# Recent questions and answers in Fluid Mechanics Which of the following conditions is used to determine the stable equilibrium of all partially submerged floating bodies? Centre of buoyancy must be above the centre of gravity Centre of buoyancy must be below the centre of gravity Metacentre must be at a higher level than the centre of gravity Metacentre must be at a lower level than the centre of gravity
A closed vessel contains pure water, in thermal equilibrium with its vapour at $25^\circ C$(Stage$\#1$), as shown. The vessel in this stage is then kept aside an isothermal oven which is having an atmosphere of hot air maintained at $80^\circ C$ ... through Valve $A$ Nothing will happen - the vessel will continue to remain in equilibrium All the vapor inside the vessel will immediately condense
Water (density $1000 \: kg/m^3$) flows through an inclined pipe of uniform diameter. The velocity, pressure and elevation at section $\textbf{A}$ are $V_A=3.2 \: m/s, \: p_A=186 \text{kPa}$ and $z_A=24.5 \: m$, respectively and those at section $\textbf{B}$ are ... . If acceleration due to gravity is $10 \: m/s^2$ then the head lost due to friction is ________ $m$ (round off to one decimal place)
Water flows through a tube of $3$ cm internal diameter and length $20$ ... $^\circ C$ (round off to one decimal place
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With increase in pressure the bulk modulus of elasticity__?
Froude number is the ratio of buoyancy forces to viscous forces inertia forces to viscous forces buoyancy forces to inertia forces inertia forces to gravity forces
Match the following non-dimensional numbers with the corresponding definitions: ... $P-3, Q-1, R-2, S-4$ $P-4, Q-3, R-1, S-2$ $P-3, Q-1, R-4, S-2$
The velocity field of an incompressible flow in a Cartesian system is represented by $\overrightarrow{V}=2\left ( x^{2}-y^{2} \right )\widehat{i}+v\widehat{j}+3\widehat{k}$ Which one of the following expressions for $v$ is valid? $-4xz + 6xy$ $– 4xy – 4xz$ $4xz – 6xy$ $4xy + 4xz$
Consider steady, viscous, fully developed flow of a fluid through a circular pipe of internal diameter $\text{D}$. We know that the velocity profile forms a paraboloid about the pipe centre line, given by: $V=-C\left(r^{2}-\dfrac{D^{2}}{4}\right) m/s$, where $C$ is a ... $\text{A-B}$, as shown in the figure, is proportional to $D^{n}$. The value of $n$ is ________.
Air discharges steadily through a horizontal nozzle and impinges on a stationary vertical plate as shown in figure. The inlet and outlet areas of the nozzle are $0.1\:m^{2}\:\text{and}\:0.02\:m^{2}$ ... of air is $0.36\:kPa$, the gauge pressure at point $O$ on the plate is __________ $kPa$ (round off to two decimal places).
A two-dimensional incompressible frictionless flow field is given by $\overrightarrow{u} = x \hat{i} – y \hat{j}$. If $\rho$ is the density of the fluid, the expression for pressure gradient vector at any point in the flow field is given as $\rho(x \hat{i}+y \hat{j})$ $– \rho(x \hat{i}+y \hat{j})$ $\rho(x \hat{i} – y \hat{j})$ $– \rho(x^2 \hat{i}+y^2 \hat{j})$
Water enters a circular pipe of length $L=5.0$ m and diameter $D=0.20$m with Reynolds number $Re_D=500$. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit. The Reynolds number at the exit of the pipe is _________
Water flows through two different pipes $A$ and $B$ of the same circular cross-section but at different flow rates. The length of pipe $A$ is $1.0 \: m$ and that of pipe $B$ is $2.0 \: m$. The flow in both the pipes is laminar and fully developed ... head loss across the length of the pipes is same, the ratio of volume flow rates $Q_B/Q_A$ is __________ (round off to two decimal places).
The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of $0.1$ with the windows and the roof closed. With the windows and the roof open, the drag coefficient becomes $0.8$. The car travels at $44$ km/h with the windows and roof ... (round off to two decimal places), is __________ $km/h$ (The density of air and the frontal area may be assumed to be constant).
