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For a two dimensional flow field, the stream function Y is given as Ψ = 3/2(y2−x2). The magnitude of discharge occurring between the streamlines passing through points (0, 3) and (3, 4) is:
- a)6
- b)3
- c)1.5
- d)2
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
For a two dimensional flow field, the stream function Y is given as Ψ...
Given, Ψ = 3/2(y2−x2) and points (0, 3) and (3, 4)
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So, Q = ψ1 − ψ2
= 5/2(9−0) − 3/2(16−9)
= 3 units.
Most Upvoted Answer
For a two dimensional flow field, the stream function Y is given as Ψ...
To find the magnitude of discharge between the streamlines passing through points (0, 3) and (3, 4), we need to calculate the difference in stream function values at these two points.
Given stream function Ψ = 3/2(y^2−x^2)
1. Calculating Ψ at (0, 3):
- Substitute x = 0 and y = 3 into the stream function equation:
Ψ = 3/2(3^2 − 0^2)
Ψ = 3/2(9 - 0)
Ψ = 3/2(9)
Ψ = 27/2
2. Calculating Ψ at (3, 4):
- Substitute x = 3 and y = 4 into the stream function equation:
Ψ = 3/2(4^2 − 3^2)
Ψ = 3/2(16 - 9)
Ψ = 3/2(7)
Ψ = 21/2
3. Calculating the difference in stream function values:
Difference in Ψ = Ψ2 - Ψ1
Difference in Ψ = 21/2 - 27/2
Difference in Ψ = -6/2
Difference in Ψ = -3
The magnitude of discharge is the absolute value of the difference in stream function values. Therefore, the magnitude of discharge between the streamlines passing through points (0, 3) and (3, 4) is 3, which corresponds to option B.
Given stream function Ψ = 3/2(y^2−x^2)
1. Calculating Ψ at (0, 3):
- Substitute x = 0 and y = 3 into the stream function equation:
Ψ = 3/2(3^2 − 0^2)
Ψ = 3/2(9 - 0)
Ψ = 3/2(9)
Ψ = 27/2
2. Calculating Ψ at (3, 4):
- Substitute x = 3 and y = 4 into the stream function equation:
Ψ = 3/2(4^2 − 3^2)
Ψ = 3/2(16 - 9)
Ψ = 3/2(7)
Ψ = 21/2
3. Calculating the difference in stream function values:
Difference in Ψ = Ψ2 - Ψ1
Difference in Ψ = 21/2 - 27/2
Difference in Ψ = -6/2
Difference in Ψ = -3
The magnitude of discharge is the absolute value of the difference in stream function values. Therefore, the magnitude of discharge between the streamlines passing through points (0, 3) and (3, 4) is 3, which corresponds to option B.
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For a two dimensional flow field, the stream function Y is given as Ψ = 3/2(y2−x2). The magnitude of discharge occurring between the streamlines passing through points (0, 3) and (3, 4) is:a)6b)3c)1.5d)2Correct answer is option 'B'. Can you explain this answer?
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