Concept explainers
Which choice is the differential , incompressible, two-dimensional continuity equation in Cartesian coordinates?
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
Fluid Mechanics: Fundamentals and Applications
- The two components of the velocity vector are given as Vx = –ay/(x2+ y2)1/2 and Vy = ax/(x2+ y2)1/2 where a is a constant in cm/s. Find the vorticity of a fluid element located at x = y = 1 cm. [Ans.: 1.41a k ].arrow_forwardThe equation shown is the continuity equation for steady, compressible flow. P1Q1=P2Q2 TRUE FALSEarrow_forward1. For a flow in the xy-plane, the y-component of velocity is given by v = y2 −2x+ 2y. Find a possible x-component for steady, incompressible flow. Is it also valid for unsteady, incompressible flow? Why? 2. The x-component of velocity in a steady, incompressible flow field in the xy-plane is u = A/x. Find the simplest y-component of velocity for this flow field.arrow_forward
- Consider two sinusoidal sine waves traveling along a string, modeled as y1 (x, t) = 0.3 m sin (4 m−1 x − 3 s−1 (t)) and y2 (x, t) = 0.3 m sin (4 m−1 x + 3 s−1 (t)). What is the wave function of the resulting wave? [Hint: Use the trig identity sin(u ± v) = sin u cos v ± cos u sin varrow_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 2D velocity field is given by V = (u, v) = (2.7 - 1.9x, 0.65 + 1.6y), where the coordinates are in m and the velocity is in m/s. Find the linear strain rate (in s^(-1)) in the x-direction.arrow_forward
- Which one of the following statements is false concerning the derivation or usage of Bernoulli’s equation?(a) The fluid must be non-viscous. (b) Streamline flow is assumed. (c) The fluid must be incompressible. (d) The work-energy theorem is used to derive Bernoulli’s equation. (e) Vertical distancesare always measured relative to the lowest point within the fluid.arrow_forwardIn fluid flow, it is assumed that the fluid is ideal. a. trueb. falsec. cannot be definedarrow_forward24. In a two-dimensional incompressible flow, the component Vx of the velocity vector is given as Vx = –x2y. Find Vy. [Ans.: Vy = xy2 + C].arrow_forward
- A 2D velocity field is given by V = (u, v) = (2.8 - 1.6x, 0.7 + 1.6y), where the coordinates are in m and the velocity is in m/s. Find the magnitude of the vorticity.arrow_forwardVelocity components in the flow of an ideal fluid in a horizontal plane; Given as u = 16 y - 12 x , v = 12 y - 9 x a) Is the current continuous?(YES OR NO) b) Can the potential function be defined?(YES OR NO) c) Find the unit width flow passing between the origin and the point A(2,4). (y(0,0)=0) d) Calculate the pressure difference between the origin and the point B(3;3).arrow_forwardA steady, incompressible, two-dimensional velocity field is given by V-›= (u, ? ) = (2.5 − 1.6x) i-›+ (0.7 + 1.6y) j-› where the x- and y-coordinates are in meters and the magnitude of velocity is in m/s. The x-component of the acceleration vector ax is (a) 0.8y (b) −1.6x (c) 2.5x − 1.6 (d ) 2.56x − 4 (e) 2.56x + 0.8yarrow_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