Hot questions in Fluid Mechanics and Thermal Sciences / GO Mechanical

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GATE2016-3-42
Two large parallel plates having a gap of $10 \: mm$ in between them are maintained at temperatures $T_1 = 1000 \: K$ and $T_2 = 400 \: K$. Given emissivity values, $\epsilon _1 = 0.5$, $\epsilon _2=0.25$ and Stefan-Boltzmann constant $\sigma =5.67 \times 10^{−8} \: W/m^2-K^4$, the heat transfer between the plates (in $kW/m^2$) is __________

Two large parallel plates having a gap of $10 \: mm$ in between them are maintained at temperatures $T_1 = 1000 \: K$ and $T_2 = 400 \: K$. Given emissivity values, $\ep...

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GATE2015-3-9
Couette flow is characterized by steady, incompressible, laminar flow through a straight circular pipe fully developed turbulent flow through a straight circular pipe steady, incompressible, laminar flow between two fixed parallel plates steady, incompressible, laminar flow between one fixed plate and the other moving with a constant velocity

Couette flow is characterized bysteady, incompressible, laminar flow through a straight circular pipefully developed turbulent flow through a straight circular pipesteady...

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GATE2015-3-39
Air in a room is at $35^\circ C$ and $60 \%$ relative humidity (RH). The pressure in the room is $0.1 \: MPa$. The saturation pressure of water at $35^ \circ C$ is $5.63 kPa$. The humidity ratio of the air (in $gram/kg$ of dry air) is ________

Air in a room is at $35^\circ C$ and $60 \%$ relative humidity (RH). The pressure in the room is $0.1 \: MPa$. The saturation pressure of water at $35^ \circ C$ is $5.63...

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GATE2015-2-12
If the fluid velocity for a potential flow is given by $V(x,y)=u(x,y)i+v(x,y)j$ with usual notations, then the slope of the potential line at $(x,y)$ is $\dfrac{v}{u} \\$ $-\dfrac{u}{v} \\$ $\dfrac{u^2}{v^2} \\$ $\dfrac{u}{v}$

If the fluid velocity for a potential flow is given by $V(x,y)=u(x,y)i+v(x,y)j$ with usual notations, then the slope of the potential line at $(x,y)$ is$\dfrac{v}{u} \\$$...

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GATE2015-1-48
Match the following pairs: \begin{array}{|l|l|l|l|} \hline &\textbf{Equation} && \textbf{Physical Interpretation} \\ \hline P. & \nabla \times \overrightarrow{V}=0 & I. & \text{ Incompressible continuity equation} \\ \hline Q. & \nabla \bullet \overrightarrow{V}=0 & II. ... $P-IV, Q-III, R-I, S-II$ $P-III, Q-I, R-IV, S-II$ $P-III, Q-I, R-II, S-IV$

Match the following pairs:\begin{array}{|l|l|l|l|} \hline &\textbf{Equation} && \textbf{Physical Interpretation} \\ \hline P. & \nabla \times \overrightarrow{V}=0 & I. & ...

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GATE2015-1-49
The velocity field of an incompressible flow is given by $V=(a_1x+a_2y+a_3z)i+(b_1x+b_2y+b_3z)j+(c_1x+c_2y+c_3z)z$, where $a_1$ = $2$ and $c_3$ = − $4$. The value of $b_2$ is ___________

The velocity field of an incompressible flow is given by $V=(a_1x+a_2y+a_3z)i+(b_1x+b_2y+b_3z)j+(c_1x+c_2y+c_3z)z$, where $a_1$ = $2$ and $c_3$ = − $4$. The value of $b...

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GATE2015-1-12
A stream of moist air (mass flow rate $= 10.1 \: kg/s$) with humidity ratio of $0.01 \: \dfrac{kg}{\text{kg dry air}}$ mixes with a second stream of superheated water vapour flowing at $0.1 \: \text{kg/s}$. Assuming proper and uniform mixing with no condensation, the humidity ratio of the final stream $\big($in $\dfrac{kg}{\text{kg dry air}} \big )$ is _____________

A stream of moist air (mass flow rate $= 10.1 \: kg/s$) with humidity ratio of $0.01 \: \dfrac{kg}{\text{kg dry air}}$ mixes with a second stream of superheated water va...

