# Recent questions tagged fluid-mechanics-and-thermal-science

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 $\dfrac{V}{r} \\$ $\dfrac{V}{2r} \\$ $\dfrac{2V}{3r} \\$ $\dfrac{3V}{2r}$
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
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)
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)
The spectral distribution of radiation from a black body at $T_1=3000 \: K$ has a maximum at wavelength $\lambda_{\text{max}}$. The body cools down to a temperature $T_2$. If the wavelength corresponding to the maximum of the spectral distribution at $T_2$ is $1.2$ times of the original wavelength $\lambda_{\text{max}}$, then the temperature $T_2$ is _________ $K$ (round off to nearest integer)
Water flows through a tube of $3$ cm internal diameter and length $20$ ... $^\circ C$ (round off to one decimal place
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 ...
Match the following ... $P-1,\:Q-1,\:R-3\:,S-2$ $P-3,\:Q-3,\:R-1\:,S-3$ $P-4,\:Q-3,\:R-2\:,S-1$
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? $-4xz + 6xy$ $– 4xy – 4xz$ $4xz – 6xy$ $4xy + 4xz$
For an ideal gas, the value of the Joule-Thomson coefficient is positive negative zero indeterminate
For an ideal gas, a constant pressure line and a constant volume line intersect at a point, in the Temperature $(T)$ versus specific entropy $\text{(s)}$ diagram. $C_{P}$ is the specific heat at constant pressure and $C_{V}$ is the specific heat at constant volume.The ratio of the slopes of the constant ... $\dfrac{C_{P}}{C_{V}} \\$ $\dfrac{C_{P}-C_{V}}{C_{V}} \\$ $\dfrac{C_{V}}{C_{P}}$
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).
In a concentric tube counter-flow heat exchanger, hot oil enters at $102^{\circ}C$ and leaves at $65^{\circ}C$. Cold water enters at $25^{\circ}C$ and leaves at $42^{\circ}C$. The log mean temperature difference $(LMTD)$ is ________ $^{\circ}C$ (round off to one decimal place).
A small metal bead $(\text{radius}\: 0.5\: mm)$, initially at $100^{\circ}C$ , when placed in a stream of fluid at $20^{\circ}C$ , attains a temperature of $28^{\circ}C$ in $4.35$ ... the convective heat transfer coefficient $(in\:W/m^{2}.K)$ between the metal bead and the fluid stream is $283.3$ $299.8$ $149.9$ $449.7$
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).
Air (ideal gas) enters a perfectly insulated compressor at a temperature of $310\: K$. The pressure ratio of the compressor is $6$. Specific heat at constant pressure for air is $1005\: J/kg . K$ and ratio of specific heats at constant pressure and constant ... the difference in enthalpies of air between the exit and the inlet of the compressor is _________ $kJ/kg$ (round off to nearest integer).
One kg of air, initially at a temperature of $127^{\circ}C$ , expands reversibly at a constant pressure until the volume is doubled. If the gas constant of air is $287\: J/kg.K$, the magnitude of work transfer is ________ $kJ$ (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 $3\: kJ/kg$. The specific steam consumption is _________ $kg/kW.h$ round 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 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 $10\: kW$. The ratio of specific heats at constant pressure and constant volume is $1.4$. The ... efficiency of the engine is $80$ percent. The brake power output of the engine is _________$kW$ (round off to one decimal place).
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 $\rho(x \hat{i}+y \hat{j})$ $– \rho(x \hat{i}+y \hat{j})$ $\rho(x \hat{i} – y \hat{j})$ $– \rho(x^2 \hat{i}+y^2 \hat{j})$
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 $0.0625$ $0.25$ $0.5$ $1.0$
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
For a simple compressible system, $v, s, p$ and $T$ are specific volume, specific entropy, pressure and temperature, respectively. As per Maxwell's relations, $\bigg( \dfrac{\partial v}{\partial s} \bigg) _p$ is equal to $\bigg( \dfrac{\partial s}{\partial T} \bigg) _p \\$ ... $- \bigg( \dfrac{\partial T}{\partial v} \bigg) _p \\$ $\bigg( \dfrac{\partial T}{\partial p} \bigg) _s$
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
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 _________
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 surroundings ... first plate is $h_1$ and that for the second plate is $h_2$, the value of the ratio $h_1/h_2$ is ____________
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, $T_1 >T_3>T_2$ ... $\text{COP}= 1 + \eta$ $\text{COP}= \eta^{-1}$ $\text{COP}= \eta^{-1} -1$
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).
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 temperature of ... is $45^{\circ} C$, the log mean temperature difference (LMTD) of the heat exchanger is __________ $K$ (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 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)
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).