Recent questions in Kinematics of Fluid Motion

The velocity components in $x$ - and $y$-directions of a two-dimensional, incompressible flow field are $u(x, y)=2 x^{2}+y^{3}$ and $v(x, y)=x^{3}-2 x y+f(x, y)$, respect...

Which of the following statements about streamlines, pathlines, and streaklines is/are correct?A streamline is a curve that is everywhere tangent to the instantaneous loc...

The velocity of a fluid particle in a flow is given as:$$\vec{V}=(a-x) \hat{\imath}+(b+y) \hat{\jmath}+(c+z) \hat{k}$$where $a, b, c$ are constants, and $\hat{\imath}, \h...

Which of the following combinations of forces is/are balanced in a cyclostrophic motion?Pressure Gradient, Coriolis, and CentrifugalPressure Gradient and CentrifugalCentr...

For an incompressible fluid, the velocity components ( $u, v$, and $w$) are given as:$\begin{array}{rcl}u(x,y,z) & = & 2x + y + 2z \\v(x,y,z) & = & ax + by + cz \\w(x,y,z...

​​​Fluid at a constant flow rate passes through a long, straight, cylindrical pipe that has an axisymmetric convergent section at the end.Which one of the following optio...

​Consider the following Statements $ $ and $ $.Statement $ $: The Eulerian study focusses attention on individual particle and its motion is observed as a function of tim...

​​​Conservation of mass for a steady axisymmetric flow field in the cylindrical $(r, z)$ coordinates is:$$\frac{1}{r} \frac{\partial\left(r V_{r}\right)}{\partial r}+\fra...

An incompressible fluid is flowing between two infinitely large parallel plates separated by $5 \mathrm{mm}$ distance. The bottom plate is stationary and the top plate is...

The locus of temporary locations of all particles that have passed through a fixed point in the flow field at a particular instant is known asstreamline.streakline.pathli...

Consider the velocities $u, v$, and $w$ in $x$-, $y$-, and $z$-directions, respectively. The vorticity expression in the $y-z$ plane is$\frac{\partial v}{\partial x}-\fra...

The velocity in a one-dimensional flow is given by $u(x)=\frac{a}{(b-x)^{2}} \mathrm{~m} / \mathrm{s}$, where $a=8 \mathrm{~m}^{3} / \mathrm{s}$ and $b=4 \mathrm{~m}$. Th...

Among the following non-dimensional numbers, which one characterizes periodicity present in a transient flow?Froude numberStrouhal numberPeclet numbeLewis number

For a two-dimensional flow field given as $\vec{V}=-x \hat{\imath}+y \hat{\jmath}$, a streamline passes through points $(2,1)$ and $(5, p)$. The value of $p$ is$5$$5 / 2$...

\begin{tabular}{|c|c|}\hline Q. 32 & \begin{tabular}{l}A two-dimensional incompressible flow field is defined as, \\$\qquad \vec{V}(x, y)=(A x y) \hat{\imath}+\left(B y^{...

\begin{tabular}{l|l}Q. 35 & In a steady two-dimensional compressible flow, $u$ and $v$ are the $x$ - and $y$ - \\components of flow velocity, respectively and $\rho$ is t...

Q. 38 The velocity and acceleration of a fluid particle are given as $\vec{V}=(-\hat{\imath}+2 \hat{\jmath}) \mathrm{m} / \mathrm{s}$ and $\vec{a}=(-2 \hat{\imath}-4 \hat...

Which of the following statement(s) is/are true for streamlines in a steady incompressible flow?Two streamlines cannot intersect each other.Flow rate increases between tw...

For an inviscid fluid with density } 1 \mathrm{~kg} / \mathrm{m}^{3}, \text { the Cartesian velocity field is given as:$\mathbf{u}=(-2 x+y) t \mathbf{i}+(2 x+y) t \mathbf...