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GATE2015-1-6
Consider fully developed flow in a circular pipe with negligible entrance length effects. Assuming the mass flow rate, density and friction factor to be constant, if the length of the pipe is doubled and the diameter is halved, the head loss due to friction will increase by a factor of $4$ $16$ $32$ $64$

Consider fully developed flow in a circular pipe with negligible entrance length effects. Assuming the mass flow rate, density and friction factor to be constant, if the ...

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GATE2016-3-14
For a certain two-dimensional incompressible flow, velocity field is given by $2xy\hat{i}-y^2\hat{j}$ . The streamlines for this flow are given by the family of curves $x^2y^2 = \text{constant}$ $xy^2 = \text{constant}$ $2xy − y^2 \text{constant}$ $xy = \text{constant}$

For a certain two-dimensional incompressible flow, velocity field is given by $2xy\hat{i}-y^2\hat{j}$ . The streamlines for this flow are given by the family of curves$...

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GATE2015-2-18
The Van der Waals equation of state is $(p+\dfrac{a}{v^2})(v-b)=RT$ where $p$ is pressure, $v$ is specific volume, $T$ is temperature and $R$ is characteristic gas constant. The SI unit of $a$ is $J/kg – K $ $m^3/kg$ $m^5/kg-s^2$ $Pa/kg$

The Van der Waals equation of state is $(p+\dfrac{a}{v^2})(v-b)=RT$ where $p$ is pressure, $v$ is specific volume, $T$ is temperature and $R$ is characteristic gas const...

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GATE2015-1-10
A Carnot engine ($CE_1$) works between two temperature reservoirs $A$ and $B$, where $T_A$ = $900$ $K$ and $T_B$ = $500$ $K$. A second Carnot engine ($CE_2$) works between temperature reservoirs $B$ and $C$, where $T_C$ = $300$ $K$ ... $CE_1$ from reservoir $A$ is $150$ $MJ$, the net heat rejected to reservoir $C$ by $CE_2$ (in $MJ$) is ______________

A Carnot engine ($CE_1$) works between two temperature reservoirs $A$ and $B$, where $T_A$ = $900$ $K$ and $T_B$ = $500$ $K$. A second Carnot engine ($CE_2$) works betwee...

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GATE2015-3-23
A rigid container of volume $0.5 m^3$ contains $1.0$ kg of water at $12^\circ C$ $(v_f = 0.00106 m^3/kg$, $v_g= 0.8908 m^3/kg)$. The state of water is compressed liquid saturated liquid a mixture of saturated liquid and saturated vapor superheated vapor

A rigid container of volume $0.5 m^3$ contains $1.0$ kg of water at $12^\circ C$ $(v_f = 0.00106 m^3/kg$, $v_g= 0.8908 m^3/kg)$. The state of water iscompressed liquidsat...

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GATE2015-2-45
One kg of air ($R=287 \: J/kg – K$) undergoes an irreversible process between equilibrium state $1(20^{\circ}C$, $0.9 \: m^3$) and equilibrium state $2 ( 20^{\circ} C$, $0.6\: m^3$). The change in entropy $s_2 – s_1$ (in $J/kg – K$) is _______

One kg of air ($R=287 \: J/kg – K$) undergoes an irreversible process between equilibrium state $1(20^{\circ}C$, $0.9 \: m^3$) and equilibrium state $2 ( 20^{\circ} C$,...

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GATE2015-1-9
For an ideal gas with constant values of specific heats, for calculation of the specific enthalpy, it is sufficient to know only the temperature both temperature and pressure are required to be known both temperature and volume are required to be known both temperature and mass are required to be known

For an ideal gas with constant values of specific heats, for calculation of the specific enthalpy,it is sufficient to know only the temperatureboth temperature and pressu...

