velocity field

Consider a velocity field $\vec{V} = 3z\hat{i} + 0\hat{j} + Cx \hat{k}$, where C is a constant. If the flow is irrotational, the value of C is _________ (rounded off to 1 decimal p...

Consider a velocity field $\vec{V}=3 z \hat{i}+0 \hat{j}+C x \hat{k}$, where $C$ is a constant. if the flow is irrotational, the value of C is ________ (rounded off to 1 decimal pl...

The velocity field of a two-dimensional, incompressible flow is given by V⃗ = 2 sinh x î + v(x, y) ĵ where î and ĵ denote the unit vectors in x and y directions, respectively. If v...

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}$ and $\underset{\dot{}}{j}$ de...

The velocity field of a certain two-dimensional flow is given by V(x, y) = k(xî – yĵ) where k = 2 s^-1. The coordinates x and y are in meters. Assume gravitational effects to be ne...

Consider a unidirectional fluid flow with the velocity field given by V(x, y, z, t) = u(x, t) î where u(0, t) = 1. If the spatially homogeneous density field varies with time t as...

The velocity field of a certain two-dimensional flow is given by V(𝑥, 𝑦) = 𝑘(𝑥𝑖̂ − 𝑦𝑗̂) where 𝑘 = 2 s -1 . The coordinates 𝑥 and 𝑦 are in meters. Assume gravitational eff...

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 in the fluid is $\vec V = (2x)...

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 two dimensional flow has velocities in x and y directions given by u = 2xyt and v = -y^2t, where t denotes time. The equation for streamline passing through x = 1, y = 1 is

A two-dimensional incompressible frictionless flow field is given by $\vec{u} = x\hat{i} - y\hat{j}$. If $\rho$ is the density of the fluid, the expression for pressure gradient ve...

Water flows through a pipe with a velocity given by $\vec{V} = (\frac{4}{t} + x + y)\hat{j}$ m/s, where $\hat{j}$ is the unit vector in the y direction, $t (> 0)$ is in seconds, an...

Consider the two-dimensional velocity field given by $\vec{V} = (5 + a_1x + b_1y)\hat{i} + (4 + a_2x + b_2y)\hat{j}$, where $a_1, b_1, a_2$ and $b_2$ are constants. Which one of th...

For a steady flow, the velocity field is $\vec{V} = (-x^2 + 3y)\hat{i} + (2xy)\hat{j}$. The magnitude of the acceleration of a particle at $(1,-1)$ is

For a steady flow, the velocity field is $$\overrightarrow V = \left( { - {x^2} + 3y} \right)\widehat i + \left( {2xy} \right)\widehat j.$$ The magnitude of the acceleration of the...

Consider the two-dimensional velocity field given by $$\overrightarrow V = \left( {5 + {a_1}x + {b_1}y} \right)\widehat i + \left( {4 + {a_2}x + {b_2}y} \right)\widehat j,$$ where...

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 $$\wid...

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 given by the family of curves

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_...

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...

For an incompressible flow field , $$\overrightarrow {V,} $$ which one of the following conditions must be satisfied?

Consider a velocity field $$\overrightarrow V = K\left( {y\widehat i + x\widehat k} \right),$$ where $$K$$ is a constant. The vorticity, $${\Omega _z},$$ is

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 terms of the two - dimensiona...

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 distance along the axis of the no...

In a two-dimensional velocity field with velocities $$u$$ and $$v$$ along $$x$$ and $$y$$ directions respectively, the convective acceleration along the $$x$$-direction is given by

A fluid flow is represented by the velocity field $$\overrightarrow V = ax\,\overrightarrow i + ay\,\overrightarrow j ,$$ where a constant . The equation of stream line passing thr...

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 of $$\lambda $$ for a possible...

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 if (i) It represents an incompre...

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 shear deformation $${\varepsilon...