# Recent questions tagged applications

A circular disk of radius $r$ is confined to roll without slipping at $P$ and $Q$ as shown in the figure. If the plates have velocities as shown, the magnitude of angular velocity of the disk is $\dfrac{V}{r} \\$ $\dfrac{V}{2r} \\$ $\dfrac{2V}{3r} \\$ $\dfrac{3V}{2r}$
For an air-standard Diesel cycle, heat addition is at constant volume and heat rejection is at constant pressure heat addition is at constant pressure and heat rejection is at constant pressure heat addition is at constant pressure and heat rejection is at constant volume heat addition is at constant volume and heat rejection is at constant volume
Consider a flow through a nozzle, as shown in the figure below. The air flow is steady, incompressible and inviscid. The density of air is $1.23 \: kg/m^3$. The pressure difference, $(p_1-p_{\text{atm}})$ is _________ kPa (round off to $2$ decimal places)
Air is contained in a frictionless piston-cylinder arrangement as shown in the figure. The atmosphere pressure is $100$ kPa and the initial pressure of air in the cylinder is $105$ kPa. The area of piston is $300 \: cm^2$. Heat is now added and the piston ... N/mm. Considering the air inside the cylinder as the system, the work interaction is _________ J (round off to the nearest integer)
Moist air at $105$ kPa, $30^\circ C$ and $80\%$ relative humidity flows over a cooling coil in an insulated air-conditioning duct. Saturated air exits the duct at $100$ kPa and $15^\circ C$. The saturation pressures of water at $30^\circ C$ and $15^\circ C$ ... air is $28.94$ g/mol. The mass of water condensing out from the duct is ______ g/kg of dry air (round off to the nearest integer).
In a steam power plant, superheated steam at $10$ MPa and $500^\circ C$, is expanded isentropically in a turbine until it becomes a saturated vapour. It is then reheated at constant pressure to $500 ^\circ C$. The steam is next expanded isentropically in another turbine until it reaches the condenser ...
Keeping all other parameters identical, the Compression Ratio (CR) of an air standard diesel cycle is increased from $15$ to $21$. Take ratio of specific heats $=1.3$ and cut-off ratio of the cycle $r_c=2$ ... $\%$ (round off to one decimal place).
The compressor of a gas turbine plant, operating on an ideal intercooled Brayton cycle, accomplishes an overall compression ratio of $6$ in a two-stage compression process. Intercooling is used to cool the air coming out from the first stage to the inlet temperature ... gas are constant, the intercooling pressure for minimum compressor work is __________ $kPa$ (rounded off to $2$ decimal places).
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 $4\:m$ ... $300\:rpm$. The blade outlet angle $\beta$ is ________ degrees (round off to one decimal place).
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, $T_1 >T_3>T_2$ ... $\text{COP}= 1 + \eta$ $\text{COP}= \eta^{-1}$ $\text{COP}= \eta^{-1} -1$
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 temperature at the ... and $300 \: K$, respectively, then the specific net work output of the cycle is _____ $kJ/kg$ (round off to two decimal places).
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
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 ... of performance is the same as that of the original cycle Refrigerating effect is lower than that of the original cycle
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 aircraft while ... and the nose goes down $162.9 \: N \cdot m$ and the nose goes up $162.9 \: N \cdot m$ and the nose goes down
1 vote
A steam power cycle with regeneration as shown below on the $T-s$ diagram employs a single open feedwater heater for efficiency improvement. The fluid mix with each other in an open feedwater heater. The turbine is isentropic and the input (bleed) to the feedwater heater from ... bled from the turbine as a percentage of the total mass flow rate at the inlet to the turbine at state $1$ is _______
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 perfect gas ... both the cases, the isentropic efficiency of the turbine at the pressure ratio of $5$ is ___________ (round off to two decimal places)
1 vote
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 $0.2$ kg/s. Properties for $R-134a$ are as follows: The power required for the compressor in kW is $5.94$ $1.83$ $7.9$ $39.5$
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 saturated vapor and leaves the condenser as saturated liquid. The mass flow rate of the refrigerant is $0.2$ kg/s. ... The rate at which heat is extracted, in Kj/s from the refrigerated space is $28.3$ $42.9$ $34.4$ $14.6$
A room contains $35$ kg of dry air and $0.5$ kg of water vapor. The total pressure and temperature of air in the room are $100$ kPa and $25^{\circ}$C respectively. Given that the saturation pressure for water at $25^{\circ}$ C is $3.17$ kPa, the relative humidity of the air in the room is $67 \%$ $55 \%$ $83 \%$ $71 \%$
Steam enters an adiabatic turbine operating at steady state with an enthalpy of $3251.0 \: kJ/kg$ and leaves as a saturated mixture at $15 \:kPa$ with quality (dryness fraction) $0.9$. The enthalpies of the saturated liquid and vapor at $15 \: kPa$ ... $6.5$ $8.9$ $9.1$ $27.0$
An engine working on air standard Otto cycle is supplied with air at $0.1 MPa$ and $35^{\circ} \: C$. The compression ratio is $8$. The heat supplied is $500 \: kJ/kg \: K$. The maximum temperature (in $K$) of the cycle is _______ (correct to one decimal place)
Steam flows through a nozzle at a mess flow rate of $m=0.1 \: kg/s$ with a heat loss of $5 \: kW$. The enthalpies at inlet and exit are $2500 \: kJ/kg$ and $2350 \: kJ/kg$, respectively. Assuming negligible velocity in inlet ($C_1 \approx 0$), the velocity ($C_2$) of steam (in $m/s$) at the nozzle exit is _____ (correct to two decimal places).