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GATE2015-3-11
The ratio of momentum diffusivity $(ν)$ to thermal diffusivity $(\alpha)$, is called Prandtl number Nusselt number Biot number Lewis number

The ratio of momentum diffusivity $(ν)$ to thermal diffusivity $(\alpha)$, is calledPrandtl numberNusselt numberBiot numberLewis number

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GATE2015-2-17
The COP of a Carnot heat pump operating between $6^{\circ}C$ and $37^{\circ}C$ is ___________

The COP of a Carnot heat pump operating between $6^{\circ}C$ and $37^{\circ}C$ is ___________

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GATE2015-2-47
In a Rankine cycle, the enthalpies at turbine entry and outlet are $3159$ $kJ/kg$ and $2187$ $kJ/kg$, respectively. If the specific pump work is $2$ $kJ/kg$, the specific steam consumption (in $kg/kW$-$h$) of the cycle based on net output is _______________

In a Rankine cycle, the enthalpies at turbine entry and outlet are $3159$ $kJ/kg$ and $2187$ $kJ/kg$, respectively. If the specific pump work is $2$ $kJ/kg$, the specific...

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GATE2015-1-18
A swimmer can swim $10$ $km$ in $2$ hours when swimming along the flow of a river. While swimming against the flow, she takes $5$ hours for the same distance. Her speed in still water (in $km/h$) is _____

A swimmer can swim $10$ $km$ in $2$ hours when swimming along the flow of a river. While swimming against the flow, she takes $5$ hours for the same distance. Her speed i...

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GATE2015-2-16
In the laminar flow of air ($P_r$ = $0.7$) over a heated plate, if $\delta$ and $\delta _T$ denote, respectively, the hydrodynamic and thermal boundary layer thicknesses, then $\delta =\delta _T$ $\delta > \delta _T$ $\delta < \delta _T$ $\delta =0$ but $\delta _T\neq 0$

In the laminar flow of air ($P_r$ = $0.7$) over a heated plate, if $\delta$ and $\delta _T$ denote, respectively, the hydrodynamic and thermal boundary layer thicknesses,...

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GATE2015-1-40
A ball of mass $0.1 \text{ kg}$, initially at rest, is dropped from height of $1$m. Ball hits the ground and bounces off the ground. Upon impact with the ground, the velocity reduces by $20 \%$. The height (in $m$) to which the ball will rise is _______

A ball of mass $0.1 \text{ kg}$, initially at rest, is dropped from height of $1$m. Ball hits the ground and bounces off the ground. Upon impact with the ground, the velo...

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GATE2015-3-22
Three parallel pipes connected at the two ends have flow-rates $Q_1$, $Q_2$ and $Q_3$ respectively, and the corresponding frictional head losses are $h_{L1}$, $h_{L2}$ and $h_{L3}$ respectively. The correct expressions for total flow rate $(Q)$ and frictional head loss across the two ends ($h_L$) ... $Q = Q_1 = Q_2 = Q_3; h_L = h_{L1} = h_{L2} = h_{L3}$

Three parallel pipes connected at the two ends have flow-rates $Q_1$, $Q_2$ and $Q_3$ respectively, and the corresponding frictional head losses are $h_{L1}$, $h_{L2}$ an...

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GATE2016-2-6
A point mass having mass $M$ is moving with a velocity $V$ at an angle $\theta$ to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with the smooth wall and rebounds. The total change (final minus initial) in the momentum of the mass is $-2MV \cos\theta \hat{j}$ $2MV \sin\theta \hat{j}$ $2MV \cos\theta \hat{j}$ $-2MV \sin\theta \hat{j}$

A point mass having mass $M$ is moving with a velocity $V$ at an angle $\theta$ to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with ...

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GATE2016-1-20
The “Jominy test” is used to find Young’s modulus hardenability yield strength thermal conductivity

The “Jominy test” is used to findYoung’s modulushardenabilityyield strengththermal conductivity

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GATE Mechanical 2014 Set 2 | Question: 45
Consider laminar flow of water over a flat plate of length 1 m. If the boundary layer thickness at a distance of $0.25$ $m$ from the leading edge of the plate is $8$ $mm$, the boundary layer thickness (in $mm$), at a distance of $0.75$ $m$, is _______

Consider laminar flow of water over a flat plate of length 1 m. If the boundary layer thickness at a distance of $0.25$ $m$ from the leading edge of the plate is $8$ $mm$...

