Yes the equation satisfies the requirements of both continuity and irrotationality. The required solution is provided below aloma with bonus part.
The following equation has been proposed as a function for the potential function of a fluid...
The following equation has been proposed as a function for the potential function of a fluid flow: $ = 3x²y – 3x - y3 Does this equation satisfy the requirement of irrotationality and continuity? Bonus: Write the velocity profiles vx and vy (1 pt)
The following equation has been proposed as a function for the potential function of a fluid flow: 0 = 3x?y - 3x - y Does this equation satisfy the requirement of irrotationality and continuity? Bonus: Write the velocity profiles vx and yy (1 pt)
The following equation has been proposed as a function for the potential function of a fluid flow: $ = 3x²y – 3x – y3 Does this equation satisfy the requirement of irrotationality and continuity?
The following equation has been proposed as a function for the potential function of a fluid flow: 0 = 3x²y - 3x - y Does this equation satisfy the requirement of irrotationality and continuity?
5. The following equation is a classic function for potential of a fluid flow: $ = -a/2 (x² - y2) Does this equation satisfy the requirement of continuity and irrotationality? (10 pts)
The following equation is a classic function for potential of fluid flow: phi= -a/2 (x2–y2)Does this equation satisfy the requirement of continuity and irrotationality?
1.1) Complete the following sentence: In any two- dimensional flow, the . exists and it must satisfy the...... function 1.2) A velocity potential function for a flow is given by the following expression Check if the irrotationality is satisfied by this velocity potential function 1.3) determine the corresponding stream function (v) for this flow
In addition, derive the "wave equation" for an incompressible
fluid. Use the continuity equation and the linearized euler
equation.
Linearized Euler:
A flow is incompressible if a fluid element does not change its density as the element moves. From Problem 54.1, this means (7p/dt) u . ρ-0. (a) Show that for an incompressible fluid the equation of continuity reduces to V -u -0. (b) Write Euler's equation for the flow of an incompressible fluid. (c) What is c for an...
2) The stream function and potential function for inviscid flow satisfy the continuity equation and the conservation of momentum equation. True or False. Explain ? note: this question using the book Fundamentals of Momentum, Heat and Mass Transfer, Sixth Edition “ chapter 10 “
Given the velocity potential for a 2-D incompressible flow, (x, y) = xy + x2 - y2 (a) Does the potential satisfy the Laplace Equation (i.e. V20 = 0)? What is the physical intepretation of this? (b) Find u(x,y) and v(x,y) (the corresponding velocity field of the flow). (c) Does the stream function y (x,y) exist? If so: (a) Find the stream function. (b) Find the implicit equation of streamline that passes through (x,y) = (1, 2).