Hot questions in Fluid Mechanics and Thermal Sciences / GO Mechanical

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GATE2017 ME-2: 14
A mass $m$ of a perfect gas at pressure $p_{1}$ and volume $V_{1}$ undergoes an isothermal process. The final pressure is $p_{2}$ and volume is $V_{2}$. The work done on the system is considered positive. If $R$ is the gas constant and $T$ is the temperature, then the work done in the ... $RT \ln \dfrac{V_{2}}{V_{1}} \\$ $-mRT \ln \dfrac{P_{2}}{P_{1}}$

A mass $m$ of a perfect gas at pressure $p_{1}$ and volume $V_{1}$ undergoes an isothermal process. The final pressure is $p_{2}$ and volume is $V_{2}$. The work done on ...

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GATE2017 ME-1: 11
The molar specific heat at constant volume of an ideal gas is equal to $2.5$ times the universal gas constant ($8.314$ J/mol.K). When the temperature increases by $100$K, the change in molar specific enthalpy is __________ J/mol.

The molar specific heat at constant volume of an ideal gas is equal to $2.5$ times the universal gas constant ($8.314$ J/mol.K). When the temperature increases by $100$K,...

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GATE2017 ME-2: 16
For the stability of a floating body the Centre of buoyancy must coincide with the centre of gravity. Centre of buoyancy must be above the centre of gravity. Centre of gravity must be above the centre of buoyancy. Metacentre must be above the centre of gravity.

For the stability of a floating body theCentre of buoyancy must coincide with the centre of gravity.Centre of buoyancy must be above the centre of gravity.Centre of gravi...

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GATE2017 ME-1: 32
For a steady flow, the velocity field is $\vec{V}=(-x^{2}+3y)\hat{i}+(2xy)\hat{j}$. The magnitude of the acceleration of a particle at $(1, -1)$ is $2$ $1$ $2\sqrt{5}$ $0$

For a steady flow, the velocity field is $\vec{V}=(-x^{2}+3y)\hat{i}+(2xy)\hat{j}$. The magnitude of the acceleration of a particle at $(1, -1)$ is$2$$1$$2\sqrt{5}$$0$

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GATE2017 ME-1: 10
Saturated steam at $100^{\circ} C$ condenses on the outside of a tube. Cold fluid enters the tube at $20^{\circ} C$ and exits at $50^{\circ} C$. The value of the Log mean Temperature Difference (LMTD) is ________ $^{\circ}$ C.

Saturated steam at $100^{\circ} C$ condenses on the outside of a tube. Cold fluid enters the tube at $20^{\circ} C$ and exits at $50^{\circ} C$. The value of the Log mean...

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GATE2017 ME-2: 19
The emissive power of a blackbody is $P$. If its absolute temperature is doubled, the emissive power becomes $2 P$ $4 P$ $8 P$ $16 P$

The emissive power of a blackbody is $P$. If its absolute temperature is doubled, the emissive power becomes$2 P$$4 P$$8 P$$16 P$

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GATE2017 ME-1: 33
One kg of an ideal gas (gas constant, $R= 400 J/kg.K$; specific heat at constant volume, $c_{v}=1000 J/kg.K$) at $1$ bar, and $300$ K is contained in a sealed rigid cylinder. During an adiabatic process, $100$ kJ of work is done on the system by a stirrer. The increase in entropy of the system is _______ $J/K$.

One kg of an ideal gas (gas constant, $R= 400 J/kg.K$; specific heat at constant volume, $c_{v}=1000 J/kg.K$) at $1$ bar, and $300$ K is contained in a sealed rigid cylin...

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GATE2017 ME-2: 18
The heat loss from a fin is $6$ W. The effectiveness and efficiency of the fin are $3$ and $0.75$, respectively. The heat loss (in W) from the fin, keeping the entire fin surface at base temperature, is _______.

The heat loss from a fin is $6$ W. The effectiveness and efficiency of the fin are $3$ and $0.75$, respectively. The heat loss (in W) from the fin, keeping the entire fin...

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GATE2017 ME-1: 36
Air contains $79\%$ $N_{2}$ and $21\%$ $O_{2}$ on a molar basis. Methane $(CH_{4})$ is burned with $50\%$ excess air than required stoichiometrically. Assuming complete combustion of methane, the molar percentage of $N_{2}$ in the products is _______.

