GATE ME
Fluid Mechanics
Fluid Kinematics
Previous Years Questions

## Marks 1

Consider the two-dimensional velocity field given by $$\overrightarrow V = \left( {5 + {a_1}x + {b_1}y} \right)\widehat i + \left( {4 + {a_2}x + {b_... For a certain two-dimensional incompressible flow, velocity field is given by$$2xy\widehat i - {y^2}\widehat j.$$The streamlines for this flow are g... A channel of width$$450mm$$branches into two sub-channels having width$$300mm$$and$$200mm$$as shown in figure. If the volumetric ... The volume tric flow rate (per unit depth) between two streamlines having stream functions$${\psi _1}$$&$${\psi _2}$$is If the fluid velocity for a potential flow is given by$$V\left( {x,y} \right) = u\left( {x,y} \right)i + v\left( {x,y} \right)j$$with usual notation... A flow field which has only convective acceleration is A flow field which has only convective acceleration is For an incompressible flow field ,$$\overrightarrow {V,} $$which one of the following conditions must be satisfied? A streamline and an equipotential line in a flow field For a continuity equation given$$\nabla .\overrightarrow V = 0$$to be valid,$$\overrightarrow V $$where is the velocity vector, which one of the ... In a steady flow through a nozzle, the flow velocity on the nozzle axis is given by$$u = {u_0}\left( {1 + 3x/L} \right),\,\,$$where$$x$$is the dis... A two-dimensional flow field has velocities along the$$x$$and$$y$$directions given by$$u = {x^2}t$$and$$v = - 2xyt$$respectively, where$$t$$... In a two-dimensional velocity field with velocities$$u$$and$$v$$along$$x$$and$$y$$directions respectively, the convective acceleration along t... The velocity components in the$$x$$and$$y$$directions of a two dimensional potential flow are$$u$$and$$v$$, respectively. Then$${{\partial u} ...
A fluid flow is represented by the velocity field $$\overrightarrow V = ax\,\overrightarrow i + ay\,\overrightarrow j ,$$ where a constant . The equ...
Streamlines, path lines and streak lines are virtually identical for
In a flow field, the streamlines and equipotential lines
For a fluid element in a two dimensional flow field ($$x-y$$ plane), it will undergo
Circulation is defined as line integral of tangential component of velocity about a _________ (fill in the blank)
Existence of velocity potential implies that

## Marks 2

For a steady flow, the velocity field is $$\overrightarrow V = \left( { - {x^2} + 3y} \right)\widehat i + \left( {2xy} \right)\widehat j.$$ The magni...
For a two-dimensional flow, the velocity field is $$\overrightarrow u = {x \over {{x^2} + {y^2}}}\widehat i + {y \over {{x^2} + {y^2}}}\widehat j,$$ ...
Match the following pairs: ...
The velocity field on an incompressible flow is given by $$V = \left( {{a_1}x + {a_2}y + {a_3}z} \right)i + \left( {{b_1}x + {b_2}y + {b_3}z} \right)... Consider the following statements regarding streamline(s): (i) It is a continuous line such that the tangent at any point on it shows the velocity vec... Consider a velocity field$$\overrightarrow V = K\left( {y\widehat i + x\widehat k} \right),$$where$$K$$is a constant. The vorticity,$${\Omega _z...
Velocity vector of a flow fields is given as $$\overrightarrow V = 2xy\widehat i - {x^2}z\widehat j.$$ The vorticity vector at $$(1,1,1)$$ is
You are asked to evaluate assorted fluid flows for their suitability in a given laboratory application. The following three flow choices. Expressed in...
The gap between a moving circular plate and a stationary surface is being continuously reduced, as the circular plate comes down at a uniform speed $$... The gap between a moving circular plate and a stationary surface is being continuously reduced, as the circular plate comes down at a uniform speed$$...
Which combination of the following statements about steady incompressible forced vortex flow is correct? P: Shear stress is zero at all points in the...
A leaf is caught in a whirlpool. At a given instant, the leaf is at a distance of $$120$$ $$m$$ from the centre of the whirlpool. The whirlpool can be...
A closed cylinder having a radius $$R$$ and height $$H$$ is filled with oil of density $$\rho .$$ If the cylinder is rotated about its axis at an angu...
For a fluid flow through a divergent pipe of length $$L$$ having inlet and outlet radii of $${R_1}$$ and $${R_2}$$ respectively and a constant flow ra...
The $$2$$ - $$D$$ flow with, velocity $$\overrightarrow v = \left( {x + 2y + 2} \right)\overrightarrow i + \left( {4 - y} \right)\overrightarrow j ... The velocity components in the$$x$$and$$y$$directions are given by$$u = \lambda x{y^3} - {x^2}y,v = x{y^2} - {3 \over 4}{y^4}.$$The value o... A velocity field is given as$$$\overrightarrow V = 3{x^2}y\widehat i - 6xyz\widehat k$$Where$$x,y,z$$are in$$m$$and$$Vm/s.$$Determine ... The stream function in a two dimensional flow field is given by$$\Psi = {x^2} - {y^2}$$The magnitude of the velocity at point$$(1,1)$$is A Newtonian fluid has the following velocity field :$$$\overrightarrow V = {x^2}y\widehat i + 2x{y^2}z\widehat j - y{z^3}\widehat k\$ The rate of ...
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