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3. The figure shows a two-dimensional cascade of identical vanes, which deflect the flow through an angle and change the pressure from p₁ at station 1 to a different p₂ at station 2. Lines AB and DC are streamlines. The distance from A to D is the same as the distance from B to C and is equal to h. (This distance h is also the spacing between vanes.) You may wish to use a control volume bounded by ABCDA. The flow is steady, incompressible and with negligible viscous effects. The width of the cascade (in and out of the page) is d. W₁ Station 1 D U₁ F Station 2 U₂ W2 V₂ B A Vane cascade for problem 3. (a) Show that u2 must equal u₁ but that w₂ cannot equal w₁. (b) Find the components of force acting on the vane in terms of p, u₁, w₁, w₂, h, and d. (That is, find the x and x components of the force acting on the vane within the control volume.) Note: Since the vanes and the spacing are identical, the streamlines AB and DC are also identical. Thus the pressure at a point along streamline AB will be the same as the pressure at a point along streamline DC having the same a location.

3. The figure shows a two-dimensional cascade of identical vanes, which deflect the flow through an angle and change the pressure from p₁ at station 1 to a different p₂ at station 2. Lines AB and DC are streamlines. The distance from A to D is the same as the distance from B to C and is equal to h. (This distance h is also the spacing between vanes.) You may wish to use a control volume bounded by ABCDA. The flow is steady, incompressible and with negligible viscous effects. The width of the cascade (in and out of the page) is d. W₁ Station 1 D U₁ F Station 2 U₂ W2 V₂ B A Vane cascade for problem 3. (a) Show that u2 must equal u₁ but that w₂ cannot equal w₁. (b) Find the components of force acting on the vane in terms of p, u₁, w₁, w₂, h, and d. (That is, find the x and x components of the force acting on the vane within the control volume.) Note: Since the vanes and the spacing are identical, the streamlines AB and DC are also identical. Thus the pressure at a point along streamline AB will be the same as the pressure at a point along streamline DC having the same a location.

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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3. The figure shows a two-dimensional cascade of identical vanes, which deflect the flow through an angle and change the pressure from p₁ at station 1 to a different p₂ at station 2. Lines AB and DC are streamlines. The distance from A to D is the same as the distance from B to C and is equal to h. (This distance h is also the spacing between vanes.) You may wish to use a control volume bounded by ABCDA. The flow is steady, incompressible and with negligible viscous effects. The width of the cascade (in and out of the page) is d. W₁ Station 1 D U₁ F Station 2 U₂ W2 V₂ B A Vane cascade for problem 3. (a) Show that u2 must equal u₁ but that w₂ cannot equal w₁. (b) Find the components of force acting on the vane in terms of p, u₁, w₁, w₂, h, and d. (That is, find the x and x components of the force acting on the vane within the control volume.) Note: Since the vanes and the spacing are identical, the streamlines AB and DC are also identical. Thus the pressure at a point along streamline AB will be the same as the pressure at a point along streamline DC having the same a location.
Transcribed Image Text:3. The figure shows a two-dimensional cascade of identical vanes, which deflect the flow through an angle and change the pressure from p₁ at station 1 to a different p₂ at station 2. Lines AB and DC are streamlines. The distance from A to D is the same as the distance from B to C and is equal to h. (This distance h is also the spacing between vanes.) You may wish to use a control volume bounded by ABCDA. The flow is steady, incompressible and with negligible viscous effects. The width of the cascade (in and out of the page) is d. W₁ Station 1 D U₁ F Station 2 U₂ W2 V₂ B A Vane cascade for problem 3. (a) Show that u2 must equal u₁ but that w₂ cannot equal w₁. (b) Find the components of force acting on the vane in terms of p, u₁, w₁, w₂, h, and d. (That is, find the x and x components of the force acting on the vane within the control volume.) Note: Since the vanes and the spacing are identical, the streamlines AB and DC are also identical. Thus the pressure at a point along streamline AB will be the same as the pressure at a point along streamline DC having the same a location.
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