Air contains $79\%$ $N_{2}$ and $21\%$ $O_{2}$ on a molar basis. Methane $(CH_{4})$ is burned with $50\%$ excess air than required stoichiometrically. Assuming complete c...

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GATE2017 ME-1: 7
Consider the two-dimensional velocity field given by $\overrightarrow{V}=(5+a_{1}x+b_{1}y)\hat{i}+(4+a_{2}x+b_{2}y)\hat{j}$, where $a_{1}, b_{1}, a_{2}$ and $b_{2}$ are constants. Which one of the following conditions needs to be satisfied for the flow to be incompressible? $a_{1}+b_{1}=0$ $a_{1}+b_{2}=0$ $a_{2}+b_{2}=0$ $a_{2}+b_{1}=0$

Consider the two-dimensional velocity field given by $\overrightarrow{V}=(5+a_{1}x+b_{1}y)\hat{i}+(4+a_{2}x+b_{2}y)\hat{j}$, where $a_{1}, b_{1}, a_{2}$ and $b_{2}$ are c...

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GATE2017 ME-2: 13
Which one of the following statements is TRUE? Both Pelton and Francis turbines are impulse turbines. Francis turbine is a reaction turbine but Kaplan turbine is an impulse turbine. Francis turbine is an axial-flow reaction turbine. Kaplan turbine is an axial-flow reaction turbine.

Which one of the following statements is TRUE?Both Pelton and Francis turbines are impulse turbines.Francis turbine is a reaction turbine but Kaplan turbine is an impulse...

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GATE2015-3-47
The torque (in $N$-$m$) exerted on the crank shaft of a two stroke engine can be described as $T = 10000 + 1000 \sin(2θ) − 1200 \cos(2θ)$, where $θ$ is the crank angle as measured from inner dead center position. Assuming the resisting torque to be constant, the power (in $kW$) developed by the engine at $100$ $rpm$ is ________

The torque (in $N$-$m$) exerted on the crank shaft of a two stroke engine can be described as $T = 10000 + 1000 \sin(2θ) − 1200 \cos(2θ)$, where $θ$ is the crank ang...

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GATE2016-2-13
The volumetric flow rate (per unit depth) between two streamlines having stream functions $\Psi _1$ and $\Psi _2$ is $\mid \Psi _1+\Psi _2\mid$ $\Psi _1\Psi _2$ $\Psi _1/\Psi _2$ $\mid\Psi _1-\Psi _2\mid$

The volumetric flow rate (per unit depth) between two streamlines having stream functions $\Psi _1$ and $\Psi _2$ is$\mid \Psi _1+\Psi _2\mid$$\Psi _1\Psi _2$$\Psi _1/\Ps...

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GATE2015-3-52
Which of the following statements are TRUE, when the cavitation parameter $\sigma =0$? the local pressure is reduced to vapor pressure cavitation starts boiling of liquid starts cavitation stops (i), (ii) and (iv) only (ii) and (iii) only (i) and (iii) (i), (ii) and (iii)

Which of the following statements are TRUE, when the cavitation parameter $\sigma =0$?the local pressure is reduced to vapor pressurecavitation startsboiling of liquid st...

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GATE2016-2-14
Assuming constant temperature condition and air to be an ideal gas, the variation in atmospheric pressure with height calculated from fluid statics is linear exponential quadratic cubic

Assuming constant temperature condition and air to be an ideal gas, the variation in atmospheric pressure with height calculated from fluid statics islinearexponentialqua...

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GATE2016-1-46
An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript $1$) and at the end (subscript $2$) of the process with usual notation are: $p_1 = 100 \: kPa$, $V_1 = 0.2 \: m^3$ ... $R=0.275\:kJ/kg-K$. The magnitude of the work required for the process (in $kJ$) is ________

An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript $1$) and at the end (subscript $2$) ...

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GATE2015-2-14
Within a boundary layer for a steady incompressible flow, the Bernoulli equation holds because the flow is steady holds because the flow is incompressible holds because the flow is transitional does not hold because the flow is frictional

Within a boundary layer for a steady incompressible flow, the Bernoulli equationholds because the flow is steadyholds because the flow is incompressibleholds because the ...

