Recent questions in Fluid Mechanics

For a laminar, incompressible, and fully-developed flow through a circular pipe, the ratio of the maximum velocity to the average velocity of the flow is$1.5$$2$$3$$4$

Air flows with a freestream velocity $U$ over four different bodies having same frontal area facing to the flow direction, as shown in the figure. Which one of the follow...

Consider a steady, and incompressible flow over a body with characteristic length $\text{L}$. The boundary layer thickenss at a distance $x$ from the leading edge is $\de...

Three different siphons steadily discharge water at velocities $V_{\mathrm{I}}, V_{\mathrm{II}}$, and $V_{\mathrm{IIII}}$, as shown in the figure. The tubes of the siphon...

Consider the following statements:Assertion (a)Surface tension acts along the interface of two fluids.Reason (r)The pressure of the fluid inside a bubble is higher than t...

The basic dimensions, i.e., mass, length, and time are represented by $M, L$, and $T$, respectively. The correct dimension of dynamic viscosity is$M L T^{-2}$$M^{0} L^{2}...

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...

Consider two different cases of water flowing through a smooth pipe of $50$ $\mathrm{cm}$ diameter. The mass flow rates for the two cases are $\text{(i)}$ $0.25 \mathrm{~...

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...

A gas is pressurized in a vertical frictionless piston-cylinder device, as shown in the figure. The piston has a mass of $4$ kg and a cross-sectional area of $40 \mathrm{...

A ship is designed to sail at a speed of $8 \mathrm{~m} \cdot \mathrm{~s}^{-1}$. A designer makes a $1/10$ scaled model to test the ship in a water tunnel. The model and ...

A rectangular block (density $=600 \mathrm{~kg} \cdot \mathrm{~m}^{-3}$ ) with base area of $0.06 \mathrm{~m}^{2}$ and height $15$ cm is partially submerged in water (den...

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...

Air flows through a pipe of diameter $D$ with an average velocity of $3 \mathrm{~m}. \mathrm{s}^{-1}$. The Darcy friction factor of the pipe is $0.02$. Assume acceleratio...

A stream of moist air enters an adiabatic saturator at $45^{\circ} \mathrm{C}$ and $101$ $\mathrm{kPa}$ and leaves as a saturated mixture at $30^{\circ} \mathrm{C}$. Make...

Water is flowing at $100$ $\mathrm{litres}/ \mathrm{min}$ through a pipe with a diameter of $5$ $\mathrm{cm}$. Assume the coefficient of viscosity of water to be $0.001$ ...

For a given temperature difference between the top and bottom surfaces of a flat metal plate, Fourier's law of heat conduction implies thattemperature gradient increases ...

What is the approximate value of annual-mean pH of seawater at the surface in the northern Indian Ocean?$4.5$$5.0$$8.0$$11.0$

In a stable atmosphere, the change in pressure (in kilo Pascal) at a height of $100 \mathrm{~m}$ from the mean sea level is $\_\_\_\_$. (rounded off to three decimal plac...

The mass (in $\mathrm{kg}$) of dry air in a room, measuring $10 m \times 7 m \times 3 m$, is $\_\_\_\_$. (rounded off to two decimal places)[Density of dry air is $1.029 ...

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...

The luminous efficacy of an electric light bulb is measured in which one of the following units?lumen $\mathrm{W}^{-1}$lumen $\mathrm{W}^{-1} \mathrm{~h}^{-1}$lumen $\mat...

A hydro turbine works under a head of $20$ $\mathrm{m}$ and has a maximum volume flow rate of $4 \mathrm{~m}^{3} \mathrm{~s}^{-1}$ and a speed of $750$ $\mathrm{rpm}$. De...

The useful heat gain in Watt (rounded off to one decimal place) of a solar flat plate collector using Hottel-Whillier-Bliss equation is $\_\_\_\_$.Assume:Collector heat r...

​​​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...

​​​Statement of Reynolds Transport Theorem is given below with three blanks.The rate of change of $\_\_\_\_\_$ extensive property can be calculated by summing the rate of...

​​​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...

​​$\textbf{Group-I}$ indicates different properties of fluid and $\textbf{Group-II}$ defines their basic dimensions in terms of Force $(F)$, Length ( $L$ ), and Time ( $T...

​​​Consider the steady, incompressible, and fully developed laminar flow of a fluid through a circular pipe. Here, $\Delta P$ is the pressure drop in the direction of the...

​A doublet is the resulting flow pattern when a sink and a source of equal strength are brought together.Which one of the following options correctly represents the natur...