Assign1-1 - Problem Statement 50 The water in a tank is...

Problem Statement:
50
The water in a tank is pressurized by air, and the pressure is measured by a mulitfluid manometer
as shown below. Determine the gage pressure of air in the tank if:
0.20 m 0.30 m 0.46 m
Schematic:
Assumptions/Approximations:
101.33 kPa
Physical Laws:
[Equation 1-15]
Properties/Sources:
1000.00 Conversions:
850.00 1 N = 1.00
13600.00 1 kPa = 1000.00
g = 9.81
Calculations:
In the diagram above for absolute pressure, Check units:
h
1
= h
2
= h
3
=
P
ATM
=
P = ρ *g*h
P
GAGE
= P
ABS
- P
ATM
ρ
H2O
=
kg/m 3
ρ
OIL
=
kg/m 3 kg*m/s 2
ρ
Hg
=
kg/m 3 N/m 2
m/s
2

158.215 kPa
56.89 kPa
Reasoning/Verification/Discussion:
By using Pascal's Law and the sum of Forces rule from statics, you could determine the answer using
each reference point as a place to sum forces. We will learn that "Forcing Functions" are required for any
P
ATM
= P
1
+ ρ
H2O
*g*h
1
+ ρ
OIL
*g*h
2
- ρ
Hg
*g*h
3
(kg/m
3
)*(m/s
2
)*(m) = kg/(m*s
2
) = kg*m/(m
2
*s
2
) = N/m
2
P
1
= P
ATM
- ρ
H2O
*g*h
1
- ρ
OIL
*g*h
2
+ ρ
Hg
*g*h
3
=
[Note that ρ *g*h is divided by 1000 for units]
P
1GAGE
= P
1
- P
ATM
=
change in energy state such as ∆ P or ∆ T.