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GATE2015-3-36
A Prandtl tube (Pitot-static tube with $C$=$1$) is used to measure the velocity of water. The differential manometer reading is $10$ $mm$ of liquid column with a relative density of $10$. Assuming $g$ = $9.8$ $m$/$s^2$, the velocity of water (in $m/s$) is ________

A Prandtl tube (Pitot-static tube with $C$=$1$) is used to measure the velocity of water. The differential manometer reading is $10$ $mm$ of liquid column with a relative...

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GATE2015-3-45
A bullet spins as the shot is fired from a gun. For this purpose, two helical slots as shown in the figure are cut in the barrel. Projections $A$ and $B$ on the bullet engage in each of the slots. Helical slots are such that one turn of helix is completed over a ... $m$. If velocity of bullet when it exits the barrel is $20$ $m/s$, its spinning speed in $rad/s$ is ________

A bullet spins as the shot is fired from a gun. For this purpose, two helical slots as shown in the figure are cut in the barrel. Projections $A$ and $B$ on the bullet en...

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GATE2016-1-41
A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream velocity of the fluid is $U_o$. The velocity profile at the inlet $a-b$ is uniform, while that at a downstream location $c-d$ ... rate, $\dot{m}_{bd}$ leaving through the horizontal section $b-d$ to that entering through the vertical section $a-b$ is ___________

A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream velocity of the fluid is $U_o$. The velocity profile at the inlet $a-b...

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GATE2016-1-44
A fluid (Prandtl number, $P_r=1$) at $500\:K$ flows over a flat plate of $1.5\:m$ length, maintained at $300\: K$. The velocity of the fluid is $10 \: m/s$. Assuming kinematic viscosity,$v=30\times 10^{-6}$ $m^2/s$, the thermal boundary layer thickness (in $mm$) at $0.5 \:m$ from the leading edge is __________

A fluid (Prandtl number, $P_r=1$) at $500\:K$ flows over a flat plate of $1.5\:m$ length, maintained at $300\: K$. The velocity of the fluid is $10 \: m/s$. Assuming kine...

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GATE2016-1-19
The INCORRECT statement about regeneration in vapor power cycle is that it increases the irreversibility by adding the liquid with higher energy content to the steam generator heat is exchanged between the expanding fluid in the turbine and the compressed ... the principle is similar to the principle of Stirling gas cycle it is practically implemented by providing feed water heaters

The INCORRECT statement about regeneration in vapor power cycle is thatit increases the irreversibility by adding the liquid with higher energy content to the steam gener...

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GATE2015-3-54
A brick wall $\left(k=0.9\displaystyle{\frac{W}{m.k}}\right)$ of thickness $0.18$ $m$ separates the warm air in a room from the cold ambient air. On a particular winter day, the outside air temperature is $−5^\circ C$ ... resistance of the air inside the room, the heat loss, in $\displaystyle{\frac{W}{m^2}}$, is $88$ $110$ $128$ $160$

A brick wall $\left(k=0.9\displaystyle{\frac{W}{m.k}}\right)$ of thickness $0.18$ $m$ separates the warm air in a room from the cold ambient air. On a particular winter d...

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GATE2016-1-13
The instantaneous stream-wise velocity of a turbulent flow is given as follows: $u(x,y,z,t)=\overline{u}(x,y,z)+{u}'(x,y,z,t)$ The time-average of the fluctuating velocity ${u}'(x,y,z,t)$ is $\displaystyle{\frac{u'}{2}} \\$ $\displaystyle{\frac{-\overline{u}}{2}} \\$ $\text{zero}\\$ $\displaystyle{\frac{\overline{u}}{2}}$

The instantaneous stream-wise velocity of a turbulent flow is given as follows:$u(x,y,z,t)=\overline{u}(x,y,z)+{u}'(x,y,z,t)$The time-average of the fluctuating velocity ...

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GATE2015-3-55
A mixture of ideal gases has the following composition by mass: $\begin{array}{|c|c|c|} \hline N_2 & O_2 & CO_2 \\ \hline 60\% & 30\% & 10 \% \\ \hline \end{array}$ If the universal gas constant is $8314 \: J/kmol-K$, the characteristic gas constant of the mixture (in $J/kg-K$) is ________

A mixture of ideal gases has the following composition by mass:$\begin{array}{|c|c|c|} \hline N_2 & O_2 & CO_2 \\ \hline 60\% & 30\% & 10 \% \\ \hline \end{array}$If the ...

