GATE CE · Fluid Mechanics And Hydraulics

Fluid Kinematics Practice Questions

Generate GATE-level questions on Fluid Kinematics in Fluid Mechanics And Hydraulics. Focus on core concepts, previous year patterns, and numerical problem-solving techniques.

24 questions · 4 PYQs · 0 AI practice · GATE CE 2027

Q21GATE 2004MCQ

The x component of velocity in a two dimensional incompressible flow is given by u=1.5x. At the point (x,y) = (1,0), the y component of velocity v=0. The equation for the y component of velocity is

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📖 Explanation

For equation of stream line in two dimensions is given as

\begin{aligned} \frac{\partial U}{\partial x}+\frac{\partial V}{\partial y}&=0 \\ \Rightarrow \quad 1.5+\frac{\partial V}{\partial y} &=0 \\ \Rightarrow \quad \frac{\partial V}{\partial y}&=-1.5 \\ \Rightarrow \quad v&=-1.5 \mathrm{y}+\mathrm{C}\\ \text { But at } \quad y&=0, v=0\\ \therefore \quad 0&=-15 \times 0+C \\ \Rightarrow \quad C&=0\\ \text { Thus } \quad v&=-1.5 \mathrm{y} \end{aligned}

Q22GATE 2004MCQ

A velocity field is given as $\vec{V}=2y\vec{i}+3x\vec{j}$ , where x and y are in metres. The acceleration of a fluid particle at (x,y)=(1,1) in the x direction is

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📖 Explanation

\begin{aligned} \text { Given } \quad \nabla&=2 y \hat{\imath}+3 x \hat{\jmath}\\ u&=2 y and v=3 x \\ a_{x}&=\frac{\partial u}{\partial t}+u \frac{\partial u}{\partial x}+v \frac{\partial u}{\partial y} \\ \Rightarrow \quad a_{x}&=0+(2 y \times 0)+(3 x \times 2) \\ \Rightarrow \quad a_{x}&=6 x\\ \text{Now at }(1,1)\\ a_{1}&=6 x=6 \times 1=6 \mathrm{m} / \mathrm{s}^{2} \end{aligned}

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