Questions without answers 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...