A stream function is given by Ψ = 2x²y + (x+1)y². The flow rate across a line joining points (3,0) and (0,2) is
- A0.4 units
- B1.1 units
- C4.0 unitsCorrect
- D5.0 units
Solution
Concept
Flow rate between two points = difference of stream function
Formula
q = ψ₂ − ψ₁
Step-by-step solution
1. ψ = 2x²y + (x + 1)y². 2. At (3, 0): ψ = 0 + 0 = 0. 3. At (0, 2): ψ = 0 + (1)(4) = 4. 4. q = 4 − 0 = 4 units.
Explanation
The discharge per unit width between two points equals the difference between the values of the stream function at those points.
Shortcut
Just compute ψ at both points and subtract.
Common mistake
Substituting x and y in the wrong order.
Correct answer: C) 4.0 units