Answer:
Using the equation of continuity:
A
1
v
1
=
A
2
v
2
0.08
(
10
)
=
A
2
(
225
)
A
2
=
3.55
×
10
−
3
m
2
Q
2
=
A
2
v
2
Q
2
=
3.55
×
10
−
3
×
225
Q
2
=
0.798
m
3
/
s
Explanation:
Steady Flow Energy Equation:
The steady flow energy equation is a representation of the first law of thermodynamics. It is the conservation of energy law for an open system. A nozzle is an open system in the context of thermodynamics. It is used to produce a high velocity by reducing its pressure.
The steady flow energy equation can be given by the following formula:
h
1
+
1
2
v
2
1
+
g
z
1
+
q
=
h
2
+
1
2
v
2
2
+
g
z
2
+
w
where 'h' is enthalpy, 'v' is velocity, 'z' is height, 'q' is the heat and 'w' is work.
h
=
C
p
d
T
Answer and Explanation:
Given:
initial temp,
T
1
=
400
0
C
initial Pressure,
p
1
=
800
k
P
a
Initial Velocity,
v
1
=
10
m
/
s
Final temp,
T
2
=
300
0
C
Final Pressure,
p
2
=
200
k
P
a
Rate of heat loss, Q = 25 KW
Inlet Area,
A
1
=
800
c
m
2
As per the steady flow energy equation:
h
1
+
1
2
v
2
1
+
g
z
1
+
q
=
h
2
+
1
2
v
2
2
+
g
z
2
+
w
Since, there is external work, w= 0. Also, consider there is a negligible change in KE.
h
1
+
1
2
v
2
1
+
q
=
h
2
+
1
2
v
2
2
h
1
−
h
2
+
1
2
v
2
1
+
q
=
1
2
v
2
2
C
p
(
T
1
−
T
2
)
+
1
2
(
10
)
2
+
25000
=
1
2
v
2
2
2
(
400
−
300
)
+
50
+
25000
=
1
2
v
2
2
2
(
400
−
300
)
+
50
+
25000
=
1
2
v
2
2
25250
=
1
2
v
2
2
v
2
≈
225
which is the answer.
Using the equation of continuity:
A
1
v
1
=
A
2
v
2
0.08
(
10
)
=
A
2
(
225
)
A
2
=
3.55
×
10
−
3
m
2
Now, volume flow rate,
Q
2
=
A
2
v
2
Q
2
=
3.55
×
10
−
3
×
225
Q
2
=
0.798
m
3
/
s
