Transcript Chapter 14

CHAPTER-14
Fluids
Ch 14-2, 3 Fluid Density and Pressure
 Fluid: a substance that can
flow
 Density  of a fluid having
a mass m and a volume V is
given by :  = m/V
(uniform density)
Density Units: kg/m3
 Density of a compressible
material such as gases
depends upon the pressure
P, where P is given by:
P=F/A
Ch 14-4 Fluid at Rest
• Hydrostatic Pressure:
(Pressure due to fluid at rest)
The pressure at a point in a fluid in static
equilibrium depends upon the depth of
that point but not on any horizontal
dimension of the fluid or container.
Consider the imaginary water cylinder with
horizontal base , with weight mg,
enclosed between two depths y1 and
y2.The cylinder has a volume V, face
area A and height y1-y2, Water is in
static equilibrium. Three forces F1, F2
and mg acts such that F2-F1-mg=0;
F2=F1+mg
But p1=F1/A; p2=F2/A; m=Vg= A(y1-y2)
p2=p1+g(y1-y2)
Ch 14-4 Absolute Pressure and Gauge Pressure
p2=p1+g(y1-y2)
If p2=p; p1=p0 and y1=0 ; y2=-h
p=p0+gh
p =p-p0=gh
P is Absolute pressure
p is Gauge pressure
Ch 14-4 Absolute Pressure and Gauge Pressure
Ch 14-6 Pascal’s Principle
 Pascal’s Principle : A change in the
pressure applied to an enclosed
incompressible fluid is transmitted
undiminished to every portion of
the fluid and to the walls of its
container.
 A change in pressure P at input of
hydraulic lever is converted to
change in pressure P at output of
hydraulic lever
P=Fi/Ai=Fo/Ao; Fo= Ao(Fi/Ai),FoFi
 If input piston moves through a
distance di , then the output piston
moves through a smaller distance
do because V=Aidi=Aodo
 With a hydraulic lever, a given
force applied over a given distance
can be transformed to a greater
force applied over a smaller
distance
Ch 14-7 Archimedes’ Principle
 Archimedes’ Principle:
 Buoyant Force FB: Upward force on a fully
or partially submerged object by the
fluid surrounding the object , magnitude
of the force FB equal to weight of the
displaced fluid mfg= Vfg. Vf is volume of
the displaced fluid.
 Floating Object: When an object floats in
a fluid, the magnitude of FB is equal to
magnitude of the gravitational force Fg
(=mg). Then
FB= Fg =mg= mfg= Vfg
 A floating object displaces its own weight
of fluid
 For objects submerged in a fluid, its
Apparent weight Wapp is less than true
weight W
Apparent weight Wapp= W-FB
Ch 14-8 Ideal Fluid in Motion
Four assumptions related to ideal
flow:
 Steady flow: the velocity of the
moving fluid at any fixed point
does not change with time
 Incompressible Flow: Fluid has
constant density
 Nonviscous flow: an object can
move through the fluid at
constant speed- no resistive force
within the fluid to moving objects
through it
 Irrotational flow: Objects moving
through the fluid do not rotate
about an axis through its center
of mass
Ch 14-9 Equation of Continuity
 Equation of Continuity: A relation
between the speed v of an ideal
fluid flowing through a tube of
cross sectional area A in steady
flow state
 Since fluid is incompressible,
equal volume of fluid enters and
leaves the tube in equal time
 Volume V flowing through a
tube in time t is
V = Ax =Avt
Then V = A1v1t =A2v2t

A1v1=A2v2
 RV=A1v1=constant (Volume flow
rate)
 Rm=A1v1=constant (Mass flow
rate)
Ch 14-10 Bernoulli’s Equation
• Bernoulli’s Equation:
• If y1,v1 and p1 are the
elevation, speed and pressure of
the fluid entering the tube and
and y2,v2 and p2 are the
elevation, speed and pressure of
the fluid leaving the tube
• Then
p1+ (v12)/2+gy1=p2+ (v22)/2+gy2
or
p+ (v2)/2+gy = constant