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GATE2015-2-43
A cylindrical uranium fuel rod of radius $5 \: mm$ in a nuclear reactor is generating heat at the rate of $4 \times 107 \: W/m^3$. The rod is cooled by a liquid (convective heat transfer coefficient $1000 \: W/m^2-K$) at $25^{\circ}C$. At steady state, the surface temperature (in $K$) of the rod is $308$ $398$ $418$ $448$

A cylindrical uranium fuel rod of radius $5 \: mm$ in a nuclear reactor is generating heat at the rate of $4 \times 107 \: W/m^3$. The rod is cooled by a liquid (convecti...

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GATE2016-1-17
Propane ($C_3H_8$) is burned in an oxygen atmosphere with $10$% deficit oxygen with respect to the stoichiometric requirement. Assuming no hydrocarbons in the products, the volume percentage of $CO$ in the products is __________.

Propane ($C_3H_8$) is burned in an oxygen atmosphere with $10$% deficit oxygen with respect to the stoichiometric requirement. Assuming no hydrocarbons in the products, t...

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GATE2015-3-53
One side of a wall is maintained at $400 \: K$ and the other at $300 \: K$. The rate of heat transfer through the wall is $1000 \: W$ and the surrounding temperature is $25^\circ C$. Assuming no generation of heat within the wall, the irreversibility (in $W$) due to heat transfer through the wall is ________

One side of a wall is maintained at $400 \: K$ and the other at $300 \: K$. The rate of heat transfer through the wall is $1000 \: W$ and the surrounding temperature is $...

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GATE2016-2-19
Consider a simple gas turbine (Brayton) cycle and a gas turbine cycle with perfect regeneration. In both the cycles, the pressure ratio is $6$ and the ratio of the specific heats of the working medium is $1.4$. The ratio of minimum to maximum ... $K$) in the regenerative cycle. The ratio of the thermal efficiency of the simple cycle to that of the regenerative cycle is _________

Consider a simple gas turbine (Brayton) cycle and a gas turbine cycle with perfect regeneration. In both the cycles, the pressure ratio is $6$ and the ratio of the specif...

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GATE2015-1-55
Steam enters a well insulated turbine and expands isentropically throughout. At an intermediate pressure, $20$ percent of the mass is extracted for process heating and the remaining steam expands isentropically to $9 \: kPa$ ... If the flow rate of steam entering the turbine is $100$ $kg/s$, then the work output (in $MW$) is _________

Steam enters a well insulated turbine and expands isentropically throughout. At an intermediate pressure, $20$ percent of the mass is extracted for process heating and th...

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GATE2016-3-40
The water jet exiting from a stationary tank through a circular opening of diameter $300 \: mm$ impinges on a rigid wall as shown in the figure. Neglect all minor losses and assume the water level in the tank to remain constant. The net horizontal force experienced by the wall is ___________ $kN$. Density of water is $1000 \: kg/m^3$. Acceleration due to gravity $g=10 \: m/s^2$.

The water jet exiting from a stationary tank through a circular opening of diameter $300 \: mm$ impinges on a rigid wall as shown in the figure. Neglect all minor losses ...

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GATE2016-2-53
For the situation shown in the figure below the expression for $H$ in terms of $r$, $R$ and $D$ is $H=D+\sqrt{r^2+R^2}$ $H=(R+r)+(D+r)$ $H=(R+r)+\sqrt{D^2-R^2}$ $H=(R+r)+\sqrt{2D(R+r)-D^2}$

For the situation shown in the figure below the expression for $H$ in terms of $r$, $R$ and $D$ is $H=D+\sqrt{r^2+R^2}$$H=(R+r)+(D+r)$$H=(R+r)+\sqrt{D^2-R^2}$$H=(R+r)+\sq...

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GATE2016-2-40
Consider fluid flow between two infinite horizontal plates which are parallel (the gap between them being $50 \: mm$). The top plate is sliding parallel to the stationary bottom plate at a speed of $3\: m/s$. The flow between the plates is solely due to the motion of the top plate. The ... $N/m^2$. Viscosity of the fluid $μ = 0.44 \:kg/m-s$ and density $\rho = 888 \: kg/m^3$.

