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Air is flowing steadily over a series of turning vanes. The vanes are spaced 15 cm apart and arranged periodically, so identical control volumes can be drawn around each vane as shown in the figure. (the entry and exit planes are vertical). Air enters the control volumes at a uniform velocity of 15 m/s and an average gauge pressure of 60 Pa. Air leaves the control volume with a uniform velocity ₂ and a gauge pressure of 0 Pa. Pressure forces on the other surfaces will cancel due to the periodic arrangement of the vanes and do not need to be considered. The turning angle is 30°. Use a constant air density of 1.225 kg/m³ in your analysis, i.e. assume incompressible flow. Also, gravity may be neglected. (a) Using the continuity equation, find an expression for the vector velocity at the exit, ₂. (b) What are the lift and drag forces (per unit span) acting on each turning vane? Note, the lift and drag are directly related, but not equal to the vector F representing the force acting on the fluid, due to the vane.

Air is flowing steadily over a series of turning vanes. The vanes are spaced 15 cm apart and arranged periodically, so identical control volumes can be drawn around each vane as shown in the figure. (the entry and exit planes are vertical). Air enters the control volumes at a uniform velocity of 15 m/s and an average gauge pressure of 60 Pa. Air leaves the control volume with a uniform velocity ₂ and a gauge pressure of 0 Pa. Pressure forces on the other surfaces will cancel due to the periodic arrangement of the vanes and do not need to be considered. The turning angle is 30°. Use a constant air density of 1.225 kg/m³ in your analysis, i.e. assume incompressible flow. Also, gravity may be neglected. (a) Using the continuity equation, find an expression for the vector velocity at the exit, ₂. (b) What are the lift and drag forces (per unit span) acting on each turning vane? Note, the lift and drag are directly related, but not equal to the vector F representing the force acting on the fluid, due to the vane.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Fig3 ū₁ 15m/s p= 60 Pa (gage) 15cm more vanes тоге vanes streamline 15cm pro Pa(gage)
Transcribed Image Text:Fig3 ū₁ 15m/s p= 60 Pa (gage) 15cm more vanes тоге vanes streamline 15cm pro Pa(gage)
Air is flowing steadily over a series of turning vanes. The vanes are spaced 15 cm apart and arranged periodically, so identical control volumes can be drawn around each vane as shown in the figure. (the entry and exit planes are vertical). Air enters the control volumes at a uniform velocity of 15 m/s and an average gauge pressure of 60 Pa. Air leaves the control volume with a uniform velocity u₂ and a gauge pressure of 0 Pa. Pressure forces on the other surfaces will cancel due to the periodic arrangement of the vanes and do not need to be considered. The turning angle is 30°. Use a constant air density of 1.225 kg/m³ in your analysis, i.e. assume incompressible flow. Also, gravity may be neglected. (a) Using the continuity equation, find an expression for the vector velocity at the exit, ₂. (b) What are the lift and drag forces (per unit span) acting on each turning vane? Note, the lift and drag are directly related, but not equal to the vector F representing the force acting on the fluid, due to the vane.
Transcribed Image Text:Air is flowing steadily over a series of turning vanes. The vanes are spaced 15 cm apart and arranged periodically, so identical control volumes can be drawn around each vane as shown in the figure. (the entry and exit planes are vertical). Air enters the control volumes at a uniform velocity of 15 m/s and an average gauge pressure of 60 Pa. Air leaves the control volume with a uniform velocity u₂ and a gauge pressure of 0 Pa. Pressure forces on the other surfaces will cancel due to the periodic arrangement of the vanes and do not need to be considered. The turning angle is 30°. Use a constant air density of 1.225 kg/m³ in your analysis, i.e. assume incompressible flow. Also, gravity may be neglected. (a) Using the continuity equation, find an expression for the vector velocity at the exit, ₂. (b) What are the lift and drag forces (per unit span) acting on each turning vane? Note, the lift and drag are directly related, but not equal to the vector F representing the force acting on the fluid, due to the vane.
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