Water flowing at the rate of $1$ kg/s through a system is heated using an electric heater such that the specific enthalpy of the water increases by $2.50 \: kJ/kg$ and the specific entropy increases by $0.007 \: kJ/kg \cdot K$. The power input to the ... . Assuming an ambient temperature of $300 \: K$, the irreversibility rate of the system is __________ $kW$ (round off to two decimal places).
An idealized centrifugal pump (blade outer radius of $50 \: mm$) consumes $2 \: kW$ power while running at $3000 \: rpm$. The entry of the liquid into the pump is axial and exit from the pump is radial with respect to impeller. If the losses are neglected, then the mass flow rate of the liquid through the pump is ___________ $kg/s$ (round off to two decimal places)
For a hydrodynamically and thermally fully developed laminar flow through a circular pipe of constant cross-section, the Nusselt number at constant wall heat flux $(Nu_q)$ and that at constant wall temperature $(Nu_T)$ are related as $Nu_q > Nu_T$ $Nu_q < Nu_T$ $Nu_q = Nu_T$ $Nu_q = (Nu_T)^2$
Water flows through a pipe with a velocity given by $\overrightarrow{V}= \bigg( \dfrac{4}{t}+x+y \bigg) \hat{j} \: m/s$, where $\hat{j}$ is the unit vector in the $y$ direction, $t(>0)$ is in seconds, and $x$ and $y$ are in meters. The magnitude of total acceleration at the point $(x,y)=(1,1)$ at $t=2\: s$ is ______$m/s^2$
The wall of a constant diameter pipe of length $1 \: m$ is heated uniformly with flux $q''$ by wrapping a heater coil around it. The flow at the inlet to the pipe is hydrodynamically fully developed. The fluid is incompressible and the flow is assumed to be laminar and steady all ... Among the location P, Q and R, the flow is thermally developed at P, Q and R P and Q only Q and R only R only
Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, $2 \: m$ ... upper fluid, $\mu_1$, then the velocity at the interface (round off to two decimal places) is _______ $m/s$.
A cube of side $100 \: mm$ is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is $800 \: kg/m^3$. Liquid of density $1000 \: kg/m^3$ is now poured into the container. The minimum height to which the liquid needs to be poured into the container for the cube to just lift up is __________$mm$.
A large tank with a nozzle attached contains three immiscible, inviscid fluid as shown. Assuming that the changes in $h_1, h_2$ and $h_3$ ...
Consider two infinitely long thin concentric tubes of circular cross section as shown in the figure. If $D_1$ and $D_2$ are the diameters of the inner and outer tubes respectively, then the view factor $F_{22}$ is given by $\bigg( \dfrac{D_1}{D_2} \bigg) -1 \\$ $\text{zero} \\$ $\bigg( \dfrac{D_1}{D_2} \bigg) \\$ $1- \bigg( \dfrac{D_1}{D_2} \bigg)$
An incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is $1$ mm at a location where the Reynolds number is $1000$. If the velocity of the fluid alone is increased by a factor of $4$, then the boundary layer thickness at the same location, in mm will be $4$ $2$ $0.5$ $0.25$
The velocity triangles at the inlet and exit of the rotor of a turbomachine are shown. $V$ denotes the absolute velocity of the fluid, $W$ denotes the relative velocity of the fluid and $U$ denotes the blade velocity. Subscripts $1$ and $2$ refer to inlet and outlet respectively. If $V_2 =W_1$ and $V_1=W_2$, then the degree of reaction is $0$ $1$ $0.5$ $0.25$
An ideal gas of mass $m$ and temperature $T_1$ undergoes a reversible isothermal process from an initial pressure $P_1$ to final pressure $P_2$. The hear loss during the process is $Q$. The entropy change $\Delta S$ of the gas is $mR \: \ln \bigg( \dfrac{P_2}{P_1} \bigg) \\$ $mR \: \ln \bigg( \dfrac{P_1}{P_2} \bigg) \\$ $mR \: \ln \bigg( \dfrac{P_2}{P_1} \bigg) - \dfrac{Q}{T_1} \\$ $\text{zero}$
