ÖLÇME DEĞERLENDİRME
FORMÜL VE TABLOLAR
Birinci mertebe dinamik sistem : cx& + kx = F ( t ) , x( 0 ) = xo
t
−
xt − x ∞
=e τ
Basamak giriş cevabı:
xo − x∞
Harmonik giriş cevabı: F (t ) = Fo sin ω t ise
x(t ) = Ce−t / τ +
A / ao
2 1/ 2
1 + (ωτ )


Genlikteki azalma :
sin(ω t − φ )
1
2 1/ 2
1 + (ωτ )


,
φ (ω ) = − tan −1 (ωτ )
,
∆t =
φ (ω )
ω
İkinci mertebe dinamik sistem : m&x& + cx& + kx = F ( t ) , x( 0 ) = xo , x&( 0 ) = v o
&x& + 2ζω n x& + ω n2 x = f o cos ω 1t ; (harmonik giriş)
ωn = k / m
φ = tan −1
ζ = c / cc
;
2(c / cc )(ω1 / ωn )
1 − (ω1 / ωn )
Genlikler oranı :
2
;
,
x( t ) =
f o = Fo / m
cc = 2 mk
[1 − (ω
( Fo / k ) cos( ω1t − φ )
1
/ ωn )
]
2 2
1
2 2
2
1 − (ω / ω )
+ [ 2(c / cc )(ω1 / ωn )]
n
1


+ [2( c / cc )( ω1 / ω n )]
2
Hata Fonksiyonu Tablosu
erfη1 =
1
π
+η1
∫η e
−
−η 2
dη
1
Normal hata dağılımı
p( x ) =
 ( x − xm )2 
exp −

2σ 2 
σ 2π

1
;
P=
1
2π
+η1
∫ η exp( −η
−
1
2
/ 2 )dη
Chauvenet Kriteri
Tablosu
Okuma
Sayısı, n
3
4
5
6
7
10
15
25
50
100
∆=
∆=
v=
1.38
1.54
1.65
1.73
1.80
1.96
2.13
2.33
2.57
2.81
tσ
n
zσ
n
σ 12 / n1 + σ 22 / n2 
(σ
2
1
/ n1 )
n1 − 1
t=
dmax/σ
2
(σ
+
2
2
2
/ n2 )
2
n2 − 1
xm1 − xm 2
1/ 2
 σ 12 σ 22 
+


n
n2 
1

2
2
 ∂R  2  ∂R
 ∂R
 

wR = 
w1  + 
w2  + ... + 
wn  
∂x
∂x

 ∂xn
 
 1   2
1
2
Güvenilirlik Güvenilirlik
Önem
aralığı
seviyesi, % Seviyesi, %
3.3
99.9
0.1
3
99.7
0.3
2.57
99
1
2
95.4
4.6
1.96
95
5
1.65
90
10
( x 2 − x1 ) o =
x o (ω1 / ω n ) 2
2
n
1
Q=
ao = ω12 xo
{[1 − (ω / ω ) ] + [2(c / c )(ω / ω )] }
2 2
c
2 ( p1 − p2 )
Cd A2
1 − ( A2 / A1 )
p − pa = gh( ρ m − ρ f )
ρ=
n
1
, ( p1 − p2 ) = ( ρ m − ρ ) ⋅ g ⋅ h
ρ
2
1/ 2
p
RT
R1
g=9,81 m/s2
R2
A
p1 − p2 = L( sin θ + A2 / A1 )( ρ m − ρ ) g
ρ Su = 996 kg/m3
B
EAC
R3
R4
1 atm = 1.01325 × 105 Pa
C
D
R = 287,1 J/kg ⋅ K
1 bar = 1 × 105 Pa
c = 20.04T 1/ 2
p
=
po
ρ=
m/s
p
RT
h=
1
{[1− (ω / ω ) ] + [2h(ω / ω )] }
2 2
1
n
c=20.04 T1/2 m/s
2
1
n
1/ 2
2µ
ρ cr 3
ωn =
3LV
π
π r 2c 2
V (L + 0,5πr )
ωn =
h=
π r 2 c2
V ( L + π 2 r 2 / 2)
2µ
ρcr 3
3LV
π
V

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