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Cavity flow is generated when a plate is dragged at speed U over the top of a cavity (of height 8) filled with an incompressible liquid. As shown in the sketch below, the plate drags fluid to the right, which causes pressure to build up on the right side of the cavity. This high pressure (compared to the left end of the cavity) drives fluid to the left, resulting in a circulation of fluid within the cavity. Because the fluid is incompressible, the net volumetric flowrate within the cavity is zero. Plate Using the Cartesian coordinate system shown in the sketch (with y = 0 at the bottom of the cavity), the flow profile near the lateral center is given by e, +0g, +0e, a) Calculate the rate of strain tensor and vorticity vector for this flow field. b) For which y positions are there are no stretching motions? Are there rotational motions for all values of y? c) Find the position (not including the lower wall, y = 0) where v= 0. Evaluate e and o at this position.

Cavity flow is generated when a plate is dragged at speed U over the top of a cavity (of height 8) filled with an incompressible liquid. As shown in the sketch below, the plate drags fluid to the right, which causes pressure to build up on the right side of the cavity. This high pressure (compared to the left end of the cavity) drives fluid to the left, resulting in a circulation of fluid within the cavity. Because the fluid is incompressible, the net volumetric flowrate within the cavity is zero. Plate Using the Cartesian coordinate system shown in the sketch (with y = 0 at the bottom of the cavity), the flow profile near the lateral center is given by e, +0g, +0e, a) Calculate the rate of strain tensor and vorticity vector for this flow field. b) For which y positions are there are no stretching motions? Are there rotational motions for all values of y? c) Find the position (not including the lower wall, y = 0) where v= 0. Evaluate e and o at this position.

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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Cavity flow is generated when a plate is dragged at speed U over the top of a cavity (of height 6) filled with an incompressible liquid. As shown in the sketch below, the plate drags fluid to the right, which causes pressure to build up on the right side of the cavity. This high pressure (compared to the left end of the cavity) drives fluid to the left, resulting in a circulation of fluid within the cavity. Because the fluid is incompressible, the net volumetric flowrate within the cavity is zero. Plate Using the Cartesian coordinate system shown in the sketch (with y = 0 at the bottom of the cavity), the flow profile near the lateral center is given by y = U e +0g, +0e, a) Calculate the rate of strain tensor and vorticity vector for this flow field. b) For which y positions are there are no stretching motions? Are there rotational motions for all values of y? c) Find the position (not including the lower wall, y = 0) where v= 0. Evaluate e and o at this position d) At the position determined in (c), analyze fluid stretching and rotational components, indicating the direction of stretch and rotation with sketches using (dr, dy) coordinates.
Transcribed Image Text:Cavity flow is generated when a plate is dragged at speed U over the top of a cavity (of height 6) filled with an incompressible liquid. As shown in the sketch below, the plate drags fluid to the right, which causes pressure to build up on the right side of the cavity. This high pressure (compared to the left end of the cavity) drives fluid to the left, resulting in a circulation of fluid within the cavity. Because the fluid is incompressible, the net volumetric flowrate within the cavity is zero. Plate Using the Cartesian coordinate system shown in the sketch (with y = 0 at the bottom of the cavity), the flow profile near the lateral center is given by y = U e +0g, +0e, a) Calculate the rate of strain tensor and vorticity vector for this flow field. b) For which y positions are there are no stretching motions? Are there rotational motions for all values of y? c) Find the position (not including the lower wall, y = 0) where v= 0. Evaluate e and o at this position d) At the position determined in (c), analyze fluid stretching and rotational components, indicating the direction of stretch and rotation with sketches using (dr, dy) coordinates.
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