Concept explainers
Consider the following steady, three-dimensional velocity field in Cartesian coordinates:
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
Fluid Mechanics: Fundamentals and Applications
- A steady, two-dimensional, incompressible flow field in the xy-plane has the following stream function: ? = ax2 + bxy + cy2, where a, b, and c are constants. (a) Obtain expressions for velocity components u and ?. (b) Verify that the flow field satisfies the incompressible continuity equation.arrow_forwardAn Eulerian velocity field in Cartesian coordinates is given by u = x2y, v = −xy2,w = 2xy. (a) Is the flow field two- or three-dimensional? (b) Is this flow field compressible or incompressible? (c) Is this flow field rotational or irrotational?arrow_forwardConsider the following steady, two-dimensional velocity field: V-›= (u, ? ) = (a2 − (b − cx)2) i-›+ (−2cby + 2c2xy) j-›Is there a stagnation point in this flow field? If so, where is it?arrow_forward
- For the velocity field that is linear in both spatial directions (x and y) is V-›= (u, ? ) = (U + a1x + b1y) i-›+ (V + a2x + b2y) j-›where U and V and the coefficients are constants, calculate the shear strain rate in the xy-plane.arrow_forwardAn Eulerian velocity vector field is described by V = 2i + yz2tj −z3t3k, where i, j and k are unit vectors in the x-, y- and z-directions, respectively. (a) Is this flow one-, two-, or three-dimensional? (b) Is this flow steady? (c) Is the flow incompressible or compressible? (d) Find the z-component of the acceleration vector.arrow_forwardFor the velocity field that is linear in both spatial directions (x and y) is V-›= (u, ? ) = (U + a1x + b1y) i-›+ (V + a2x + b2y) j-›where U and V and the coefficients are constants, calculate the linear strain rates in the x- and y-directionsarrow_forward
- What is the flow pattern? Plot the velocity field, potential field, and streamlines. Please explain it in detail.arrow_forwardconsider the 2 dimensional velocity field V= -Ayi +Axj where in this flow field does the speed equal to A? Where does the speed equal to 2A?arrow_forwardThe stream function of an unsteady two-dimensional flow field is given by ? = (4x/y2 )t Sketch a few streamlines for the given flow on the xy-plane, and derive expressions for the velocity components u(x, y, t) and v(x, y, t). Also determine the pathlines at t = 0.arrow_forward
- Consider the steady, two-dimensional velocity field given by V-› = (u, ?) = (1.6 + 2.8x) i-› + (1.5 − 2.8y) j-›. Verify that this flow field is incompressible.arrow_forwardA steady, three-dimensional velocity field is given byV-›= (0.657 + 1.73x + 0.948y + az) i-› + (2.61 + cx + 1.91y + bz) j-› + (−2.73x − 3.66y − 3.64z)k-› Calculate constants a, b, and c such that the flow field is irrotational.arrow_forwardConsider a steady, two-dimensional, incompressible velocity field with u = ax + b and ? = −ay + cx, where a, b, and c are constants: a = 0.50 s−1, b = 1.5 m/s, and c = 0.35 s−1. Generate an expression for the stream function and plot some streamlines of the flow in the upper-right quadrant.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY