02actuator_disk - Actuator Disk stream tube assume:...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Actuator Disk u i n s p r e b t a m , D 0 A 0 (10.2) (10.3) (10.3a) (force = mass flow * delta velocity) V A , p 0 , D 0 V A + Δ v, D 1 p 0 V stream tube actuator disk A assume: propeller is a disk with diameter D and area A frictionless no rotation - upstream or downstream model propeller as thin "actuator disk" causing instantaneous increase in pressure A 1 , D 1 , V A + Δ v , DA , V V A , Thrust = T = A ⋅Δ p (10.1) continuity . .. ρ⋅ V A = constant m_dot = V A A 0 = ( V A ) VA + Δ v ρ A 1 V A D 0 2 2 ( Δ v ) 2 = VD + = V A D 1 = 2 V 2 2 V 2 D D D 0 D 1 = = V A V A + Δ v V V D 0 := D V A D 1 := D + Δ v Δ V A Δ _in_momentum = thrust_on_disk = T = m_dot out ( V A + Δ v ) m_dot in V A T = A 1 ( V A + Δ v ) 2 A 0 V A 2 2 2 (10.4) T := ρπ⋅ D 1 ( V A + Δ v ) 2 ρ π⋅ D 0 V A 2 4 4 1 2 T simplify ⋅ρπ⋅ using (10.3a) above (10.5) Δ v 4 now using Bernoulli equation p + 1 ⋅ρ⋅ v 2 = constant 2 on both sides of the disk (a force is applied at the disk) 9/8/2006 1 9/8/2006
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ahead . ..
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

02actuator_disk - Actuator Disk stream tube assume:...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online