Discussion
For a two-dimensional flow field given as \(\vec{V} = -x\hat{i} + y\hat{j}\), a streamline passes through points (2, 1) and (5, \(p\)). The value of \(p\) is
Answer: C
The value is \(p = \frac{2}{5}\).
A streamline is everywhere tangent to the velocity, so \(\frac{dx}{u} = \frac{dy}{v}\):
\[ \begin{aligned} \frac{dx}{-x} &= \frac{dy}{y} \\ -\ln x &= \ln y + C \\ xy &= \text{constant} \end{aligned} \]
Through (2, 1) the constant is 2, so at \(x = 5\), \(5p = 2\) and \(p = 2/5\).
5/2 is what results from writing \(y/x\) = constant, which ignores the minus sign in \(u = -x\). 2 and 5 would require the streamline to be horizontal or to pass through the points on a line through the origin.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development