Download Measurement of Pressure Question: What is the difference between

€ Measurement of Pressure
Question: What is the difference between the real (absolute) pressure
and the gauge pressure?
The gauge pressure, pg: Relative pressure to the atmospheric pressure
( p g > 0 or p g < 0 , while pabs > 0 always)
∴ pabs = p g + patm > 0
€ Pressure measuring techniques: Manometry
Ú Necessary information: Pressure in an incompressible fluid
- Depending only on height or depth (vertical)
1. Barometer (Mercury tube): Measuring patm (Atmospheric p)
patm = γh + pvapor
In case of Mercury,
pvapor = 0.16 Pa << patm = 101300 Pa
∴ patm ≈ γh
e.g. Mercury: h = 760 mm = 14.7 in.
patm = 760 mmHg = 760 Torr
cf. For water: h ≈ 34 ft = 10.36 m !
2. Piezometer Tube (Vertical tube: open at the top)
Question: What is the pressure at A?
∴ p A = p1= γ 1h1 + po
where po : Pressure at the top
Let po be zero (Gauge pressure)
∴ p A = p1= γ 1h1
Ú Advantage: Simple and accurate
Disadvantage: p A > patm
(Why?)
Only for relatively small p A - Reasonable h
Gauge fluid: Liquid rather than gas
3. U-tube Manometer (Two kind of fluids)
y Finding the pressure PA
(Start at A → (1) → (2) → (3) → top)
Increase
by γ 1h1
No
change
Then,
Decrease
by γ 2 h2
No
change
p A + γ 1h1 − γ 2 h2 = ptop
Let ptop be zero (gauge pressure),
p A + γ 1h1 − γ 2 h2 = 0
&
∴ p A = γ 2 h2 − γ 1h1
Ú Advantages
1. Gauge fluid: Deferent from the container fluid
2. Applicable to both liquid and gas
e.g. In case of gas: At the step (1) → (2), γ 1h1 : negligible (Why?)
∴ p A = γ 2 h2
3. Applicable to wide range of p A due to Adjustable h (How?)
e.g. For very large (small) p A , use a heavy (light) gauge fluid
Large (Small) γ 2 of a gauge fluid
&
Reasonable h2
Ú Useful application - Pressure difference between two containers
Q. What is the pressure difference between A and B as shown?
y Finding the pressure difference Δp = p A − p B
(Start at A → (1) → (2) → (3) → (4) → (5) → B)
Increase
No
change
Decrease
No
change
Then, p A + γ 1h1 − γ 2 h2 − γ 3h3 = p B
∴ Δp = p A − p B = γ 2 h2 + γ 3h3 − γ 1h1
No
change
3) Inclined-Tube Manometer (Measuring small pressure change)
y Finding the pressure difference Δp = p A − p B
(Start at A → (1) → (2) → B)
1
2
3
Step 1 [A → (1)] : Increase by γ 1h1
Step 2 [(1) → (2)] : Decrease by γ 2l2 sin θ  (Height h2 = l2 sin θ 
Step 3 [(2) → B] : Decrease by  γ 3h3
Then,
p A + γ 1h1 − γ 2l2 sin θ − γ 3h3 = p B
∴ Δp = p A − p B = γ 2l2 sin θ + γ 3h3 − γ 1h1
If pipes A and B contain gas
( γ 1h1 & γ 3h3 : Negligible),
p A − p B = γ 2l2 sin θ or
∴ l2 =
p A − pB
γ 2 sin θ