Advanced Fluid Mechanics. Now, we note that m/2 = πbU, so following this constant streamline gives the outline of the body: Then, describes the half-body outline. = 0 represents a closed oval-shaped body, whose maximum width h is given by the solution of the equation. P8.31. Location of stagnation points - ii. The flow around a Rankine oval: (a) superposition of source–sink pair and a uniform flow; (b) replacement of streamline ψ = 0 with solid boundary to form Rankine oval. A uniform flow of velocity 6 m/s is flowing along x axis over a source & sink which are situated along x axis. The strength of source and sink is 15 m2/s and they are at a distance of 1.5m apart.

For the stream velocity and body dimension shown, compute (a) the source strength m in m 2 /s, (b) the distance a, (c) the distance h, and (d) the total velocity at point A. Equation of profile of the Rankine body -

(3.88) Ψ = 0 34 velocity distribution Rankine’s oval q2=u 2+ w 2 3.11 Flow around a Cylinder Superposition of Doublet and Free Stream r = R as the radius of the circle strength of the doublet 35 It becomes a circular cylinder as the source–sink pair approach each other. m. The body generated by the superposition of a uniform stream and a source-sink pair is called a Rankine body. Lengths & width of the Rankine oval - iii. For the conditions shown, compute (a) the source strength m in m2/s; (b) the distance a; (c) the distance h; and (d) the total velocity at point A.

Superposition of Potential Flows: Rankine Half-Body Now, the stagnation streamline can be defined by evaluating ψ at r = b, and θ= π. 2.25.
P8.31. A Rankine half-body is formed as shown in Fig. h = a cot.

πUh. Irrotational flows are potential fields.

3.10 Superposition of Sources and Free Stream: Rankine’s Oval The stagnation streamline ϑ1= ϑ 2= π & z = 0 ϑ1= ϑ 2= 0& z = 0 Eq. Determine: - i. So, the source and uniform can be used to describe an aerodynamic body. •Learn more about the classical assumption of irrotational flow and its meaning that the vorticity is everywhere zero.

: You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. Note that this also implies inviscid flow. This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license. A Rankine half-body is formed as shown in Fig.
Potential Flow 3 LEARNING OBJECTIVES •Learn to calculate the air flow and pressure distribution around various body shapes.