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Determine the third velocity component such that continuity equation is satisfied if two components are u=x2+y2+z2, v=xy2 – yz2 + xy
- a)-3xz-2xyz+z2/3+f(y,z)
- b)-3xz+2xyz+z3/3+f(y,z)
- c)-3xz-2xyz+z3/3+f(x,z)
- d)-3xz-2xyz+z3/3+f(x,y)
Correct answer is option 'D'. Can you explain this answer?
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Determine the third velocity component such that continuity equation i...
Explanation: The continuity equation for incompressible is du/dx+dv/dy+dw/dz = 0.
Here du/dx=2x and v=2xy-z2
On solving by integrating, we get w = -3xz-2xyz+z3/3+f(x,y),
Here du/dx=2x and v=2xy-z2
On solving by integrating, we get w = -3xz-2xyz+z3/3+f(x,y),
Most Upvoted Answer
Determine the third velocity component such that continuity equation i...
Z2 and the flow is incompressible.
The continuity equation for an incompressible flow is:
∇·v = ∂u/∂x + ∂v/∂y + ∂w/∂z = 0
where v = (u, v, w) is the velocity vector.
Given u = x^2y^2z^2 and v = xy^2z^2, we can calculate the third component of the velocity vector as follows:
∂w/∂z = - (∂u/∂x + ∂v/∂y)
Taking partial derivatives of u and v with respect to x and y, we get:
∂u/∂x = 2xy^2z^2
∂v/∂y = 2xyz^2
Substituting these values into the continuity equation, we get:
∂w/∂z = - (2xy^2z^2 + 2xyz^2)
Integrating both sides with respect to z, we get:
w = -xy^2z^3 - xyz^3 + f(x,y)
where f(x,y) is an arbitrary function of x and y.
Therefore, the third component of the velocity vector is:
w = -xy^2z^3 - xyz^3 + f(x,y)
where f(x,y) is an arbitrary function of x and y.
The continuity equation for an incompressible flow is:
∇·v = ∂u/∂x + ∂v/∂y + ∂w/∂z = 0
where v = (u, v, w) is the velocity vector.
Given u = x^2y^2z^2 and v = xy^2z^2, we can calculate the third component of the velocity vector as follows:
∂w/∂z = - (∂u/∂x + ∂v/∂y)
Taking partial derivatives of u and v with respect to x and y, we get:
∂u/∂x = 2xy^2z^2
∂v/∂y = 2xyz^2
Substituting these values into the continuity equation, we get:
∂w/∂z = - (2xy^2z^2 + 2xyz^2)
Integrating both sides with respect to z, we get:
w = -xy^2z^3 - xyz^3 + f(x,y)
where f(x,y) is an arbitrary function of x and y.
Therefore, the third component of the velocity vector is:
w = -xy^2z^3 - xyz^3 + f(x,y)
where f(x,y) is an arbitrary function of x and y.
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Determine the third velocity component such that continuity equation is satisfied if two components are u=x2+y2+z2, v=xy2– yz2+ xya)-3xz-2xyz+z2/3+f(y,z)b)-3xz+2xyz+z3/3+f(y,z)c)-3xz-2xyz+z3/3+f(x,z)d)-3xz-2xyz+z3/3+f(x,y)Correct answer is option 'D'. Can you explain this answer?
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