GATE ME 2019 Set 1 — Question 33
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Fluid Mechanics → Fluid Kinematics & Dynamics → Local, Convective & Material Acceleration
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Question
Water flows through a pipe with a velocity given by m/s, where is the unit vector in the direction, () is in seconds, and and are in meters. The magnitude of total acceleration at the point at s is ______ m/s.
Correct answer
3 to 3
Solution
The velocity vector is , where .
The components of velocity are , , and .The acceleration components are:
Calculating the partial derivatives for :
Substituting these into the expression for :
At the point and s:
The magnitude of total acceleration is:
The components of velocity are , , and .The acceleration components are:
Calculating the partial derivatives for :
Substituting these into the expression for :
At the point and s:
The magnitude of total acceleration is:
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