If we know the location and flow properties of internal points 1 and 2, then what is the value of local streamline direction θ3 for point 3 which lies at the intersection of characteristic lines?
A. θ3 = 12[(K–)1 + (K+)2]
B. θ3 = [(K–)1 + (K+)2 ]
C. θ3 = 12[(K–)1 – (K+)2]
D. θ3 = [(K–)1 – (K+)2]
Answer:A
If we know the location and flow properties of internal points 1 and 2, then what is the value of local streamline direction θ3 for point 3 which lies at the intersection of characteristic lines?
A. θ3 = 12[(K–)1 + (K+)2] B. θ3 = [(K–)1 + (K+)2 ] C. θ3 = 12[(K–)1 – (K+)2] D. θ3 = [(K–)1 – (K+)2]
Explanation: For internal point 1 and 2 having characteristic lines C+ and C– respectively, we know the flow properties. To derive the flow properties of point 3 which lies at the intersection point of the two characteristic lines, we know that K– value is constant onver a characteristic line. Thus, K–1 = K–3 = θ1 + ν1 since it lies along the same characteristic line C+. Similarly, K+2 = K+3 = θ2 – ν2 because point 3 and 2 lie along the same characteristic line C–. Solving for the following equation: K–3 = θ1 + ν1 K+3 = θ2 – ν2 We get, θ3 = 12[(K–)1 + (K+)2]