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A 2-D flow having velocity V = (x + 2y + 2)i + (4 - y)j will be
A stream function is
A stream function is defined by following characteristic:
The partial derivative of stream function w.r.t y will give velocity in x-direction.
The partial derivative of stream function w.r.t x will give velocity in negative y-direction.
It is valid for steady, incompressible flow since, is satisfies the continuity equation
The continuity equation for steady incompressible flow is expressed in vector notation as
In a converging steady flow there is
In two dimensional flow, the equation of a streamline is given as
The concept of stream function which is based on the principle of continuity is applicable to
Velocity potential function is valid for 3-dimensional flow while stream function is valid for 2 dimensional flow.
Which of the following velocity potentials satisfies continuity equation?
For the velocity potential function to satisfy continuity equation:
Where φ is velocity potential, φ = x2 - y2 satisfies this equation
In a two dimensional incompressible steady flow around an airfoil, the stream lines are 2 cm apart at a great distance from the airfoil, where the velocity is 30 m/sec. The velocity near the airfoil, where the stream lines are 1.5 cm apart, is
V1y1 = V2y2
⇒ 30 x 2 = V2 x 1.5 ⇒ v2 = 40 cm/s
The velocity potential function for a source varies with distance r as
Velocity at any point r in the flow field of source is given by, Vr = q/2πr.
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