Fluid Kinematics · Fluid Mechanics · GATE ME

The velocity field of a two-dimensional, incompressible flow is given by $\overrightarrow{V} = \ 2sin{h}\,x\,\hat{i} + v(x,y)\hat{j}$ where $ \hat{i...

The velocity field in a fluid is given to be $\vec{V}=(4xy)\hat{i}+2(x^2-y^2)\hat{j}$ Which of the following statement(s) is/are correct?...

A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to the fluid. The velocity field ...

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_...

The volume tric flow rate (per unit depth) between two streamlines having stream functions $${\psi _1}$$ & $${\psi _2}$$ is

A channel of width $$450$$ $$mm$$ branches into two sub-channels having width $$300$$ $$mm$$ and $$200$$ $$mm$$ as shown in figure. If the volumetric ...

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...

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...

In a flow field, the streamlines and equipotential lines

Streamlines, path lines and streak lines are virtually identical for

Existence of velocity potential implies that

Circulation is defined as line integral of tangential component of velocity about a _________ (fill in the blank)

For a fluid element in a two dimensional flow field ($$x-y$$ plane), it will undergo

A steady two-dimensional flow field is specified by the stream function ψ = kx3y, where x and y are in meters and the constant k = 1 m-2s-...

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 $$V$$ $$m/s.$$ 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 ...