What is the equation of streamline in an unsteady flow?

Solution: a) Streamline: Here Ux=(1+At +Bt2) and Uy=x. Since the slope of the streamline (dy/dx) is the same as the slope (Uy/Ux) of the velocity vector.

What is the example of unsteady flow?

Example for unsteady flow: flow through a pipe of variable diameter under variable pressure due to an increasing/decreasing water level of the reservoir or opening or closure of a valve or stopping/starting hydraulic machines connected to the pipe.

Can stream function be defined for compressible flow?

The stream function in a compressible flow is proportional to the mass flux and the convergence and divergence of lines in the flow over the flap shown earlier is a reflection of variations of mass flux over different parts of the flow field.

What does the stream function represent?

The stream function represents a particular case of a vector potential of velocity , related to velocity by the equality . If there is a curvilinear system of coordinares in which has only one component, then it is exactly this system that represents the stream function for the given flow.

How a streamline is defined?

1 : the path of a particle in a fluid relative to a solid body past which the fluid is moving in smooth flow without turbulence. 2a : a contour designed to minimize resistance to motion through a fluid (such as air) b : a smooth or flowing line designed as if for decreasing air resistance. streamline.

What is steady and unsteady flow with example?

Steady non-uniform flow. Conditions change from point to point in the stream but do not change with time. An example is flow in a tapering pipe with constant velocity at the inlet – velocity will change as you move along the length of the pipe toward the exit. Unsteady non-uniform flow.

How do you define a stream function?

The stream function is defined for incompressible (divergence-free) flows in two dimensions – as well as in three dimensions with axisymmetry. Since streamlines are tangent to the flow velocity vector of the flow, the value of the stream function must be constant along a streamline.

Which of the following is an example of incompressible flow?

Example of incompressible fluid flow: The stream of water flowing at high speed from a garden hose pipe.

What defines steady flow?

Definition of steady flow : a flow in which the velocity of the fluid at a particular fixed point does not change with time. — called also stationary flow. — compare uniform flow.

What is steady flow and unsteady flow?

• steady: A steady flow is one in which the conditions (velocity, pressure and cross- section) may differ from point to point but DO NOT change with time. • unsteady: If at any point in the fluid, the conditions change with time, the flow is described as unsteady.

Why is the stream function constant along a streamline?

Since streamlines are tangent to the flow velocity vector of the flow, the value of the stream function must be constant along a streamline. The usefulness of the stream function lies in the fact that the flow velocity components in the x- and y- directions at a given point are given by the partial derivatives of the stream function at that point.

What is streamstream function in fluid mechanics?

Stream function. Streamlines – lines with a constant value of the stream function – for the incompressible potential flow around a circular cylinder in a uniform onflow.

How do you find the velocity components of a stream function?

The stream function can be used to plot the streamlines of the flow and find the velocity. For two-dimensional flow the velocity components can be calculated in Cartesian coordinates by (10.5)u = − ∂ ψ ∂ y v = ∂ ψ ∂ x, and for axisymmetric flow in spherical coordinates:

What is the difference between streamstream and velocity potential?

Stream function exists for two-dimensional flow. It exists for both rotational (viscous) and irrotational (non-viscous) flows. Velocity potential function exists for both 2D and 3D flows. Velocity potential flow exists only for irrotational (non-viscous) flows.