Concept explainers
Air flows downward toward an infinitely wide horizontal flat plate. The velocity field is given by
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
- 1. For a velocity field described by V = 2x2i − zyk, is the flow two- or threedimensional? Incompressible? 2. For an Eulerian flow field described by u = 2xyt, v = y3x/3, w = 0, find the slope of the streamline passing through the point [2, 4] at t = 2. 3. Find the angle the streamline makes with the x-axis at the point [-1, 0.5] for the velocity field described by V = −xyi + 2y2jarrow_forwardFluid mechanics It is given as u=2 (1 + t), v=3 (1 + t), w=4 (1 + t) in a flow field. Accordingly, find the velocity and acceleration values at the points (3,2,4) at t = 2 seconds.arrow_forwardA two dimensional, steady, incompressible and potential flow field of water (ρ=1000 kg/m3) is given with velocity components u and v. If the velocity component, u is given as u=2xy m/s with the magnitude of maximum pressure in the field as 52108 Pa. a) At x=+1 m and y=+2 m point, what is the magnitude of the velocity component v (in m/s)? (Please use 2 decimal digits in your answer) b) At x=+1 m and y=+2 m point, what is the magnitude of dynamic pressure (in Pa)? (Please do not use any decimal digit in your answer) c) At x=+1 m and y=+2 m point, what is the magnitude of static pressure (in Pa)? (Please do not use any decimal digit in your answer)arrow_forward
- Two 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_forward2. Consider a stream function given by = (²+x²). (a) Does this flow satisfy conservation of mass? Show your work. (b) Plot the streamlines for this flow. Let K= 2. Be sure to indicate the direction of the flow. (c) Is this flow irrotational? If so, find the velocity potential for this flow. If not, show that a velocity potential does not exist. (d) Describe the flow represented by this stream function.arrow_forwardThe components of a two-dimensional velocity field are u = 4 + y³ and v = 16. The equation for a streamline can be written as y++ Ay + Bx + C = 0. Determine the values of the coefficients for the streamline passing through (3, 1). A = i B = i C= iarrow_forward
- HW2_Q3. Streamline. For the velocity field V¯=4î+ where A = 2m?s, and the coordinates are measured in meters. (a). Obtain an equation for the flow streamline that passes through the point (x, y) = (1, 3). Select one: a. y = x O b. y = C*x O c. y = C*(1/x) d. y = x + C e. y = C*(x^2)arrow_forwardIf the velocity field, V=3y2 i. Which of the following is NOT TRUE? Select one: The flow is steady The flow is irrotational The flow is horizontal d. The flow is incompressible Consider the velocity field, V=(x2+y2-4)i+(xy-y)j. Which of the following is not a stagnation point? A stagnation point is a point in the velocity field where the velocity is 0. (2, 0) (-2, 0) (1, √3) (-1, √3)arrow_forwardIn a stream of glycerine in motion, at a certain point the velocity gradient is 0.25 meter per sec per meter. The mass density of fluid is 1268.4 kg per cubic meter and kinematic viscosity is 6.30 x 10^-4 square meter per second. Calculate the shear stress in Pascal at the point.arrow_forward
- A velocity vector in a flow field is given by, 3x? V = i+ 2j + 3yk where V is in m/s and the coordinates are measured in meters. a. Making necessary calculations and/or stating your reason, classify this flow: 1-D, 2-D or 3-D? Steady or not steady? Compressible or incompressible? b. Obtain an equation for the streamline in x-y plane that passes through the point (x.y)=(2,1). c. Is the flow uniform or non-uniform? State your reason by making necessary calculations.arrow_forwardThe velocity components for a three dimensional incornpressible flow is given by : u=x° -y-z'x, v=y' -z 3 w = - 3x'z - 3y'z + Check whether the flow satisfies continuity ?arrow_forward1. Let V = Vx ((x+ yz)i) be the velocity field for a fluid flow. (a) Verify that this fluid flow is two-dimensional and incompressible. (b) Describe the streamlines for this flow.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