Most answered questions in Fluid Mechanics and Thermal Sciences / GO Mechanical

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GATE2020-ME-1: 53
For an ideal Rankine cycle operating between pressures of $30$ bar and $0.04$ bar,the work output from the turbine is $903\: kJ/kg$ and the work input to the feed pump is $3\: kJ/kg$. The specific steam consumption is _________ $kg/kW.h$ round off to $2$ decimal places).

For an ideal Rankine cycle operating between pressures of $30$ bar and $0.04$ bar,the work output from the turbine is $903\: kJ/kg$ and the work input to the feed pump is...

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GATE2020-ME-1: 54
For a Kaplan (axial flow) turbine, the outlet blade velocity diagram at a section is shown in the figure. The diameter at this section is $3\:m$.The hub and tip diameters of the blade are $2\:m$ and $4\:m$, respectively. The water volume flow ... rotational speed of the turbine is $300\:rpm$. The blade outlet angle $\beta$ is ________ degrees (round off to one decimal place).

For a Kaplan (axial flow) turbine, the outlet blade velocity diagram at a section is shown in the figure. The diameter at this section is $3\:m$.The hub and tip diam...

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GATE2020-ME-1: 55
The indicated power developed by an engine with compression ratio of $8$, is calculated using an air-standard Otto cycle (constant properties). The rate of heat addition is $10\: kW$ ... of the engine is $80$ percent. The brake power output of the engine is _________$kW$ (round off to one decimal place).

The indicated power developed by an engine with compression ratio of $8$, is calculated using an air-standard Otto cycle (constant properties). The rate of heat addition ...

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GATE2019 ME-2: 9
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})$

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...

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GATE2019 ME-2: 10
Sphere $1$ with a diameter of $0.1$ m is completely enclosed by another sphere $2$ of diameter $0.4$m. The view factor $F_{12}$ is $0.0625$ $0.25$ $0.5$ $1.0$

Sphere $1$ with a diameter of $0.1$ m is completely enclosed by another sphere $2$ of diameter $0.4$m. The view factor $F_{12}$ is$0.0625$$0.25$$0.5$$1.0$

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GATE2019 ME-2: 11
One-dimensional steady state heat conduction takes places through a solid whose cross-sectional area varies linearly in the direction of heat transfer. Assume there is no heat generation in the solid and the thermal conductivity of the material is constant and independent of temperature. The temperature distribution in the solid is Linear Quadratic Logarithmic Exponential

One-dimensional steady state heat conduction takes places through a solid whose cross-sectional area varies linearly in the direction of heat transfer. Assume there is no...

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GATE2019 ME-2: 12
For a simple compressible system, $v, s, p$ and $T$ are specific volume, specific entropy, pressure and temperature, respectively. As per Maxwell's relations, $\bigg( \dfrac{\partial v}{\partial s} \bigg) _p$ ... $ - \bigg( \dfrac{\partial T}{\partial v} \bigg) _p \\$ $\bigg( \dfrac{\partial T}{\partial p} \bigg) _s$

For a simple compressible system, $v, s, p$ and $T$ are specific volume, specific entropy, pressure and temperature, respectively. As per Maxwell’s relations, $\bigg( \...

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GATE2019 ME-2: 13
Which one of the following modifications of the simple ideal Rankine cycle increases the thermal efficiency and reduces the moisture content of the steam at the turbine outlet? Increasing the boiler pressure Decreasing the boiler pressure Increasing the turbine inlet temperature decreasing the condenser pressure

Which one of the following modifications of the simple ideal Rankine cycle increases the thermal efficiency and reduces the moisture content of the steam at the turbine o...

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GATE2019 ME-2: 23
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 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...

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GATE2019 ME-2: 24
A thin vertical flat plate of height $L$, and infinite width perpendicular to the plane of the figure, is losing heat to the surroundings by natural convection. The temperatures of the plate and the surroundings by natural convection. The temperatures of the plate and the ... plate is $h_1$ and that for the second plate is $h_2$, the value of the ratio $h_1/h_2$ is ____________

A thin vertical flat plate of height $L$, and infinite width perpendicular to the plane of the figure, is losing heat to the surroundings by natural convection. The tempe...

