Static fluids:
-Fluid dynamics
-
density (e)
memes =
-
ms Force (FB):Weighto ffwid (well
my
Broyant
-
anyoneis"
submerged (Vsrb)
vowmswinebois
rowme
Force (1)
=
Pressure (P) s submerged
=
(uniform force) fraction
-
=
=
Area(A) Volume object( robj)
rowmelv Area (A) velocity (v)
(a)
=
P (non-uniform force) Flow rate
=
= =
time (t)
P. P2
= EE =
(hyaraic systems) Area (A.) velocity
=
(v) Area=
(A2) velocity (v2)
=
A, vi number ofbranches
=
(n2) Ae v2
branches (n.)
= =
gravity (y)
= =
(m) kg m/s number of
=
=
Force (F) mass
=
=
ir2
cylinder (a)
=
gravity (9) Flow rate
-
liquid (W)= (m)
Weigh m a ss
(t)
=
of
time
vowme l iquid
of
(V) Area (A) =
height(h)
= m2
=
m
x
Work net
(Wnet) I
=
mass
verocity
-
-
mass
I verocity-
-
(V) density(e) Area (A) height(h)
density (e)
volume = =
l iquid (m)
= =
mass
Ee egU, IfVe
of
P. Pe
=
+ =
+
eque
+ +
Force (F) Weight(W) g A h
g
=
=
= = =
A n g
p +ggh constant
+ =
1
x
x =
Pressure (P) =
E =
A
=egh
4, +9gh, Petfgnz
=
(when vi v2)
=
Pressure (P) P0 19h
IfV2"
=
Ovi
+ pa
=
4, +
=
P2 +
(when ni n2)
=
Garge Pressure (PG) =
4-Datm
=
v,
v
2gh
+
m
m (v) Area (A)
velocity
+
farg
=
v
Force (F) viscosity (N)
length (1)
=
ofcircle (A) i radius (r)2 m2
Area
=
(P -pi)
=
Rr4
=
Frow rate (0) Bosisiana (R)
= =
8M1
Area sphere (A) G R
of
=
radius
= (r)" m2
viscosity (n) length (e)
8
=
= =
Resistance (R)
=
4
M =r
ofwater 100kgimb =1glcme
density
U cycliner Mrch =
latm 1.013
=
W5
= Pa 101325px 101.3 kPa
=
=
Circumference 2 Mr
=
9.81 MIS2
gravity (g)
=
Simple Harmonic Motion
Traveningwaves
->
-
waveengin* =
(F) constant (K):displacement (x)
Restoring force spring
=-
1f
(v)
=
velocity
=
Elastic potential energy (PEel) IK x2
=
VAt
Dx
=
(Ex)
2x
force (Fapp)
=
Applied y(x) Asin
=
Mass (m) velocity
(v)2 W+)
Kinetic energy (KE) bCx,1) Asin(kx
y(x,t) Asin(k w+)
=
= +
=
I =
x =
frearencyit seriousin
k =
(m)
of
string
linear density (M) mass =
of
length string (1)
4)
ammore
x(t) A cos(w +
+
=
v(+) a
=
=
- Awsin(w++4)
vct) = -
Vmax sin (w + +
y)
Umax Aw
= A
=
m - > sound
a(t) =
2
=
-
Awcos(w++4) AP P =
max sin(2 =
xw+ +
P)
a(t) = -
a max cos(w+ y)
+
S(x,t) Smax
=
coS(kx w
=
+
+
y)
AW2 vw f
=
amax
=
Gwer()
Phase constant(9) (**) Intensity
(I) =
Areas s
=
cos
-
(Fret) (F) damping force (Fal
Force Espring
+
net
=
I =
damping force (Fa) damping coefficient (b) verocity (v) Io w/m2
-
= -
no
=
=
x(t)
Are-E
=
cos (w+ 9)
+
Ipain 1 W/M> =
w
(
=
B 10
=
Woy,( E0) B aB
=
period penanum (T)
i
=
ar
=
y eig
=
log10(b) -
rog,ot)
=
10y,0 ()
9 4r2
=
z 10910(1) 0
=
Coy,0(10)
=
1
Driving force (Fa)=Fsin(WH) 10g (x2) aLog(x)
=
b
wy(2) a
=
from
doppler shift stationary observer Observer moving towards source observer moving away
source
loy (ab) roy(a) roy(b)
+
=
fo fs(r) fo fs(EV)
=
stationary source fo fs
= =
109b(n) =-
b*=n
=
source moving towards observer to =
ts (Fus) to ts(s)
=
to 5s(E)
=
fs(Irs) fo= fs (is) fo
fs(s)
=
fo
=
moving away
source or the
-Fluid dynamics
-
density (e)
memes =
-
ms Force (FB):Weighto ffwid (well
my
Broyant
-
anyoneis"
submerged (Vsrb)
vowmswinebois
rowme
Force (1)
=
Pressure (P) s submerged
=
(uniform force) fraction
-
=
=
Area(A) Volume object( robj)
rowmelv Area (A) velocity (v)
(a)
=
P (non-uniform force) Flow rate
=
= =
time (t)
P. P2
= EE =
(hyaraic systems) Area (A.) velocity
=
(v) Area=
(A2) velocity (v2)
=
A, vi number ofbranches
=
(n2) Ae v2
branches (n.)