Consider fluid flow between two infinite horizontal plates which are parallel (the gap between them being $50 \: mm$). The top plate is sliding parallel to the stationary...

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GATE2016-3-15
Steady one-dimensional heat conduction takes place across the faces $1$ and $3$ of a composite slab consisting of slabs $A$ and $B$ in perfect contact as shown in the figure, where $k_A$ , $k_B$ denote the respective thermal conductivities. Using the data as given in the figure, the interface temperature $T_2$ (in $^\circ C$) is __________

Steady one-dimensional heat conduction takes place across the faces $1$ and $3$ of a composite slab consisting of slabs $A$ and $B$ in perfect contact as shown in the fig...

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GATE2015-2-53
A resistance-capacitance relaxation circuit is used in an electrical discharge machining process. The discharge voltage is $100$ $V$. At a spark cycle time of $25$ $μs$, the average power input required is $1$ $kW$. The capacitance (in $μF$) in the circuit is $2.5$ $5.0$ $7.5$ $10.0$

A resistance-capacitance relaxation circuit is used in an electrical discharge machining process. The discharge voltage is $100$ $V$. At a spark cycle time of $25$ $μs$,...

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GATE2015-3-38
Steam enters a turbine at $30$ bar, $300^\circ C \: (u = 2750 \: kJ/kg$, $h = 2993 \: kJ/kg)$ and exits the turbine as saturated liquid at $15 \: kPa \: (u = 225 \: kJ/kg$, $h = 226 \: kJ/kg)$. Heat loss to the ... $kJ/kg$ of steam) is ________

Steam enters a turbine at $30$ bar, $300^\circ C \: (u = 2750 \: kJ/kg$, $h = 2993 \: kJ/kg)$ and exits the turbine as saturated liquid at $15 \: kPa \: (u = 225 \: kJ/kg...

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GATE2016-3-39
Consider a fully developed steady laminar flow of an incompressible fluid with viscosity $μ$ through a circular pipe of radius $R$. Given that the velocity at a radial location of $R/2$ from the centerline of the pipe is $U_1$, the shear stress at the wall is $KμU_1$/$R$, where $K$ is __________

Consider a fully developed steady laminar flow of an incompressible fluid with viscosity $μ$ through a circular pipe of radius $R$. Given that the velocity at a radial l...

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GATE2016-1-43
An infinitely long furnace of $0.5\:m\times 0. 4 \:m$ cross-section is shown in the figure below. Consider all surfaces of the furnace to be black. The top and bottom walls are maintained at temperature $T_1=T_3=927^\circ C$ ... loss or gain on side $1$ is_________ $W/m$. Stefan-Boltzmann constant = $5.67 \times 10^{-8}$ $W/m^2-K^4$

An infinitely long furnace of $0.5\:m\times 0. 4 \:m$ cross-section is shown in the figure below. Consider all surfaces of the furnace to be black. The top and bottom wal...

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GATE2016-1-45
For water at $25^\circ C$, $dp_s/dT_s = 0.189 \: kPa/K$ ($p_s$ is the saturation pressure in $kPa$ and $T_s$ is the saturation temperature in $K$) and the specific volume of dry saturated vapour is $43.38 \: m^3/kg$. Assume that the ... vapour. Using the Clausius-Clapeyron equation, an estimate of the enthalpy of evaporation of water at $25^\circ C$ (in $kJ / kg$) is __________

For water at $25^\circ C$, $dp_s/dT_s = 0.189 \: kPa/K$ ($p_s$ is the saturation pressure in $kPa$ and $T_s$ is the saturation temperature in $K$) and the specific volum...

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GATE2015-1-50
A $10$ $mm$ diameter electrical conductor is covered by an insulation of $2\:mm$ thickness. The conductivity of the insulation is $0.08$ $W/m-K$ and the convection coefficient at the insulation surface is $10$ $W/m^2-K$. Addition of ... heat loss continuously increase heat loss to a maximum and then decrease heat loss decrease heat loss to a minimum and then increase heat loss

A $10$ $mm$ diameter electrical conductor is covered by an insulation of $2\:mm$ thickness. The conductivity of the insulation is $0.08$ $W/m-K$ and the convection coeffi...

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