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GATE2019 ME-2: 33
The figure shows a heat engine (HE) working between two reservoirs. The amount of heat $(Q_2)$ rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire work output $(W)$ of the heat engine. If temperatures, $T_1 >T_3>T_2$, then the relation between ... $\text{COP}= 1 + \eta$ $\text{COP}= \eta^{-1}$ $\text{COP}= \eta^{-1} -1 $

The figure shows a heat engine (HE) working between two reservoirs. The amount of heat $(Q_2)$ rejected by the heat engine is drawn by a heat pump (HP). The heat pump rec...

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GATE2019 ME-2: 43
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 ... 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).

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 ...

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GATE2019 ME-2: 44
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 ... round off to two decimal places), is __________ $km/h$ (The density of air and the frontal area may be assumed to be constant).

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 ope...

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GATE2019 ME-2: 46
Hot and cold fluids enter a parallel flow double tube heat exchanger at $100^{\circ}C$ and $15^{\circ} C$, respectively. The heat capacity rates of hot and cold fluids are $C_h=2000 \: W/K$ and $C_c =1200 \: W/K$, respectively. If the outlet ... $45^{\circ} C$, the log mean temperature difference (LMTD) of the heat exchanger is __________ $K$ (round off to two decimal places).

Hot and cold fluids enter a parallel flow double tube heat exchanger at $100^{\circ}C$ and $15^{\circ} C$, respectively. The heat capacity rates of hot and cold fluids ar...

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GATE2019 ME-2: 47
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 ... an ambient temperature of $300 \: K$, the irreversibility rate of the system is __________ $kW$ (round off to two decimal places).

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 th...

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GATE2019 ME-2: 48
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)

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 a...

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GATE2019 ME-2: 49
An air standard Otto cycle has thermal efficiency of $0.5$ and the mean effective pressure of the cycle is $1000 \: kPa$. For air, assume specific heat ratio $\gamma=1.4$ and specific gas constant $R=0.287 \: kJ/kg \cdot K$. If the pressure and ... $300 \: K$, respectively, then the specific net work output of the cycle is _____ $kJ/kg $ (round off to two decimal places).

An air standard Otto cycle has thermal efficiency of $0.5$ and the mean effective pressure of the cycle is $1000 \: kPa$. For air, assume specific heat ratio $\gamma=1.4$...

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GATE2019 ME-1: 8
During a non-flow thermodynamic process $(1-2)$ executed by a perfect gas, the heat interaction is equal to the work interaction $(Q_{1-2} = W_{1-2})$ when the process is Isentropic Polytropic Isothermal Adiabatic

During a non-flow thermodynamic process $(1-2)$ executed by a perfect gas, the heat interaction is equal to the work interaction $(Q_{1-2} = W_{1-2})$ when the process is...

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GATE2019 ME-1: 9
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 $Nu_q > Nu_T$ $Nu_q < Nu_T$ $Nu_q = Nu_T$ $Nu_q = (Nu_T)^2$

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...

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GATE2019 ME-1: 10
As per common design practice, the three types of hydraulic turbines, in descending order of flow rate, are Kaplan, Francis, Pelton Pelton, Francis, Kaplan Francis, Kaplan, Pelton Pelton, Kaplan, Francis

As per common design practice, the three types of hydraulic turbines, in descending order of flow rate, areKaplan, Francis, PeltonPelton, Francis, KaplanFrancis, Kaplan, ...

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GATE2019 ME-1: 11
A slender rod of length $L$, diameter $d$ $(L > >d)$ and thermal conductivity $k_1$ is joined with another rod of identical dimensions, but of thermal conductivity $k_2$, to form a composite cylindrical rod of length $2L$. The heat transfer in radial direction and ... composite rod is $k_1+k_2 \\$ $\sqrt{k_1k_2} \\$ $\dfrac{k_1k_2}{k_1+k_2} \\$ $\dfrac{2k_1k_2}{k_1+k_2}$

A slender rod of length $L$, diameter $d$ $(L >d)$ and thermal conductivity $k_1$ is joined with another rod of identical dimensions, but of thermal conductivity $k_2$, ...

