Question
Download Solution PDFAt a point on a streamline, the velocity is 3 m/sec and the radius of curvature is 9 m. If the rate of increase of velocity along the streamline at this point is 1/3 m/sec/m, then the total acceleration at this point would be _____.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Radial acceleration (ar):
\({a_r} = \frac{{{V^2}}}{r}\)
Tangential acceleration (at):
\({a_t} = \frac{{dV}}{{dt}} = \frac{{dV}}{{ds}} \times \frac{{ds}}{{dt}} = \frac{{dV}}{{ds}} \cdot V\)
Total Acceleration (a):
a = \(\sqrt {a_t^2 + a_r^2}\)
Given:
Calculation:
Radial acceleration,
\({a_r} = \frac{{{V^2}}}{r} = \frac{{{3^2}}}{9} = 1~m/s^2\)
Tangential acceleration,
\({a_t} = \frac{{dV}}{{dt}} = \frac{{dV}}{{ds}} \times \frac{{ds}}{{dt}} = \frac{{dV}}{{ds}} \cdot V\)
\(= \frac{1}{3} \times 3 = 1 ~m/s^2\)
\(\therefore\ Total\;acceleration\;a = \sqrt {a_t^2 + a_r^2} = \sqrt {{1^2} + {1^2}} = \sqrt 2\) m/sec2Last updated on Jul 15, 2025
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