Speed & acceleration Hydroelectric power & mass flow
∆x Coriolis force : F c =−2 m ( ωv )=2 mωv∗sinφ
v=
∆t
Mass flow :
∆v
a= dW =dK + dU
∆t
a rad =
v2 4 π2 R
R
= 2
T
F 1 x 1−F 2 x 2= ( 12 mv − 12 mv )+(mg y −mg y )
2
2
2
1 2 1
1
v x =v 0+ a x t p1 A 1 dx 1− p2 A 2 dx 2= ρdV ( v 22−v 21 ) + ρdVg ( y 2− y 1 )
2
1 2
x=x 0 +v 0 t+ a x t 1 2 2
2 ( p1− p2 ) = 2 ρ ( v 2 −v 1 ) + ρg ( y 2− y1 )
v 2x =v 20+ 2 ax ( x−x 0 ) Conservation of E :∆ K +∆ U + ∆ U∫ ¿=0 ¿
1
x−x 0= ( v 0 +v x ) t Hydroelectric power P=ρQgh
2
Amount of E stored : E=mgh
Work, energy & power
' p 1 2
W =mas=Fs in J;Nm Bernoull i s equation: + v + gh=constant
ρ 2
W car 2
ή¿ L 2 8 fL Q
U fuel ∗v ∗1
d π2 g
Head loss :hf = ∗Q=
E=Pt
Peltonin J
wheel
2g D5
E
∆ pot
p=2=mgh
mw ( v j−v c ) Wind turbine
1
∆1p v2
3
E kin = m
Pmax =0.59 ρA c p v
F= =2 ρQ ( v j−v c ) 2
∆2t
Heat
P=FQ=Cm
∆W
v c
∆T
Pt =( 4 a ( 1−a )2 ) ( 12 ρ A v )
t
3
0
P= 1 =Fv 2in W;J/s
Pmax = ∆ t ρQ v j Rω 2 πR v tip
2 tip−speed ratio :λ¿ = =
Force u0 nd v0
Gravitation & pull
F z =mg ω
m1 m2 f=
F g=G 2π
2
F res =ma r
v tip 2 π rad
Angular velocity :ω= = ∈
1 m1 m 2
Uair=−G R T s
F = ρA Cr d v 2
2
P
Torque τ= ∈NM
FFft=−μmg
1 R 1∗m 2 ω
=
F t 2 R 2∗m 1
∑ F=0 E gen , act E gen , act
Load Factor LF= =
Egen , max Pmax∗8760
∑ F=ma
Moment of inerti a=∑ mr 2
F AonB=−F BonA
1 2
Other Rotational E kin : K = I ω
2
m=ρV Momentum
2
Area windmill=5 D p=mv= ρA u0
2
∆x Coriolis force : F c =−2 m ( ωv )=2 mωv∗sinφ
v=
∆t
Mass flow :
∆v
a= dW =dK + dU
∆t
a rad =
v2 4 π2 R
R
= 2
T
F 1 x 1−F 2 x 2= ( 12 mv − 12 mv )+(mg y −mg y )
2
2
2
1 2 1
1
v x =v 0+ a x t p1 A 1 dx 1− p2 A 2 dx 2= ρdV ( v 22−v 21 ) + ρdVg ( y 2− y 1 )
2
1 2
x=x 0 +v 0 t+ a x t 1 2 2
2 ( p1− p2 ) = 2 ρ ( v 2 −v 1 ) + ρg ( y 2− y1 )
v 2x =v 20+ 2 ax ( x−x 0 ) Conservation of E :∆ K +∆ U + ∆ U∫ ¿=0 ¿
1
x−x 0= ( v 0 +v x ) t Hydroelectric power P=ρQgh
2
Amount of E stored : E=mgh
Work, energy & power
' p 1 2
W =mas=Fs in J;Nm Bernoull i s equation: + v + gh=constant
ρ 2
W car 2
ή¿ L 2 8 fL Q
U fuel ∗v ∗1
d π2 g
Head loss :hf = ∗Q=
E=Pt
Peltonin J
wheel
2g D5
E
∆ pot
p=2=mgh
mw ( v j−v c ) Wind turbine
1
∆1p v2
3
E kin = m
Pmax =0.59 ρA c p v
F= =2 ρQ ( v j−v c ) 2
∆2t
Heat
P=FQ=Cm
∆W
v c
∆T
Pt =( 4 a ( 1−a )2 ) ( 12 ρ A v )
t
3
0
P= 1 =Fv 2in W;J/s
Pmax = ∆ t ρQ v j Rω 2 πR v tip
2 tip−speed ratio :λ¿ = =
Force u0 nd v0
Gravitation & pull
F z =mg ω
m1 m2 f=
F g=G 2π
2
F res =ma r
v tip 2 π rad
Angular velocity :ω= = ∈
1 m1 m 2
Uair=−G R T s
F = ρA Cr d v 2
2
P
Torque τ= ∈NM
FFft=−μmg
1 R 1∗m 2 ω
=
F t 2 R 2∗m 1
∑ F=0 E gen , act E gen , act
Load Factor LF= =
Egen , max Pmax∗8760
∑ F=ma
Moment of inerti a=∑ mr 2
F AonB=−F BonA
1 2
Other Rotational E kin : K = I ω
2
m=ρV Momentum
2
Area windmill=5 D p=mv= ρA u0
2