For a Pelton wheel with a given water jet velocity, the maximum output power from the Pelton wheel is obtained when the ratio of the bucket speed to the water jet speed is _____ (correct to two decimal places)
An ideal gas undergoes a process from state $1 \: (T_1 = 300\: K, \: p_1 = 100 \: kPa)$ to state $2 \: (T_2 = 600 \; K, \: p_2 = 500 \: kPa)$. The specific heats of the ideal gas are: $C_p = 1 \: kJ/kg-K$ and $C_v = 0.7 \: kJ/kg-K$. The change in specific entropy of the ideal gas from state $1$ to state $2$ (in $kJ/kg-K$) is ______ (correct to two decimal places).
A calorically perfect gas (specific heat at constant pressure $1000 \: J/kg .K$) enters and leaves a gas turbine with the same velocity. The temperatures of the gas at turbine entry and exit are $1100 \: K$and $400 \: K$, respectively. The power produced is $4.6\: MW$ and heat ... the turbine casing. The mass flow rate of the gas (in $kg/s$) through the turbine is $6.14$ $7.00$ $7.50$ $8.00$
In the Rankine cycle for a steam power plant, the turbine entry and exit enthalpies are $2803 \: kJ/kg$ and $1800 \: kJ/kg$, respectively. The enthalpies of water at pump entry and exit are $121 \: kJ/kg$ and $124 \: kJ/kg$, respectively. The specific steam consumption (in $kg/kW.h$) of the cycle is _________.
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.
Two disks $A$ and $B$ with identical mass $(m)$ and radius $(R)$ are initially at rest. They roll down from the top of identical inclined planes without slipping. Disk $A$ has all of its mass concentrated at the rim, while Disk $B$ has its mass uniformly distributed. At the bottom of the plane, the ... the centre of disk $B$ is $\sqrt{\dfrac{3}{4}} \\$ $\sqrt{\dfrac{3}{2}} \\$ $1 \\$ $\sqrt{2}$
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 _______.
Moist air is treated as an ideal gas mixture of water vapour and dry air (molecular weight of air$= 28.84$ and molecular weight of water $=18$). At a location, the total pressure is $100$ kPa, the temperature is $30^{\circ}$ C and the relative humidity is $55\%$. ... the saturation pressure of water at $30^{\circ} C$ is $4246$ Pa, the mass of water vapour per kg of dry air is _________ grams.
The pressure ratio across a gas turbine (for air, specific heat at constant pressure, $c_{p}=1040 J/kg.K$ and ratio of specific heats, $\gamma=1.4$) is $10$. If the inlet temperature to the turbine is $1200$ K and the isentropic efficiency is $0.9$, the gas temperature at turbine exit is ________ $K$
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 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 _______ $J/K$.
In the vapour compression cycle shown in the figure, the evaporating and condensing temperatures are $260 \: K$ and $310 \: K$, respectively. The compressor takes in liquid-vapour mixture (state $1$) and isentropically compresses it to a dry saturated vapour condition (state $2$). ... is $1054 \: kJ/kg$. The difference between the enthalpies at state points $1$ and $0$ (in $kJ/kg$) is ____________
In a $3$-stage air compressor, the inlet pressure is $p_1$, discharge pressure is $p_4$.and the intermediate pressures are $p_2$ and $p_3 ( p_2 < p_3)$. The total pressure ratio of the compressor is $10$ and the pressure ratios of the stages are equal. If $p_1 = 100$ $kPa$, the value of the pressure $p_3$ (in $kPa$) is __________
In a mixture of dry air and water vapor at a total pressure of $750$ $mm$ of $Hg$, the partial pressure of water vapor is $20$ $mm$ of $Hg$. The humidity ratio of the air in grams of water vapor per $kg$ of dry air ($g_w/kg_{da}$) is __________
The blade and fluid velocities for an axial turbine are as shown in the figure. The magnitude of absolute velocity at entry is $300$ $m/s$ at an angle of $65^\circ$ ... the downward direction. Given that the axial (horizontal) velocity is the same at entry and exit, the specific work (in $kJ/kg$) is__________
The partial pressure of the water vapour in a moist air sample of relative humidity $70\%$ is $1.6 \: kPa$,the total pressure being $101.35 \: kPa$.moist air may be treated as an ideal gas mixture of water vapour and dry air.the relation between saturation temperature ($T_s$ ... $p_o=101.325 \: kPa$. The dry bulb temperature of the moist air sample (in $_{}^{\circ}\textrm{C}$) is
A refrigerator uses $R-134a$ as its refrigerant and operates on an ideal vapour-compression refrigeration cycle between $0.14 \: MPa$ and $0.8 \: MPa$.if the mass flow rate of refrigerant is $0.05 \: kg/s$,the rate of heat rejection to the environment is_______$kW$ ... $\text{At } P=0.8 \: MPa, \: h=93.42 \: kJ/kg, \: \text{ (saturated liquid) }$
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 temperatures is ... $K$) in the regenerative cycle. The ratio of the thermal efficiency of the simple cycle to that of the regenerative cycle is _________
The heat removal rate from a refrigerated space and the power input to the compressor are $7.2$ $kW$ and $1.8$ $kW$, respectively. The coefficient of performance (COP) of the refrigerator is ______