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A 2D flow having velocity V = (x + 2y + 2)i + (4  y)j will be
A stream function is defined by following characteristic:
The partial derivative of stream function w.r.t y will give velocity in xdirection.
The partial derivative of stream function w.r.t x will give velocity in negative ydirection.
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 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 3dimensional 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 = x^{2}  y^{2} 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
V_{1}y_{1} = V_{2}y_{2}
⇒ 30 x 2 = V_{2} x 1.5 ⇒ v_{2} = 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, V_{r} = q/2πr.
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