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GATE2019 ME-1: 12
Consider an ideal vapor compression refrigeration cycle. If the throttling process is replaced by an isentropic expansion process, keeping all the other processes unchanged, which one of the following statements is true for the modified cycle? Coefficient of ... performance is the same as that of the original cycle Refrigerating effect is lower than that of the original cycle

Consider an ideal vapor compression refrigeration cycle. If the throttling process is replaced by an isentropic expansion process, keeping all the other processes unchang...

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GATE2019 ME-1: 21
A solid cube of side $1$ m is kept at a room temperature of $32^{\circ} C$. The coefficient of linear thermal expansion of the cube material is $1 \times 10^{-5} / ^{\circ}C$ and the bulk modulus is $200$ GPa. If the cube is constrained all around and heated uniformly to $42^{\circ}C$, then the magnitude of volumetric (mean) stress (in MPa) included due to heating is _______

A solid cube of side $1$ m is kept at a room temperature of $32^{\circ} C$. The coefficient of linear thermal expansion of the cube material is $1 \times 10^{-5} / ^{\cir...

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GATE2019 ME-1: 23
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 ______$m/s^2$

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 $y$ dir...

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GATE2019 ME-1: 24
Air of mass $1$ kg, initially at $300$ K and $10$ bar, is allowed to expand isothermally till it reaches a pressure of $1$ bar. Assuming air as an ideal gas with gas constant of $0.287 \: kJ/kg.K$, the change in entropy of air (in $kJ/kg.K$, round off to two decimal places) is ______

Air of mass $1$ kg, initially at $300$ K and $10$ bar, is allowed to expand isothermally till it reaches a pressure of $1$ bar. Assuming air as an ideal gas with gas cons...

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GATE2019 ME-1: 31
The rotor of a turbojet engine of an aircraft has a mass $180 \: kg$ and polar moment of inertia $10 \: kg \cdot m^2$ about the rotor axis. The rotor rotates at a constant speed of $1100 \: rad/s$ in the clockwise direction when viewed from the front of the aircraft. The ... the nose goes down $162.9 \: N \cdot m$ and the nose goes up $162.9 \: N \cdot m$ and the nose goes down

The rotor of a turbojet engine of an aircraft has a mass $180 \: kg$ and polar moment of inertia $10 \: kg \cdot m^2$ about the rotor axis. The rotor rotates at a constan...

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GATE2019 ME-1: 32
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 ... 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

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 ...

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GATE2019 ME-1: 33
A gas is heated in a duct as it flows over a resistance heater. Consider a $101 \: kW$ electric heating system. The gas enters the heating section of the duct at $100 \: kPa$ and $27^{\circ} C$ with a volume flow rate of $15 m^3/s$. If heat is lost from the gas in the duct to the ... $32^{\circ} C$ $37^{\circ} C$ $53^{\circ} C$ $76^{\circ} C$

A gas is heated in a duct as it flows over a resistance heater. Consider a $101 \: kW$ electric heating system. The gas enters the heating section of the duct at $100 \: ...

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GATE2019 ME-1: 45
Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, $2 \: m$ apart as shown below. The bottom plate is fixed and the upper plate moves to the right with a constant ... fluid, $\mu_1$, then the velocity at the interface (round off to two decimal places) is _______ $m/s$.

Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, $2 \: m$ apa...

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GATE2019 ME-1: 46
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 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 densit...

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GATE2019 ME-1: 47
Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the interfaces. The center slab experiences a non-uniform internal heat generation with an average value equal to $10000 \: Wm^{-3}$, while the left and right slabs have no ... $T_1$ is measured to be $100^{\circ} C$, the right extreme face temperature $T_2$ is ______$^{\circ} C$.

Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the interfaces. The center slab experiences a non-uniform internal heat ...

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GATE2019 ME-1: 48
If one mole of $H_2$ has occupies a rigid container with a capacity of $1000$ litres and the temperature is raised from $27^{\circ} C$ to $37^{\circ} C$, the change in pressure of the contained gas (round off to two decimal places), assuming ideal gas behaviour, is _______ Pa. $(R=8.314 \: J/mol \cdot K)$

If one mole of $H_2$ has occupies a rigid container with a capacity of $1000$ litres and the temperature is raised from $27^{\circ} C$ to $37^{\circ} C$, the change in pr...