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GATE Mechanical 2014 Set 2 | Question: 42
A hemispherical furnace of $1$ m radius has the inner surface (emissivity, $\varepsilon =1$) of its roof maintained at $800$ $K$, while its floor ($\varepsilon =5.0$) is kept at $600 K$. Stefan-Boltzmann constant is $5.668 \times 10^−8$ $W / m^2$.$K^4$. The net radiative heat transfer (in $kW$) from the roof to the floor is _______

A hemispherical furnace of $1$ m radius has the inner surface (emissivity, $\varepsilon =1$) of its roof maintained at $800$ $K$, while its floor ($\varepsilon =5.0$) is...

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GATE Mechanical 2014 Set 1 | Question: 34
An ideal water jet with volume flow rate of $0.05$ $m^3$/$s$ strikes a flat plate placed normal to its path and exerts a force of $1000$ $N$. Considering the density of water as $1000kg$/$m^3$,the diameter(in $mm$) of the water jet is _______

An ideal water jet with volume flow rate of $0.05$ $m^3$/$s$ strikes a flat plate placed normal to its path and exerts a force of $1000$ $N$. Considering the density of w...

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GATE Mechanical 2014 Set 4 | Question: 48
Two infinite parallel plates are placed at a certain distance apart. An infinite radiation shield is inserted between the plates without touching any of them to reduce heat exchange between the plates. Assume that the emissivities of plates and radiation shield are equal ... exchange between the plates with and without the shield is $1/2$ $1/3$ $1/4$ $1/8$

Two infinite parallel plates are placed at a certain distance apart. An infinite radiation shield is inserted between the plates without touching any of them to reduce he...

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GATE Mechanical 2014 Set 4 | Question: 46
Two identical metal blocks L and M (specific heat = $0.4$ $kJ/kg.K$), each having a mass of $5$ $kg$, are initially at $313$ $K$. A reversible refrigerator extracts heat from block L and rejects heat to block M until the temperature of block L reaches $293$ $K$. The final temperature (in $K$) of block M is _______

Two identical metal blocks L and M (specific heat = $0.4$ $kJ/kg.K$), each having a mass of $5$ $kg$, are initially at $313$ $K$. A reversible refrigerator extracts heat ...

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GATE Mechanical 2014 Set 3 | Question: 43
A siphon is used to drain water from a large tank as shown in the figure below. Assume that the level of water is maintained constant. Ignore frictional effect due to viscosity and losses at entry,and exit. At the exit of the siphon, the velocity of water is $\sqrt{2g(Z_Q-Z_R)} \\$ $\sqrt{2g(Z_P-Z_R)} \\$ $\sqrt{2g(Z_O-Z_R)} \\$ $\sqrt{2gZ_Q}$

A siphon is used to drain water from a large tank as shown in the figure below. Assume that the level of water is maintained constant. Ignore frictional effect due to vis...

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GATE Mechanical 2014 Set 1 | Question: 41
$1.5$ kg of water is in saturated liquid state at $2$ bar $(vf = 0.001061 \: m^3/kg, uf = 504.0 \: kJ/kg,$ $hf = 505 kJ/kg$). Heat is added in a constant pressure process till the temperature of water reaches $400^ \circ C (v = 1.5493 \: m^3/kg, u = 2967.0 kJ/kg,$ $h = 3277.0 \: kJ/kg)$. The heat added (in $kJ$) in the process is _______

$1.5$ kg of water is in saturated liquid state at $2$ bar $(vf = 0.001061 \: m^3/kg, uf = 504.0 \: kJ/kg,$ $hf = 505 kJ/kg$). Heat is added in a constant pressure proces...

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GATE Mechanical 2014 Set 3 | Question: 46
At the inlet of an axial impulse turbine rotor, the blade linear speed is $25 \: m/s$, the magnitude of absolute velocity is $100 \: m/s$ and the angle between them is $25^{\circ}$. The relative velocity and the axial component ... blade inlet and outlet velocity triangles are shown in the figure. Assuming no losses, the specific work (in $J/kg$) is _______

At the inlet of an axial impulse turbine rotor, the blade linear speed is $25 \: m/s$, the magnitude of absolute velocity is $100 \: m/s$ and the angle between them is $2...

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GATE ME 2013 | Question: 29
Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is $20$ $mm$ with uniform velocity of $2$ $m/s$. Acceleration due to gravity is $9.81$ $m/s^2$. Assuming steady, inviscid flow, constant atmospheric pressure ... effects, the diameter in mm of the stream $0.5$ $m$ below the tap is approximately $10$ $15$ $20$ $25$

Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is $20$ $mm$ with uniform velocity of $2$ $m/s$. Acceleration due t...

