Reference Guide
5-20 Equation Reference
Equations:
P
∆
ρ
-
-
-
-
-
-
-
v
2
2
v
1
2
–
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
g
+
+
y
∆
⋅
0
=
P
∆
ρ
-
-
-
-
-
-
-
v
2
2
1
A
2
A
1
-
-
-
-
-
-
-
2
–
⋅
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
g
+
+
y
∆
⋅
0
=
P
∆
ρ
-
-
-
-
-
-
-
v
1
2
A
2
A
1
-
-
-
-
-
-
-
2
1
–
⋅
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
g
+
+
y
∆
⋅
0
=
P
∆
P
2
P
1
–
=
y
∆
y
2
y
1
–
=
M
ρ
Q
⋅
=
Q
A
2
v
2
–
=
Q
A
1
v
1
–
=
A
1
π
D
1
2
⋅
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
=
A
2
π
D
2
2
⋅
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
=
Example:
Given:
P2=25_psi, P1=75_psi, y2=35_ft, y1=0_fr, D1=18_in,
ρ
=64_lb/ft^3, v1=100_ft/s.
Solution:
Q=10602.8752_ft^3/min, M=678584.0132_lb/min, v2=122.4213_ft/s, A2=207.8633_in^2,
D2=16.2684_in, A1=254.4690_in^2, ∆P= -50_psi, ∆y=35_ft.
Flow with Losses (3, 3)
These equations extend Bernoulli’s equation to include power input (or output) and head loss.
Equations:
M
P
∆
ρ
-
-
-
-
-
-
-
v
2
2
v
1
2
–
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
g
+
+
y
∆
⋅
h
L
+
⋅
W
=
P
∆
P
2
P
1
–
=
y
∆
y
2
y
1
–
=
M
ρ
Q
⋅
=
Q
A
2
v
2
⋅
=
Q
A
1
v
1
⋅
=
A
1
π
D
1
2
⋅
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
=
A
2
π
D
2
2
⋅
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
=
M
P
∆
ρ
-
-
-
-
-
-
-
v
2
2
1
A
2
A
1
-
-
-
-
-
-
-
2
–
⋅
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
g
+
+
y
∆
⋅
h
L
+
⋅
W
=
M
P
∆
ρ
-
-
-
-
-
-
-
v
1
2
A
1
A
2
-
-
-
-
-
-
-
2
1
–
⋅
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
g
+
+
y
∆
⋅
h
L
+
⋅
W
=