Formula Sheets: Fluid Pressure & Its Measurement | Fluid Mechanics for Civil Engineering - Civil Engineering (CE) PDF Download

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Fluid Mec hanics: Fluid Pressure & Its Measuremen t
F orm ula Sheet for Civil GA TE
Fluid Pressure
• Pressure Definition : Pressure at a p oin t in a fluid is the normal force p er unit area.
P =
F
A
(Units: Pa or Nm
-2
)
• Hydrostatic Pressure : Pressure at depth h in a fluid of densit y ? .
P = ?gh+P
atm
where ? is densit y (kgm
-3
), g is gra vitational acceleration (981m/s
2
), h is depth (m ),
P
atm
is atmospheric pressure.
• P ascal’s La w : Pressure applied to an enclosed fluid is transmitted undiminished to
ev ery p ortion of the fluid and the w alls of the con taining v essel.
Hydrostatic F orces on Surfaces
• F orce on a Plane Surface : T otal force on a submerged plane surface.
F = ?gh
c
A
where h
c
is the depth to the cen troid of the area, A is the area of the surface.
• Cen ter of Pressure : Depth to the cen ter of pressure (h
p
).
h
p
= h
c
+
I
c
Ah
c
where I
c
is the momen t of i nertia of the area ab out the cen troidal axis.
• F orce on Curv ed Surfaces : Horizon tal and v ertical comp onen ts.
F
h
= ?gh
c
A
pro j
, F
v
= ?gV
where A
pro j
is the pro jected area in the v ertical plane, V is the v olume of fluid ab o v e
the curv ed surface.
Pressure Measuremen t
• Manometers :
– U-T ub e Manometer : Pressure difference b et w een t w o p oin ts.
?P = ?
m
gh
m
-?
f
gh
f
where ?
m
is the manometer fluid densit y , h
m
is the heigh t difference in the
manometer, ?
f
is the fluid densit y , h
f
is the heigh t of the fluid column.
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Page 2


Fluid Mec hanics: Fluid Pressure & Its Measuremen t
F orm ula Sheet for Civil GA TE
Fluid Pressure
• Pressure Definition : Pressure at a p oin t in a fluid is the normal force p er unit area.
P =
F
A
(Units: Pa or Nm
-2
)
• Hydrostatic Pressure : Pressure at depth h in a fluid of densit y ? .
P = ?gh+P
atm
where ? is densit y (kgm
-3
), g is gra vitational acceleration (981m/s
2
), h is depth (m ),
P
atm
is atmospheric pressure.
• P ascal’s La w : Pressure applied to an enclosed fluid is transmitted undiminished to
ev ery p ortion of the fluid and the w alls of the con taining v essel.
Hydrostatic F orces on Surfaces
• F orce on a Plane Surface : T otal force on a submerged plane surface.
F = ?gh
c
A
where h
c
is the depth to the cen troid of the area, A is the area of the surface.
• Cen ter of Pressure : Depth to the cen ter of pressure (h
p
).
h
p
= h
c
+
I
c
Ah
c
where I
c
is the momen t of i nertia of the area ab out the cen troidal axis.
• F orce on Curv ed Surfaces : Horizon tal and v ertical comp onen ts.
F
h
= ?gh
c
A
pro j
, F
v
= ?gV
where A
pro j
is the pro jected area in the v ertical plane, V is the v olume of fluid ab o v e
the curv ed surface.
Pressure Measuremen t
• Manometers :
– U-T ub e Manometer : Pressure difference b et w een t w o p oin ts.
?P = ?
m
gh
m
-?
f
gh
f
where ?
m
is the manometer fluid densit y , h
m
is the heigh t difference in the
manometer, ?
f
is the fluid densit y , h
f
is the heigh t of the fluid column.
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– Piezometer : Measures pressure at a p oin t.
P = ?gh
• Bourdon Gauge: Measures gauge pressure relativ e to atmospheric pressure.
• Absolute, Gauge, and V acuum Pressure :
P
absolute
= P
gauge
+P
atm
, P
v acuum
= P
atm
-P
absolute
Buo y ancy
• Arc himedes’ Principle : Buo y an t force equals the w eigh t of the displaced fluid.
F
b
= ?gV
displaced
where V
displaced
is the v olume of fluid displaced.
Key Notes
• Standard v alues: ?
w ater
=1000kgm
-3
, g =9.81ms
-2
, P
atm
=101.3kPa .
• Ensure consisten t units (SI preferred for GA TE).
• F or manometers, accoun t for sp ecific gra vit y if giv en.
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