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GATE2019 ME-1: 50
A gas turbine with air as the working fluid has an isentropic efficiency of $0.70$ when operating at a pressure ratio of $3$. Now, the pressure ratio of the turbine is increased to $5$, while maintaining the same inlet conditions. Assume air as a ... the cases, the isentropic efficiency of the turbine at the pressure ratio of $5$ is ___________ (round off to two decimal places)

A gas turbine with air as the working fluid has an isentropic efficiency of $0.70$ when operating at a pressure ratio of $3$. Now, the pressure ratio of the turbine is in...

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GATE ME 2012 | Question: 52
Air enters an adiabatic nozzle at $300$ kPa, $500$ K with a velocity of $10$ m/s. It leaves the nozzle at $100$ kPa with a velocity of $180$ m/s. The inlet area is $80 cm^2$. The specific heat of air $C_p$ is $1008$ J/kg.K. The exit temperature of the air is $516$ K $532$ K $484$ K $468$ K

Air enters an adiabatic nozzle at $300$ kPa, $500$ K with a velocity of $10$ m/s. It leaves the nozzle at $100$ kPa with a velocity of $180$ m/s. The inlet area is $80 c...

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GATE ME 2012 | Question: 53
Air enters an adiabatic nozzle at $300$ kPa, $500$ K with a velocity of $10$ m/s. It leaves the nozzle at $100$ kPa with a velocity of $180$ m/s. The inlet area is $80 \: cm^2$. The specific heat of air $C_p$ is $1008$ J/kg.K. The exit area of the nozzle in $cm^4$ is $90.1$ $56.3$ $4.4$ $12.9$

Air enters an adiabatic nozzle at $300$ kPa, $500$ K with a velocity of $10$ m/s. It leaves the nozzle at $100$ kPa with a velocity of $180$ m/s. The inlet area is $80 \...

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GATE ME 2012 | Question: 51
A refrigerator operates between $120$ kPa and $800$ kPa in an ideal vapor compression cycle with $R-134a$ as the refrigerant. The refrigerant renters the compressor as saturated vapor and leaves the condenser as saturated liquid. The mass flow rate of the refrigerant is $0.2$ ... $5.94$ $1.83$ $7.9$ $39.5$

A refrigerator operates between $120$ kPa and $800$ kPa in an ideal vapor compression cycle with $R-134a$ as the refrigerant. The refrigerant renters the compressor as sa...

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GATE ME 2012 | Question: 50
A refrigerator operates between $120$ kPa and $800$ kPa in an ideal vapor compression cycle with $R-134a$ ... at which heat is extracted, in Kj/s from the refrigerated space is $28.3$ $42.9$ $34.4$ $14.6$

A refrigerator operates between $120$ kPa and $800$ kPa in an ideal vapor compression cycle with $R-134a$ as the refrigerant. The refrigerant renters the compressor as sa...

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GATE ME 2012 | Question: 41
Water $(C_p=4.18 \: kJ/kg.K)$ at $80^{\circ} C$ enters a counterflow heat exchanger with a mass flow rate of $0.5 \: kg/s$. Air ($C_p=1 \: kJ/kg.K$) enters at $30^{\circ} C$ with a mass flow rate of $2.09 \: kg/s$. If the effectiveness of heat exchanger is $0.8$, the LMTD (in $^{\circ} C$) is $40$ $20$ $10$ $5$

Water $(C_p=4.18 \: kJ/kg.K)$ at $80^{\circ} C$ enters a counterflow heat exchanger with a mass flow rate of $0.5 \: kg/s$. Air ($C_p=1 \: kJ/kg.K$) enters at $30^{\circ}...

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GATE ME 2012 | Question: 42
A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by $\Delta T$. If the thermal coefficient of the material is $\alpha$, Young's modulus is $E$ and the Poisson's ratio is $\upsilon$, the thermal stress developed in the cube due ... $-\dfrac{\alpha (\Delta T) E}{3 (1-2 \upsilon)}$

A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by $\Delta T$. If the thermal coefficient of the material is $\alpha$, Y...

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GATE ME 2012 | Question: 40
A large tank with a nozzle attached contains three immiscible, inviscid fluid as shown. Assuming that the changes in $h_1, h_2$ and $h_3$ ...

A large tank with a nozzle attached contains three immiscible, inviscid fluid as shown. Assuming that the changes in $h_1, h_2$ and $h_3$ are negligible, the instantaneou...

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