HP 48GII

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
∆
y2 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 v1
⋅
=
A 1
π
D 1
2
⋅
4
- - - - - - - - - - - - - - - - - -
=
A 2
π
D2
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=