GATE Civil Engineering (CE) 2018 Shift 1 Solved Paper

Question : 27 of 65

Marks: +1, -0

A flow field is given by 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)

Solution:

ω_{z} \;\; =\;{1}/{2}[\;{∂ v}/{∂ x}-\;{∂ u}/{∂ y}]

\;\; =\;{1}/{2}[\;{∂}/{∂ x}(-x y)-\;{∂}/{∂ y}(y)^{2}]

\;\; =\;{1}/{2}[-y-2 y]

\;\; =-\;{3 y}/{2}

At point

(0,-1,1) \;\; ω_{z}=-\;{3}/{2} ×-1=1.50 {rad}{/}{s}

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