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GATE ME 2013 | Question: 42
Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of $400$ $K$ and $300$ $K$. If the emissivities of the surfaces are $0.8$ and the Stefan-Boltzmann constant is $5.67$ × $10^{-8}$ $W$/$m^2$ $K^4$, the net radiation heat exchange rate in $kW$/$m^2$ between the two plates is $0.66$ $0.79$ $0.99$ $3.96$

Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of $400$ $K$ and $300$ $K$. If the emissivities of the surfaces are $0.8$...

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GATE Mechanical 2014 Set 4 | Question: 47
Steam with specific enthalpy $(h)$ $3214$ $kJ/kg$ enters an adiabatic turbine operating at steady state with a flow rate $10$ $kg/s$. As it expands, at a point where h is $2920$ $kJ/kg$, $1.5$ $kg/s$ is extracted for heating ... = $2374$ $kJ/kg$. Neglecting changes in kinetic and potential energies, the net power output (in $kW$) of the turbine is _______

Steam with specific enthalpy $(h)$ $3214$ $kJ/kg$ enters an adiabatic turbine operating at steady state with a flow rate $10$ $kg/s$. As it expands, at a point where h is...

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GATE Mechanical 2014 Set 4 | Question: 42
A plane wall has a thermal conductivity of $1.15$ $W/m.K$. If the inner surface is at $1100^{\circ} C$ and the outer surface is at $350^{\circ} C$, then the design thickness (in meter) of the wall to maintain a steady heat flux of $2500$ $W/m^2$ should be _______

A plane wall has a thermal conductivity of $1.15$ $W/m.K$. If the inner surface is at $1100^{\circ} C$ and the outer surface is at $350^{\circ} C$, then the design thickn...

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GATE Mechanical 2014 Set 2 | Question: 50
A project has four activities $P, Q, R$ and $S$ ... $9$ days, the total cost (in Rupees) of the project is _______

A project has four activities $P, Q, R$ and $S$ as shown below.$$\begin{array}{|c|c|c|c|} \hline \text{Activity} & \text{Normal duration (days)} & \text{Predecessor} & \t...

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GATE Mechanical 2014 Set 1 | Question: 14
Consider a two-dimensional laminar flow over a long cylinder as shown in the figure below. The free stream velocity is $U_\infty$ and the free stream temperature $T_\infty$ is lower than the cylinder surface temperature $T_S$. The local heat transfer coefficient is minimum at point $1$ $2$ $3$ $4$

Consider a two-dimensional laminar flow over a long cylinder as shown in the figure below.The free stream velocity is $U_\infty$ and the free stream temperature $T_\infty...

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GATE Mechanical 2014 Set 1 | Question: 40
A $200$ mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the rod is uniformly raised by $250^\circ C$. If the Young's modulus and coefficient of thermal expansion are $200$ GPa ... , respectively, the magnitude of the longitudinal stress (in MPa) developed in the rod is _______

A $200$ mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the rod is uniformly raised by $250^\circ C$. If the Yo...

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GATE ME 2013 | Question: 19
Consider one-dimensional steady state heat conduction along $x$-axis ($0 \leq x \leq L$), through a planewall with the boundary surfaces ($x = 0$ and $x = L$) maintained at temperatures of $0^{\circ} C$ and $100^{\circ}C$. ... . The temperature distribution is linear within the wall. The temperature distribution is symmetric about the mid-plane of the wall.

Consider one-dimensional steady state heat conduction along $x$-axis ($0 \leq x \leq L$), through a planewall with the boundary surfaces ($x = 0$ and $x = L$) maintained...

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GATE Mechanical 2014 Set 1 | Question: 43
Water flows through a pipe having an inner radius of $10 mm$ at the rate of $36 \: kg/hr$ at $25^ \circ C$. The viscosity of water at $25^ \circ C$ is $0.001 \: kg/m.s$. The Reynolds number of the flow is _______

Water flows through a pipe having an inner radius of $10 mm$ at the rate of $36 \: kg/hr$ at $25^ \circ C$. The viscosity of water at $25^ \circ C$ is $0.001 \: kg/m.s$....

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