最新工程流体力学完美版课件02第二章Pressure Distribution
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2
Verification:
z (up)
y
At any point in a static fluid, pressure is independent of orientation.
pn
Forces on left and up surface:
1 G g ( bxz ) 2
x
px
Consider a cube in a static fluid Pressure at the center is p;
Body forces are R Xi Yj Zk
p pleft p x p pleft Leabharlann Baidu p x dx 2 dx 2
Force on left surface Force on right surface Body force in x direction
p x X p Y y p Z z
Euler Equilibrium Equations (Euler 1775)
Applications:
Dams（水坝） Buoyancy related instrument（利用浮力的装置） Fluid power system（液压驱动系统） Connected vessel （连通器） ……
5
§ 2.2 Equilibrium of a Fluid Element
atm
mmHg
mmH2O PSI (Pound per Squire Inch)
Properties of Pressure
Vertical to the surface and point into it. At any point, pressure is independent of orientation.
Chapter 2
Pressure Distribution in a fluid
(Fluid Statics Basic)
White: Chapter 2
第一章
潘锦珊：
1
Pressure
Definition:
F p lim A0 A
Unit:
Pa N m2 (SI)
kg cm 2
dp ( Xdx Ydy Zdz )
8
p x X p Y y p Z z
p p p i j k ( Xi Yj Zk ) x y z
p R
Pressure increase in the direction of body force.
h+p0 (mmH2O) h (mmH2O)
pA 绝压 pG 表压
Water manometer （水柱压力计）
12
Homework:
P2.7
13
§ 2.4 Hydrostatic Force on Plane Surface
pleft
p
dz
dy dx
pright
6
Pressure:
p dx p x 2
p
dz
p dx p x 2
dy
dx
Body force:
Zdxdydz
Ydxdydz
Xdxdydz
dz
dy dx
7
In x direction:
p dx p dx p dydz p dydz Xdxdydz 0 x 2 x 2
Fluid Dynamics
Fluid Statics
Fluid at rest
Fluid in motion
Aerodynamics
4
§ 2.1 Fluid @ rest
Pressure is the only surface force.
Pressure distribution relates to body force only.
C p0 gz0
10
p p0 h p0 gh
Pressure at free surface Pressure due to weight on top
Any point with the same depth h under free surface has the same pressure. equipressure surface（等压面） Free surface is an equipressure surface
pz
x
Px pxby y Pn pnb sin
p x pn p p 1 gz z n 2
y sin x : p xby pnb sin
When
z 0
px pz pn p
3
Fluid Mechanics
Equipressure surface（等压面）
Surfaces in fluid with same pressure, vertical to body force everywhere, in gravity field it is a horizontal plane.
9
§ 2.3 Pressure Distribution under Gravity
11
Application ?
p0
Pressure measurement
Absolute pressure （绝对压力） Relative pressure（相对压力）
h p
Gauge pressure（表压力） Vacuum degree（真空度）
Pressure source
Connected water tube
z
p0
1
Basic rule:
dp ( Xdx Ydy Zdz)
h
z
z0 x
dp Zdz gdz p gz C
(Z g )
General solution
2
Boundary condition:
z z0 , p p0 p p0 g ( z0 z ) p p0 gh p0 h
Verification:
z (up)
y
At any point in a static fluid, pressure is independent of orientation.
pn
Forces on left and up surface:
1 G g ( bxz ) 2
x
px
Consider a cube in a static fluid Pressure at the center is p;
Body forces are R Xi Yj Zk
p pleft p x p pleft Leabharlann Baidu p x dx 2 dx 2
Force on left surface Force on right surface Body force in x direction
p x X p Y y p Z z
Euler Equilibrium Equations (Euler 1775)
Applications:
Dams（水坝） Buoyancy related instrument（利用浮力的装置） Fluid power system（液压驱动系统） Connected vessel （连通器） ……
5
§ 2.2 Equilibrium of a Fluid Element
atm
mmHg
mmH2O PSI (Pound per Squire Inch)
Properties of Pressure
Vertical to the surface and point into it. At any point, pressure is independent of orientation.
Chapter 2
Pressure Distribution in a fluid
(Fluid Statics Basic)
White: Chapter 2
第一章
潘锦珊：
1
Pressure
Definition:
F p lim A0 A
Unit:
Pa N m2 (SI)
kg cm 2
dp ( Xdx Ydy Zdz )
8
p x X p Y y p Z z
p p p i j k ( Xi Yj Zk ) x y z
p R
Pressure increase in the direction of body force.
h+p0 (mmH2O) h (mmH2O)
pA 绝压 pG 表压
Water manometer （水柱压力计）
12
Homework:
P2.7
13
§ 2.4 Hydrostatic Force on Plane Surface
pleft
p
dz
dy dx
pright
6
Pressure:
p dx p x 2
p
dz
p dx p x 2
dy
dx
Body force:
Zdxdydz
Ydxdydz
Xdxdydz
dz
dy dx
7
In x direction:
p dx p dx p dydz p dydz Xdxdydz 0 x 2 x 2
Fluid Dynamics
Fluid Statics
Fluid at rest
Fluid in motion
Aerodynamics
4
§ 2.1 Fluid @ rest
Pressure is the only surface force.
Pressure distribution relates to body force only.
C p0 gz0
10
p p0 h p0 gh
Pressure at free surface Pressure due to weight on top
Any point with the same depth h under free surface has the same pressure. equipressure surface（等压面） Free surface is an equipressure surface
pz
x
Px pxby y Pn pnb sin
p x pn p p 1 gz z n 2
y sin x : p xby pnb sin
When
z 0
px pz pn p
3
Fluid Mechanics
Equipressure surface（等压面）
Surfaces in fluid with same pressure, vertical to body force everywhere, in gravity field it is a horizontal plane.
9
§ 2.3 Pressure Distribution under Gravity
11
Application ?
p0
Pressure measurement
Absolute pressure （绝对压力） Relative pressure（相对压力）
h p
Gauge pressure（表压力） Vacuum degree（真空度）
Pressure source
Connected water tube
z
p0
1
Basic rule:
dp ( Xdx Ydy Zdz)
h
z
z0 x
dp Zdz gdz p gz C
(Z g )
General solution
2
Boundary condition:
z z0 , p p0 p p0 g ( z0 z ) p p0 gh p0 h