A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by $1 \%$ and the thickness is reduced by $1 \%$ with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is $0$ $1$ $1.08$ $2.02$
Oil flows through a $200$ mm diameter horizontal cast iron pipe (friction factor, $f=0.0225$) of length $500 m$. The volumetric flow rate is $0.2 \: m^3/s$. The head loss (in m) due to friction is (assume $g=9.81 m/s^2$) $116.18$ $0.116$ $18.22$ $232.36$
For an opaque surface, the absorptivity ($\alpha$), transmissivity ($\tau$) and reflectivity ($\rho$) are related by the equation $\alpha + \rho = \tau$ $\rho + \alpha + \tau =0$ $\alpha + \rho =1$ $\alpha + \rho =0$
In abrasive jet machining, as the distance between the nozzle tip and the work surface increases, the material removal rate increases continuously decreases continuously decreases, becomes stable and then increases increases, becomes stable and then decreases
The transition Reynolds number for flow over a flat plate is $5^*10^5$. What is the distance from the leading edge at which transition will occur for flow of water with a uniform velocity of $1 \: m/s$? (For water, the kinematic viscosity $v=0.86^*10^{-6} \:m^2/s$) $0.43 \: m$ $1 \: m$ $43 \: m$ $103 \: m$
The pressure drop for a relatively low Reynolds number flow in a $600 \: mm, \: 30 \: m$ long pipeline is $70 \: kPa$. What is the wall shear stress? $0 \: Pa$ $1400 \: Pa$ $700 \: Pa$ $350 \: Pa$
A metallic cube of side $10 \: cm$, density $6.8 \: gm/cc$ is floating in liquid mercury (density $13.6 \: gm/cc$), with $5 \: cm$ height of cube exposed above the mercury level. Water (density $1 \: gm/cc$) is filled over this, to submerge the cube fully. The new height of cube exposed above mercury level is $4.6 \: cm$ $5.4 \: cm$ $5.0 \: cm$ $5.8 \: cm$
Across a normal shock Static pressure and the static temperature rise entropy remains constant velocity and static pressure decrease density and temperature decrease
If the stream function is given by $\Psi=3xy$, then the velocity at a point $(2,3)$ will be $7.21 \: \text{unit}$ $18 \: \text{unit}$ $10.82 \: \text{unit}$ $54 \: \text{unit}$
A hydraulic press has a ram of $15 \: cm$ diameter and plunger of $1.5 \: cm$. It is required to lift a mass of $1000 \: kg$. The force required on plunger is nearly equal to $100 \: N$ $1000 \: N$ $10000 \: N$ $10 \: N$
A flat plate of width $L=1 \: m$ is pushed down with a velocity $U=0.01 \: m/s$ towards a wall resulting in the drainage of the fluid between the plate and the wall as sown in the figure. Assume two-dimensional incompressible flow and that the plate remains parallel to ... $m/s$) draining out at the instant shown in the figure is ____ (correct to three decimal places).
A frictionless circular piston of area $10^{-2} \: m^2$ and mass $100 \: kg$ sinks into a cylindrical container of the same area filled with water of density $1000 \: kg/m^3$ ... considering water to be incompressible, the magnitude of the piston velocity (in $m/s$) at the instant shown is _____ (correct to three decimal places).
Air flows at the rate of $1.5 \: m^3/s$ through a horizontal pipe with a gradually reducing cross-section as shown in the figure. The two cross-sections of the pipe have diameters of the $400 \: mm$ and $200 \: mm$. Take the air density as $1.2 \: kg/m^3$ and assume inviscid ... The change in pressure $(p_2-p_1)$ (in $kPa$) between sections $1$ and $2$ is $-1.28$ $2.56$ $- 2.13$ $1.28$
The viscous laminar flow of air over a flat plate results in the formation of a boundary layer. The boundary layer thickness at the end of the plate of length $L$ is $\delta_L$. When the plate length is increased to twice its original length, the percentage change in laminar boundary layer thickness at the end of the plate (with respect to $\delta_L$ is _______ (correct to two decimal palces).