Recent questions tagged 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...

A piezometer and a Pitot tube are tapped into a horizontal water pipe, as shown in the figure, where $h_{1}=4 \mathrm{~cm}, h_{2}=6 \mathrm{~cm}$ and $h_{3}=5 \mathrm{~cm...

A steady, laminar, and incompressible flow between a pair of infinite parallel plates is driven by a constant pressure gradient $(-d p / d x)$. The plates are separated b...

An incompressible fluid flows between a pair of infinite plates separated by a distance $L$. The top plate is moving with a constant velocity $U$, whereas the bottom plat...

A two-dimensional source flow (with stream function, $\psi_{1}=m \tan ^{-1} \dfrac{y}{x}$ ) is placed at the origin in a uniform flow (with stream function, $\psi_{2}=U y...

Consider a steady, laminar, and incompressible flow over a flat plate, as shown in the figure. With freestream velocity $U_{\infty}$ and kinematic viscosity $v_{1}$, the ...

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...

The axial velocity profile of a laminar, incompressible, and fully-developed flow in a circular pipe of radius $R$ is given as $v_{z}=\dfrac{1}{4 \mu} \dfrac{d p}{d z}\le...

A car is moving on a horizontal surface in a straight line with a constant velocity of $3 \mathrm{~m} / \mathrm{s}$. A ball is thrown vertically upwards at time $t=0$ fro...

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...

​​​A sharp flat plate of length $L$ and infinite width is immersed parallel to a fluid stream having velocity $u_{\infty}$. At a point on the plate, far away from the lea...

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

​​​For a steady and incompressible flow, the velocity field $(\vec{V})$ in Cartesian $(x, y, z)$ coordinate system is given as:$$\vec{V}=5 x i-P y j+3 k$$Here, $i, j$, an...

​​​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 figure shows a rod $\text{PQ}$, hinged at $\text{P}$, rotating counter-clockwise with a uniform angular speed of $15 \: \mathrm{rad} / \mathrm{s}$. A block $R$ tr...

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...