流体力学2流体静力学详解

Absolute, Gage, and Vacuum Pressures
Absolute Gage Pressure
Vacuum Esc Pressure
02 - 3
• Actual pressure at a give point is called the absolute pressure. • Most pressure-measuring devices are calibrated to read zero in the
• Normal stress on any plane is pressure (+ for compression)
px DAsinq
W
Dz
q
DAcosq
pz DAcosq
rg(DAcosq Dz)/2
Fx 0 : Fz 0 :
( pnDA)sinq px (DAsinq ) 0
p z DA cosq
• Integrate dp/dz =
z patm
p2
p1
dp
z2
z1
dz
Liquids : or
p2 p1 (z2 z1)
z2
z1
p2
p1
or
p z constant
z ➢ The pressure increases linearly with
the depth of the liquid.
pa = 101,350 Pa
M = 133,100 N/m3
hM
pa M
0.761 m 761 mm
➢ That’s why the pressure is sometimes said to be 761 mmHg or 29.96 inHg.
• Why mercury, not water? The height would have been 101 m or 34 ft, since
• Engineering application requires the distribution of pressure in a fluid flow.
• Assume that the fluid is under going an acceleration: a = ax i + ay j + az k
CHAPTER
02
© Tulong Zhu, All rights reserved.
School of Engineering Mechanical Engineering
ENGR 320 FLUID MECHANICS
Pressure and Fluid Statics
Pressure
Pressure
atmosphere, and therefore indicate gage pressure, pgage= pabs patm
• Pressure below atmospheric pressure is called vacuum pressure pvac= patm pabs
• Absolute pressure is used in this course unless otherwise stated.
dp dz
r
(
g
az
)
• For
a
general 3D
problem,
p x
rax ,
p y
ray ,
p z
r
(
g
az
)
• Or in a vector form
Esc
02 - 5
p r(a gk) ➢ p p i p j p k gradient of p
x y z
z
dz
y
dx x dy
p + dp
dx dy
dz
W
p
W = rg(dxdydz)
Hydrostatic Pressure Distribution
Equation of Motion
•
p x
rax
,
p y
ra
y
,
p z
r(g
az
)
Static Problems
• For static problems, ax = ay = az = 0
Pressure at a Point in a Static Fluid
• Consider the equilibrium of an arbitrary wedge element.
pn DA
q
DA sinq
• Fluid at rest (no motion) – can not support shear stress (only normal stresses)
pa p2 p1 M h M h
• Remove air in the tube and then Esc put the tube in mercury.
• The mercury in tube rise due to pa.
02 - 11
• pa can be “read” from the height of the mercury. E.g., at sea level
• Pressure on diver at 30 m?
p2 p1 (z2 z1)
patm (9790N/m3)(30m) patm 293700 Pa patm 2.89 patm 3.89 patm
• Lung volume Change. According to
Boyle’s Law: p1V1 = p2V2
• Note that the pressure is the same at the same level in the same fluid. “Jump across”.
1
Alternative Equation
Esc
• p2 p1 h
h 2
02 - 8
Example 2.1: Scuba Diving and Hydrostatic Pressure
Esc
02 - 9
Scuba Diving and Hydrostatic Pressure
1
z
h=30 m
• Pressure is defined as a normal force exerted by a fluid per unit area.
Dimension • Dimension of Pressure: {FL2} = {ML 1T2}
& Units
• SI Unit: N/m2 = Pa (Pascal).
p 0 p 0
x
y
p rg
z
➢ Pressure in a continuously distributed uniform static fluid varies only with vertical distance and is independent of the shape of the container.
Applications: The Barometer
• Atmospheric pressure is measured by a device called a barometer; thus, atmospheric pressure is often referred to as the barometric pressure.
• For a point, Dz 0,
px py pz pn
Esc
➢ Pressure at any point in a fluid is the same in all directions. A scalar variable.
02 - 4
Equation of Motion of a Fluid Element
Atmospheric • Since these slides are prepared using several books, we will
pressure
interchangeably use patm or pa as the atmospheric pressure.
Esc
02 - 2
➢ The pressure is the same at all points on a given horizontal plane in the fluid.
➢ The pressure increases with the depth in the fluid.
Hydrostatic Pressure Equation
• BG Unit: lbf/ft2 = psf (not common).
• Other units: bar, atm, kgf/cm2, lbf/in2 = psi
➢ 1 atm = 101,325 Pa = 14.696 psi
• Since the unit Pa is too small for pressures encountered in practice, kilopascal (1 kPa = 103 Pa) and megapascal (1 MPa = 106 Pa) are commonly used.
• The pressure is the same at all points on a given horizontal plane in the same fluid.
Esc
02 - 7
pa = pb = pc = pd
pA = pB = pC pD
Pressure Distribution in Liquids
pnDAcosq
1 2
rgDAcosq
Dz
0
pn px
pn
pz
1 2
rgDz
➢ No pressure change in the horizontal direction
➢ Vertical pressure change proportional to density, gravity and depth change.
Esc
02 - 6
• The hydrostatic pressure is independent of x and y. p/z can be replaced with dp/dz.
dp
dz
Variation of Pressure with Depth
• Pressure is independent of the shape of the container.
• Consider an infinitesimal fluid element as shown.
• Ignoring the viscous force, consider the equilibrium in the z direction SFz = maz:
p(dx dy) ( p dp)(dx dy) rgdx dy dz (rdx dy dz)az
w = 9790 N/m3.
Multiple Layers of Fluids
h1
p2 = p1 + rogh1
z
h2
p3 = p2 + rwgh2
h3
p4 = p3 + rGgh3
h4
p5 = p4 + rMgh4
• In each layer of fluid, we can still use p2 p1 h to calculate the pressure.
2
V1 p2 3.89 patm 3.89
V2 p1
p atm
Esc
02 - 10
➢ If you hold your breath on ascent, your lung volume would increase by a factor of about 4, which would result in embolism and/or death.
Liquid Property
• Nearly incompressible. Neglect density variation. The gravity variation can also be neglected.
Pressure Distribution
dp
dz
➢ The specific weight, , is approximately constant for liquids.
Esc
02 - 12
பைடு நூலகம்
Manometry
Manometer
Esc
02 - 13
• A simple manometer consists of a U-tube containing one or more fluids such as mercury, water, alcohol, or oil. It is used to measure the pressure pA.