文档介绍：Fluid Statics
Study of fluid at rest, . not in motion or not flowing
On any plane, shear force is zero (no velocity gradient or shear deformation) hence only pressure forces exist
Pascal’s Law
For fluid at rest, pressure at a point is the same in all direction
P = Px = Py = Pz
Proving Pascal’s Law
As element is in equilibrium :
Fy = 0
Py x z = Ps x s Sin
s Sin = z
Hence :
Py = Ps
Similarly, for Fz = 0
Pz = Ps
Basic Hydrostatic Equation for Pressure Field
Body of fluid in equilibrium :
Fy = 0
+ W = (P + dP) . A
+ g A dh = (P + dP) A
dP/dh = g =
dP/dy = - g = -
h
dh
P
P + dP
W
Rectangular free body of top area A
y
pressible Fluid
Pressure Difference between two points in a body of fluid
dP/dh = g
dP = g dh
Integrating from P1 to P2 :
If fluid is pressible and homogeneous
= constant
P2 – P1 = g (h2 – h1) = g ( h)
P1
P2
h1
h2
h
pressible Fluid
If P1 is on free water surface, . P1 = Patm :
P2 - P1 = g h
P2 - Patm = g h
P2,abs = g h + Patm
For gauge pressure measurement, Patm = 0
P2,gauge = g h
P2,abs = P2,gauge + Patm
Gauge pressure at a point h below free surface = g h
h
P2
P1=Patm
Definition of Pressure Head
Pressure head at point = P/ g (m)
Piezometric head = P/ g + y (m)
Piezometric pressure = P + g y
In fluid statics, gauge pressure head at depth h below free surface
= P/ g = g h / g = h
Datum
Pressure = P
y
h
Example
P1 = F/A = 1000 / ( ) = kPa
P2 = P1 - g () = kPa
F = P2 A2
= x = kN
1 kN
F ?
m diam
m diam
P1
P2
Pressure at liquid interface
P1 = 1gh1
P2 = 1gh1 + 2gh2
P3 = 1gh1 + 2gh2 + 3gh3
Liquid 1 1
Liquid 2 2
Liquid 3 3
h1
h2
h3
P1
P2
P3
Pressure Measurement
Absolute Pressure : Measured relative to perfect vacuum
Perfect vacuum : 0 absolute pressure
Gauge Pressure : Measured relative to local atmospheric pressure
If no specified, pressure rea