GATE Papers >> Civil >> 2018 >> Question No 27

Question No. 27 Civil | GATE 2018
A flow field is given by u=y2, v=-xy, w=0. Value of the z-component of the angular velocity (in radians per unit time, up to two decimal places) at the point (0, −1, 1) is ______

Answer : 1.50 to 1.50


Solution of Question No 27 of GATE 2018 Civil Paper

$\begin{array}{l}\mathrm u=\mathrm y^2\\\mathrm v=-\mathrm{xy}\\\mathrm w=0\end{array}$

Angular velocity at point (0.-1,1)

$\begin{array}{l}{\mathrm w}_\mathrm z=\frac12\left[\frac{\partial\mathrm v}{\partial\mathrm x}\frac{\partial\mathrm u}{\partial\mathrm y}\right]\\\;\;\;\;\;=\frac12\left[-\mathrm y-2\mathrm y\right]\\\;\;\;\;\;=\frac12\left[-3\mathrm y\right]\\\;\;\;\;\;=-\frac32\mathrm y=-\frac32(-1)\\\;\;\;\;\;=\frac32=1.5\end{array}$

$\therefore$ Correct answer [1.5].

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