lampiran 2 perhitungan torsi, daya, dan efisiensi turbin...
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LAMPIRAN 2 Perhitungan Torsi, daya, dan efisiensi turbin Darrieus NACA 0012
2.1 Perhitungan Torsi
Kecepatan 2
Dik:
U =2 m/s ω = rad/s CL1 = 1.142 sin (2.065x)
H = 0.8 m ρ = 998.2 kg/m3 CL2 = 1.749 sin (2.435x)
c = 0.18 m R = 0.3 m CD =
Torsi Lift
∫ ( )
∫ ( )
2
Sudu 1
TL1 =
(∫ ( )
)
=
(∫ ( )( )
)
=
(∫ ( )( )
)
=
∫
=
(499.1 )( ∫
= ∫
= ( )
= Nm
TL2 =
(∫ ( )
)
=
(∫ ( )
( )( )
)
=
(499.1)( (∫
)
= (∫
)
= (
= Nm
Sudu 2
TL1 =
(∫ ( (
)) ( )
)
= ∫
=
= Nm
TL2 =
(∫ ( )( )
)
= (∫ ( )
)
=( .
= Nm
Sudu 3
TL1 =
(∫ ( (
)) ( )
)
= ∫
=
=
TL2 =
(∫ ( )( )
)
=( (∫ ( )
)
=(
= Nm
TL total = ((TL1sudu1 +TL2sudu1) + (TL1sudu2 +TL2sudu2) + (TL1sudu3 +TL2sudu3))/2
=
= Nm
Torsi Drag
Sudu 1
TD =
∫ ( )
=
∫ ( )
=
∫
= ∫ ( ) ( )
∫ ( ) ( )
∫
α= , α=
∫
= ∫
+∫
= ∫
+∫
=
=
Sudu 2
TD =
∫ (
) (
) (
)
∫
∫
∫
+∫
)
= Nm
Sudu 3
TD =
∫ (
) (
) (
)
∫
∫
∫
+∫
)
= Nm
TD total = (TDsudu1+ TDsudu2+ TDsudu3)
=
Nm
TTOTAL =(TLtotal - TDtotal)
=
= Nm
Kecepatan 2.5 m/s
Dik:
U = 2.5 m/s ω = rad/s CL1 =
H = 0.8 m ρ = 998.2 kg/m3 CL2 =
c = 0.18 m R = 0.3 m CD =
Torsi Lift
Sudu 1
TL1 =
(∫ ( )
)
=
(∫ ( )
( )( )
)
=
(∫ ( )( )
)
=
∫
=
(499.1 )( ∫
=
=
TL2 =
(∫ ( )
)
TL2 =
(∫ ( )
( )( )
)
TL2 =
(499.1 )( (∫
)
TL2 =
TL2 =
Sudu 2
TL1 =
(∫ ( (
)) ( )
)
= ∫
=
=
TL2 =
(∫ ( )( )
)
= (∫ ( )
)
=
=
Sudu 3
TL1 =
(∫ ( (
)) ( )
)
= ∫
=
=
TL2 =
(∫ ( )( )
)
= (∫ ( )
)
= )
=
TL total = ((TL1sudu1 +TL2sudu1) + (TL1sudu2 +TL2sudu2) + (TL1sudu3 +TL2sudu3))/2
=
= Nm
Torsi Drag
Sudu 1
TD =
∫ ( )
=
∫ ( )
=
∫
= ∫ ( ) ( )
= ∫
+∫
=
=
Sudu 2
TD=
∫
( (
))
∫
∫
∫
+∫
= Nm
Sudu 3
TD=
∫
( (
))
∫
∫
∫
+∫
)
= Nm
TD total = (TDsudu1+ TDsudu2+ TDsudu3)
=
TTOTAL =(TLtotal+TDtotal)
=(
= Nm
Kecepatan 3 m/s
Dik:
U = 3 m/s ω = rad/s CL1 =
H = 0.8 m ρ = 998.2 kg/m3 CL2 =
c = 0.18 m R = 0.3 m CD = 1.171sin(0.2409x+1.571) + 1.157sin(4.639x-1.571)
Torsi Lift
Sudu 1
TL1 =
(∫ ( )
)
=
(∫ ( )
( )( )
)
=
(∫ ( )( )
)
=
∫
=
=
TL2 =
(∫ ( )
)
=
(∫ ( )
( )( )
)
=
(499.1)( (∫
)
=
=
Sudu 2
TL1 =
(∫ ( (
)) ( )
)
= ∫
= )
=
TL2 =
(∫ ( )( )
)
= (∫ ( )
)
=
=
Sudu 3
TL1 =
(∫ ( (
)) ( )
)
= ∫
=
=
TL2 =
(∫ ( )( )
)
= (∫ ( )
)
=
=
TL total = ((TL1sudu1 +TL2sudu1) + (TL1sudu2 +TL2sudu2) + (TL1sudu3 +TL2sudu3))/2
=
)
=
Torsi Drag
Sudu 1
TD =
∫ ( )
=
∫ ( )
=
∫
= ∫ ( ) ( )
= ∫
+∫
=
=
Sudu 2
TD =
∫ ( (
) ) ( (
) ) ( ((
)))
∫
∫ (
)
∫
+∫
= Nm
Sudu 3
TD =
∫ ( (
) ) ( (
) ) ( ((
)))
∫
∫ (
)
∫
+∫
= Nm
TD total = (TDsudu1+ TDsudu2+ TDsudu3)
= +
= Nm
TTOTAL =(TLtotal+TDtotal)
=(
=
Kecepatan 3.5 m/s
Dik:
U =3.5 m/s ω = rad/s CL1 =
H = 0.8 m ρ = 998.2 kg/m3 CL2 =
