3) In a fluid flow domain, stream lines and equipotential lines are perpendicular to each 1 poin
other. If the equation of a stream line is given by:
7x + 8y - 2 = 0 and the point of intersection with the corresponding equipotential line is
marked as (3,6) then the equation of the corresponding equipotential line is:
ADDITIONAL INFO: Stream lines represent the directions of flow and the equipotential lines
join the points with equal velocity potential.
7x – 8y – 5 = 0
8x – 7y + 36 = 0
8x + 7y + 18 = 0
24x – 21y + 54 = 0
Answers
Given : stream lines and equipotential lines are perpendicular to each other
equation of a stream line is given by: 7x + 8y - 2 = 0
the point of intersection with the corresponding equipotential line is
marked as (3,6)
To Find : equation of the corresponding equipotential line
7x – 8y – 5 = 0
8x – 7y + 36 = 0
8x + 7y + 18 = 0
24x – 21y + 54 = 0
Solution:
equation of a stream line is given by:
7x + 8y - 2 = 0
=> y = -(7/8)x + 2/8
Hence slope = -7/8
equipotential line is perpendicular hence slope = 8/7
Intersects both lines at ( 3 , 6)
Hence equation of the corresponding equipotential line is
y - 6 = (8/7)(x - 3)
=> 7y - 42 = 8x - 24
=> 8x - 7y + 18 = 0
=> 24x - 21y + 54 = 0
24x - 21y + 54 = 0 equation of the corresponding equipotential line
( Note : Question data is not completely correct as point ( 3 , 6) does not lie on 7x + 8y - 2 = 0)
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