where
V=
velocity in meters per second,
t =
time
in seconds,
x =
distance along the nozzle in m,
and
L =
length of the nozzle in m.
Find:
What is the total acceleration and what is the
pressure gradient dp/dx
when
t =
2 s, at
x=
0.25
L
?
Solution:
t
v
0
0
x
v
v
t
v
z
v
v
y
v
v
x
v
v
dt
dv
a
x
x
x
x
x
z
x
y
x
x
x
x
∂
∂
+
+
+
∂
∂
=
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
=
=
()
2
x
L
x
5
.
0
1
t
2
v
−
=
;
2
x
L
x
5
.
0
1
2
t
v
−
=
∂
∂
;
( )
L
5
.
0
L
x
5
.
0
1
2
t
2
x
v
3
x
−
−
−
=
∂
∂
−
when
t =
2 s, at
x=
0.25
L
() ( )
s
/
m
224
.
5
49
/
256
8
/
7
4
25
.
0
5
.
0
1
2
2
v
2
2
x
=
=
=
−
=
2
2
2
x
s
/
m
612
.
2
49
/
128
8
/
7
2
25
.
0
5
.
0
1
2
t
v
=
=
=
−
=
∂
∂
(
)
s
/
1
985
.
2
7
/
8
*
2
2
5
.
0
8
/
7
2
2
2
x
v
3
3
x
=
=
−
−
=
∂
∂
−
(
)
2
x
2
2
2
x
s
/
m
2
.
18
a
s
/
m
207
.
18
s
/
m
9851
.
2
s
/
m
985
.
2
224
.
5
a
=
⇒
=
+
=
Euler:
x
a
z
p
x
ρ
=
γ
+
∂
∂
−
; Since we are not given the temperature, I will assume T =4°C.
0
x
z
=
∂
∂
;
(
)
m
/
kPa
2
.
18
x
p
s
/
m
2
.
18
m
/
kg
1000
0
p
x
2
3
−
=
∂
∂
⇒
=
+
∂
∂
−
(2)
The velocity in the outlet pipe from this reservoir is 5 m/s and h = 15 m. Because of the rounded entrance to the pipe,
the flow is assumed to be irrotational.
Find:
Under these conditions, what is the pressure at
A
?
Please state any other assumptions you make to solve this
problem.
Solution:
Consider point B, on the same streamline as A.
Bernoulli’s equation:
2
v
z
p
2
v
z
p
2
B
B
B
2
A
A
A
ρ
+
γ
+
=
ρ
+
γ
+
(1)
:
s
/
m
5
v
A
=
;
m
15
z
z
A
B
=
−
Assume the cross
‐
sectional area of the tank is much less than the cross
‐
sectional area of the pipe. Continuity means if
A
B
A
A
>>
then
A
B
v
v
<<
,
so we neglect the velocity at B:
0
v
B
≈
Plugging this information in (1):
() ()
( )
0
m
15
m
/
N
9810
p
2
/
s
/
m
5
m
/
g
k
1000
p
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '08
 KimberlyHill

Click to edit the document details