What is meant by velocity potential function?

Velocity potential function is basically defined as a scalar function of space and time such that it’s negative derivative with respect to any direction will provide us the velocity of the fluid particle in that direction. Velocity potential function will be represented by the symbol ϕ i.e. phi.

What does Laplace equation represent?

In the study of heat conduction, the Laplace equation is the steady-state heat equation. In general, Laplace’s equation describes situations of equilibrium, or those that do not depend explicitly on time.

Which of these equations is satisfied by the velocity potential equation?

Laplace equation
Thus, the velocity potential is describing as the scalar function ∇ϕ. 3. Which of these equations is satisfied by the velocity potential equation? The above final equation is known as Laplace equation, thus velocity potential satisfies the Laplace equation.

What is meant by stream function and velocity potential function?

The stream function, ,, is a function specially suited for dealing with two- dimensional flow while the velocity potential, f, is a function which may be. used with either two- or three-dimensional flow.

What is the relationship between velocity and the potential function?

This function ϕ is called velocity potential, and such a flow is called potential or irrotational flow. In other words, the velocity potential is a function whose gradient is equal to the velocity vector.

What is the potential function?

A potential function ϕ(r) defined by ϕ = A/r, where A is a constant, takes a constant value on every sphere centred at the origin.

Which of the following function represent the velocity potential of a function?

irrotational
For the existence of velocity potential function in a fluid flow, the flow must be irrotational. ∴ this function represents the velocity potential of a function. i.e Flow is irrotational.

In which type of flow the stream function satisfies the Laplace equation?

irrotational flow
If the stream function satisfies the Laplace equation i.e. ∂ 2 ψ ∂ x 2 + ∂ 2 ψ ∂ y 2 = 0 , it is a case of irrotational flow.

Which of the following functions represent the velocity potential of a function?

For the existence of velocity potential function in a fluid flow, the flow must be irrotational. ∴ this function represents the velocity potential of a function. i.e Flow is irrotational.

Does the velocity potential and the stream function satisfy Laplace’s equation?

(See Section 4.15 .) Hence, On the other hand, if the flow is incompressible then is automatically satisfied by writing , where is termed the stream function. (See Section 5.2 .) Hence, We conclude that, for two-dimensional, irrotational, incompressible flow, the velocity potential and the stream function both satisfy Laplace’s equation.

What is the Laplacian of velocity potential function?

As we satisfy the zero curl equation of velocity vector using velocity vector represented as the gradient of some potential function, resulting equation is Laplacian of velocity potential function.

What are the properties of velocity potential function?

Properties of Velocity Potential Function 1 For the fluid flow to be irrotational, the rotational components are equal to zero. 2 If there exists velocity potential, then the fluid flow is rotational. 3 If the given velocity potential satisfies the Laplace equation (Eq.4), then the fluid flow is a representation of the… More

How do you find the flow pattern from velocity potential?

Consequently, when the function ϕ has been obtained, velocities u and v can also be obtained by differentiation, and thus, the flow pattern is found. This function ϕ is called velocity potential, and such a flow is called potential or irrotational flow.