= =
gravity (y)
= =
(m) kg m/s number of
=
=
Force (F) mass
=
=
ir2
cylinder (a)
=
gravity (9) Flow rate
-
liquid (W)= (m)
Weigh m a ss
(t)
=
of
time
vowme l iquid
of
(V) Area (A) =
height(h)
= m2
=
m
x
Work net
(Wnet) I
=
mass
verocity
-
-
mass
I verocity-
-
(V) density(e) Area (A) height(h)
density (e)
volume = =
l iquid (m)
= =
mass
Ee egU, IfVe
of
P. Pe
=
+ =
+
eque
+ +
Force (F) Weight(W) g A h
g
=
=
= = =
A n g
p +ggh constant
+ =
1
x
x =
Pressure (P) =
E =
A
=egh
4, +9gh, Petfgnz
=
(when vi v2)
=
Pressure (P) P0 19h
IfV2"
=
Ovi
+ pa
=
4, +
=
P2 +
(when ni n2)
=
Garge Pressure (PG) =
4-Datm
=
v,
v
2gh
+
m
m (v) Area (A)
velocity
+
farg
=
v
Force (F) viscosity (N)
length (1)
=
ofcircle (A) i radius (r)2 m2
Area
=
(P -pi)
=
Rr4
=
Frow rate (0) Bosisiana (R)
= =
8M1
Area sphere (A) G R
of
=
radius
= (r)" m2
viscosity (n) length (e)
8
=
= =
Resistance (R)
=
4
M =r
ofwater 100kgimb =1glcme
density
U cycliner Mrch =
latm 1.013
=
W5
= Pa 101325px 101.3 kPa
=
=
Circumference 2 Mr
=
9.81 MIS2
gravity (g)
=
Simple Harmonic Motion
Traveningwaves
->
-
waveengin* =
(F) constant (K):displacement (x)
Restoring force spring
=-
1f
(v)
=
velocity
=
Elastic potential energy (PEel) IK x2
=
VAt
Dx
=
(Ex)
2x
force (Fapp)
=
Applied y(x) Asin
=
Mass (m) velocity
(v)2 W+)
Kinetic energy (KE) bCx,1) Asin(kx
y(x,t) Asin(k w+)
=
= +
=
I =
x =
frearencyit seriousin
k =
(m)
of
string
linear density (M) mass =
of
length string (1)
4)
ammore
x(t) A cos(w +
+
=
v(+) a
=
=
- Awsin(w++4)
vct) = -
Vmax sin (w + +
y)
Umax Aw
= A
=
m - > sound
a(t) =
2
=
-
Awcos(w++4) AP P =
max sin(2 =
xw+ +
P)
a(t) = -
a max cos(w+ y)
+
S(x,t) Smax
=
coS(kx w
=
+
+
y)
AW2 vw f
=
amax
=
Gwer()
Phase constant(9) (**) Intensity
(I) =
Areas s
=
cos
-
(Fret) (F) damping force (Fal
Force Espring
+
net
=
I =
damping force (Fa) damping coefficient (b) verocity (v) Io w/m2
-
= -
no
=
=
x(t)
Are-E
=
cos (w+ 9)
+
Ipain 1 W/M> =
w
(
=
B 10
=
Woy,( E0) B aB
=
period penanum (T)
i
=
ar
=
y eig
=
log10(b) -
rog,ot)
=
10y,0 ()
9 4r2
=
z 10910(1) 0
=
Coy,0(10)
=
1
Driving force (Fa)=Fsin(WH) 10g (x2) aLog(x)
=
b
wy(2) a
=
from
doppler shift stationary observer Observer moving towards source observer moving away
source
loy (ab) roy(a) roy(b)
+
=
fo fs(r) fo fs(EV)
=
stationary source fo fs
= =
109b(n) =-
b*=n
=
source moving towards observer to =
ts (Fus) to ts(s)
=
to 5s(E)
=
fs(Irs) fo= fs (is) fo
fs(s)
=
fo
=
moving away
source or the