c = 0.18 m R = 0.3 m CD = 1.173 sin(0.358x+1.571) + 1.159 sin(4.522x-1.571)
Torsi Lift
Sudu 1
TL1 =
(∫ ( )
)
=
(∫ ( )
( )( )
)
=
(∫ ( )( )
)
=
∫
=
(499.1 )( ∫
=
=
TL2 =
(∫ ( )
)
=
(∫ ( )
( )( )
)
=
(499.1 )( (∫
)
=
=
Sudu 2
TL1 =
(∫ ( (
)) ( )
)
= )
TL2 =
(∫ ( )( )
)
= (∫ ( )
)
=
=
Sudu 3
TL1 =
(∫ ( (
)) ( )
)
= ∫
=
=
TL2 =
(∫ ( )( )
)
= (∫ ( )
)
=
TL total = ((TL1sudu1 +TL2sudu1) + (TL1sudu2 +TL2sudu2) + (TL1sudu3 +TL2sudu3))/2
=
=
Torsi Drag
Sudu 1
TD =
∫ ( )
=
∫ ( )
=
∫
= ∫ ( ) ( )
= ∫
+∫
=
=
Sudu 2
TD =
∫
( (
))
∫
∫ (
)
∫
+∫
= Nm
Sudu 3
TD =
∫ (
) (
) ( (
))
∫
∫ (
)
∫
+∫
= Nm
TD total = (TDsudu1+ TDsudu2+ TDsudu3)
=
= Nm
TTOTAL =(TLtotal +TDtotal)
=(
= Nm
Kecepatan 4 m/s
Dik:
U =4 m/s ω = rad/s CL1 =
H = m ρ = 998.2 kg/m3 CL2 =1.683 sin (2.432x)
c = m R = 0.3 m CD = 1.161sin(0.27x+1.571) + 1.136sin(4.1x-1.571)
Torsi Lift
Sudu 1
TL1 =
(∫ ( )
)
=
(∫ ( )
( )( )
)
=
(∫ ( )( )
)
=
∫
=
(499.1 )( ∫
=
=
TL2 =
(∫ ( )
)
=
(∫ ( )
( )
)
=
(499.1 )( (∫
)
=
=
Sudu 2
TL1 =
(∫ ( (
)) ( )
)
=
=
TL2 =
(∫ ( )( )
)
= (∫ ( )
)
=
=
Sudu 3
TL1 =
(∫ ( (
)) ( )
)
= ∫
=
=
TL2 =
(∫ ( )( )
)
= (∫ ( )
)
=
=
TL total = (TL1sudu1 +TL2sudu1) + (TL1sudu2 +TL2sudu2) + (TL1sudu3 +TL2sudu3)
=
=
Torsi Drag
Sudu 1
TD =
∫ ( )
TD =
∫ ( )
TD =
∫
=( ∫
= ( ∫
+∫
=( ∫
+∫
=(
=
Sudu 2
TD =
∫ (
) (
)( ((
)))
∫
∫
∫
+∫
= Nm
Sudu 3
TD =
∫ (
) (
) ( (
))
∫
∫
∫
+∫
Nm
TD total = (TDsudu1+ TDsudu2+ TDsudu3)
=
=
TTOTAL =(TLtotal + TDtotal)
=(
= Nm
2.2 Perhitungan Daya Turbin
Rumus: Pt = T. ω
U = 2 m/s ω = Rad/s T = Nm
Pt = T. ω
Pt = .
Pt = Watt
U = 2.5 m/s ω = Rad/s T = Nm
Pt = T. ω
Pt = .
Pt = Watt
U = 3 m/s ω = Rad/s T = Nm
Pt = T. ω
Pt = .
Pt = Watt
U = 3.5 m/s ω = Rad/s T = Nm
Pt = T. ω
Pt = .
Pt = Watt
U = 4 m/s ω = Rad/s T = Nm
Pt = T. ω
Pt = .
Pt = Watt
2.3 Perhitungan Daya Hidrolis
Rumus : Ph = ρ g Q H
= ρ g (A U)(
= ρ (A)(
= ρ (H)(D)(
U = 2 m/s H = m D= ρ = 998.2 kg/m3
Ph = ρ (H)(D)(
Ph = (998.2) ( )( )(
Ph = Watt
U = 2.5 m/s H = m D= ρ = 998.2 kg/m3
Ph = ρ (H)(D)(
Ph = (998.2) ( )( ) (
Ph = Watt
U = 3 m/s H = m D= ρ = 998.2 kg/m3
Ph = ρ (H)(D)(
Ph = (998.2) ( )( ) (
Ph = Watt
U = 3.5 m/s H = m D= ρ = 998.2 kg/m3
Ph = ρ (H)(D)(
Ph = (998.2) ( )( ) (
Ph = Watt
U = 4 m/s H = m D= ρ = 998.2 kg/m3
Ph = ρ (H)(D)(
Ph = (998.2) ( )( ) (
Ph = Watt
2.4 Perhitungan Efisiensi Turbin (ηT)
Rumus : ηT=
1. Kecepatan aliran 2 m/s
PT = Watt PH = Watt
ηT=
×
ηT=
×
ηT= %
2. Kecepatan aliran 2.5 m/s
PT = Watt PH = Watt
ηT=
×
ηT=
×
ηT=
3. Kecepatan aliran 3 m/s
PT = Watt PH = Watt
ηT=
×
ηT=
×
ηT=
4. Kecepatan aliran 3.5 m/s
PT = Watt PH= Watt
ηT=
×
ηT=
×
ηT=
5. Kecepatan aliran 4 m/s
PT = Watt PH= Watt
ηT=
×
ηT=
×
ηT=