Concept explainers
Determine the stream function for the steady incompressible flow between parallel plates. The velocity profile is parabolic and given by u = uc + ay2, where uc is the centerline velocity and y is the distance measured from the centerline. The plate spacing is 2b and the velocity is zero at each plate. Explain why the stream function is not a function of x.
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Additional Engineering Textbook Solutions
Thinking Like an Engineer: An Active Learning Approach (3rd Edition)
Fundamentals of Heat and Mass Transfer
Engineering Mechanics: Statics
Automotive Technology: Principles, Diagnosis, And Service (6th Edition) (halderman Automotive Series)
Automotive Technology: Principles, Diagnosis, and Service (5th Edition)
Engineering Mechanics: Statics & Dynamics (14th Edition)
- Consider a steady, two-dimensional flow field in the xy-plane whose x-component of velocity is given by u = a + b(x − c)2 where a, b, and c are constants with appropriate dimensions. Of what form does the y-component of velocity need to be in order for the flow field to be incompressible? In other words, generate an expression for ? as a function of x, y, and the constants of the given equation such that the flow is incompressiblearrow_forwardThe velocity field of a flow is given by V axyi + by2j where a = 1 m-1s-1 and b = - 0.5 m-1s-1. Thecoordinates are in meters. Determine whether the flow field is three-, two-, or one-dimensional. Findthe equations of the streamlines and sketch several streamlines in the upper half plane (arrow_forwardThe u velocity component of a steady, two-dimensional, incompressible flow field is u = 3ax2 − 2bxy, where a and b are constants. Velocity component ?isunknown.Generatean expression for ? as a function of x and y.arrow_forward
- consider 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_forwardConsider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. Is the flow field incompressible at all 9mes?arrow_forwardA 2-D flow field has velocity components along X-axis and y-axis given by u = x't and v = -2 xyt respectively, here, t is time. The equation of streamline for the given velocity field is : (а) ху — сonstant (с) ху' — сonstant (b) x´y = constant (d) x + y constantarrow_forward
- In a certain steady, two-dimensional flow field the fluid den- sity varies linearly with respect to the coordinate x; that is, p = Ax where A is a constant. If the x component of velocity u is given by the equation u = y, determine an expression for v.arrow_forwardIn a certain two‐dimensional flow field, the velocity is constant with components u = –4 ft/s and v = –2 ft/s.Determine the corresponding stream function and velocity potential for this flow field. Sketch theequipotential line φ = 0 which passes through the origin of the coordinate system. Could you answer and explain every step pleasearrow_forwardConsider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. Compute the convective derivative of each velocity component: Du/Dt and Dv/Dt.arrow_forward
- The equation of streamline passing through (1, 1) for the velocity function V = -y?i – 6xj isarrow_forwardAn equation for the velocity for a 2D planar converging nozzle is Uy u =U1+ w=0 L Where U is the speed of the flow entering into the nozzle, and L is the length. Determine if these satisfy the continuity equation. Write the Navier-Stokes equations in x and y directions, simplify them appropriately, and integrate to determine the pressure distribution P(x.y) in the nozzle. Assume that at x = 0, y = 0, the pressure is a known value, P.arrow_forwardTwo velocity components of a steady, incompressible flow field are known: u = 2ax + bxy + cy2 and ? = axz − byz2, where a, b, and c are constants. Velocity component w is missing. Generate an expression for w as a function of x, y, and z.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