1
GATE ME 2016 Set 3
+2
-0.6
For a two-dimensional flow, the velocity field is $$\overrightarrow u = {x \over {{x^2} + {y^2}}}\widehat i + {y \over {{x^2} + {y^2}}}\widehat j,$$ where $$\widehat i$$ and $$\widehat j\,\,$$ are the basis vectors in the $$x$$-$$y$$ Cartesian coordinate system .
Identify the CORRECT statements from below.
(1) The flow is incompressible
(3) $$y$$-component of acceleration, $${a_y} = {{ - y} \over {{{\left( {{x^2} + {y^2}} \right)}^2}}}$$
(4) $$x$$-component of acceleration , $${a_x} = {{ - \left( {x + y} \right)} \over {{{\left( {{x^2} + {y^2}} \right)}^2}}}$$

A
$$(2)$$ and $$(3)$$
B
$$(1)$$ and $$(3)$$
C
$$(1)$$ and $$(2)$$
D
$$(3)$$ and $$(4)$$
2
GATE ME 2015 Set 1
Numerical
+2
-0
The velocity field on an incompressible flow is given by
$$V = \left( {{a_1}x + {a_2}y + {a_3}z} \right)i + \left( {{b_1}x + {b_2}y + {b_3}z} \right)j$$ $$+ \left( {{c_1}x + {c_2}y + {c_3}z} \right)k,$$\$

Where $${a_1} = 2$$ and $${c_3} = - 4.$$ The value of $${b_2}$$ is _____________.

3
GATE ME 2015 Set 1
+2
-0.6
Match the following pairs: A
$$P - {\rm I}V,\,\,Q - {\rm I},\,\,R - {\rm I}{\rm I},\,\,S - {\rm I}{\rm I}{\rm I}$$
B
$$P - {\rm I}V,\,\,Q - {\rm I}{\rm I}{\rm I},\,\,R - {\rm I},\,\,S - {\rm I}{\rm I}$$
C
$$P - {\rm I}{\rm I}{\rm I},\,\,Q - {\rm I},\,\,R - {\rm I}V,\,\,S - {\rm I}{\rm I}$$
D
v$$P - {\rm I}{\rm I}{\rm I},\,\,Q - {\rm I},\,\,R - {\rm I}{\rm I},\,\,S - {\rm I}V$$
4
GATE ME 2014 Set 4
+2
-0.6
Consider the following statements regarding streamline(s):
(i) It is a continuous line such that the tangent at any point on it shows the velocity vector at that point
(ii) There is no flow across streamlines
(iii) $${{dx} \over u} = {{dy} \over v} = {{dz} \over w}$$ is the differential equation of a streamline, where $$u,v$$ and $$w$$ are velocities in directions $$x,y$$ and $$z,$$ respectively
In an unsteady flow, the path of a particle is a streamline

Which one of the following combinations of the statements is true?

A
$$\left( i \right),\,\,\left( {ii} \right),\,\,\left( {iv} \right)$$
B
$$\left( {ii} \right),\,\,\left( {iii} \right),\,\,\left( {iv} \right)$$
C
$$\left( i \right),\,\,\left( {iii} \right),\,\,\left( {iv} \right)$$
D
$$\left( i \right),\,\,\left( {ii} \right),\,\,\left( {iii} \right)$$
GATE ME Subjects
Engineering Mechanics
Strength of Materials
Theory of Machines
Engineering Mathematics
Machine Design
Fluid Mechanics
Turbo Machinery
Heat Transfer
Thermodynamics
Production Engineering
Industrial Engineering
General Aptitude
EXAM MAP
Joint Entrance Examination