Most answered questions in Others

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​​​​Consider a steady, fully-developed, uni-directional laminar flow of an incompressible Newtonian fluid (viscosity $\mu$ ) between two infinitely long horizonta...
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​​​​​​The temperatures of two large parallel plates of equal emissivity are $900 \mathrm{~K}$ and $300 \mathrm{~K}$. A reflection radiation shield of low emis...
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​​​​​Hot oil at $110{ }^{\circ} \mathrm{C}$ heats water from $30^{\circ} \mathrm{C}$ to $70{ }^{\circ} \mathrm{C}$ in a counter-current double-pipe heat exchang...
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​​​​​A solid slab of thickness $H_{1}$ is initially at a uniform temperature $T_{0}$. At time $t=0$, the temperature of the top surface at $y=H_{1}$ is increase...
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​​​​​​A gas stream containing $95 \mathrm{~mol} \% \mathrm{CO}_{2}$ and $5 \mathrm{~mol} \%$ ethanol is to be scrubbed with pure water in a counter-current, i...
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​​​​​Sulfur dioxide $\left(\mathrm{SO}_{2}\right)$ gas diffuses through a stagnant air-film of thickness $2 \mathrm{~mm}$ at 1 bar and $30^{\circ} \mathrm{C}$. ...
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​​​​​A simple distillation column separates a binary mixture of $A$ and $B$. The relative volatility of $A$ with respect to $B$ is $2$. The steady-state composi...
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​​​Alumina particles with an initial moisture content of $5 \mathrm{~kg}$ per $\mathrm{kg}$ dry solid are dried in a batch dryer. For the first two hours, the measu...
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A first-order heterogenous reaction $A \rightarrow B$ is carried out using a porous spherical catalyst. Assume isothermal conditions, and that intraphase diffusion contro...
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​​​​​​A first-order liquid phase reaction $A \rightarrow B$ is carried out in two isothermal plug flow reactors (PFRs) of volume $1 \mathrm{~m}^{3}$ each, con...
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​​​​The residence time distribution, $E$, for a non-ideal flow reactor is given in the figure. A first-order liquid phase reaction with a rate constant $0.2 \math...
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​​​​​​Let $r$ and $\theta$ be the polar coordinates defined by $x=r \cos \theta$ and $y=r \sin \theta$. The area of the cardioid $r=a(1-\cos \theta), 0 \leq \...
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​​​​​​For the block diagram shown in the figure, the correct expression for the transfer function $G_{d}=\frac{y_{1}(s)}{d(s)}$ is$\frac{-G_{p 1} G_{c 2}}{\le...
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​​​​​For purchasing a batch reactor, three alternatives $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ have emerged, as summarized in the table. For a compound inter...
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The Newton-Raphson method is used to solve $f(x)=0$, where $f(x)=e^{x}-5 x$.If the initial guess $x^{(0)}=1.0$, the value of the next iterate, $x^{(1)}$, rounded off to $...
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Consider the line integral $\int_{C} \boldsymbol{F}(\boldsymbol{r}) \cdot d \boldsymbol{r}$, with $\boldsymbol{F}(\boldsymbol{r})=x \hat{\boldsymbol{\imath}}+y \hat{\bold...
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Consider the ordinary differential equation $x^{2} \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-3 y=0$, with the boundary conditions $y(x=1)=2$ and $y(x=2)=17 / 2$. The solu...
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Consider the function $f(x, y, z)=x^{4}+2 y^{3}+z^{2}$. The directional derivative of the function at the point $P(-1,1,-1)$ along $(\hat{\boldsymbol{\imath}}+\hat{\bolds...
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Consider the process in the figure for manufacturing $B$. The feed to the process is $90 \mathrm{~mol} \% A$ and a close-boiling inert component $I$. At a particular stea...
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Methane combusts with air in a furnace as $\mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}$. The heat of reaction $\Delta H_{r x ...
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An isolated system consists of two perfectly sealed cuboidal compartments $A$ and $B$ separated by a movable rigid wall of cross-sectional area $0.1 \mathrm{~m}^{2}$ as s...
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Ethylene obeys the truncated virial equation-of-state\[\frac{P V}{R T}=1+\frac{B P}{R T}\]where $P$ is the pressure, $V$ is the molar volume, $T$ is the absolute temperat...
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A metallic spherical particle of density $7001 \mathrm{~kg} \mathrm{~m}^{-3}$ and diameter $1 \mathrm{~mm}$ is settling steadily due to gravity in a stagnant gas of densi...
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Water of density $1000 \mathrm{~kg} \mathrm{~m}^{-3}$ is pumped at a volumetric flow rate of $3.14 \times 10^{-2} \mathrm{~m}^{3} \mathrm{~s}^{-1}$, through a pipe of inn...
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A Venturi meter with a throat diameter $d=2 \mathrm{~cm}$ measures the flow rate in a pipe of diameter $D=6 \mathrm{~cm}$, as shown in the figure. A U-tube manometer is c...
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Heat is available at a rate of $2 \mathrm{~kW}$ from a thermal reservoir at $400 \mathrm{~K}$. A two-stage process harnesses this heat to produce power. Stages $1$ and $2...
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A chemostat with cell recycle is shown in the figure. The feed flow rate and culture volume are $F=75 \mathrm{~L} \mathrm{~h}^{-1}$ and $V=200 \mathrm{~L}$, respectively....
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Consider the surge drum in the figure. Initially the system is at steady-state with a hold-up $\bar{V}=5 \mathrm{~m}^{3}$, which is $50 \%$ of full tank capacity, $V_{f u...
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A $\text{PD}$ controller with transfer function $G_{c}$ is used to stabilize an open-loop unstable process with transfer function $G_{p}$, where\[G_{c}=K_{c} \frac{\tau_{...
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Consider a tray-column of diameter $120 \mathrm{~cm}$. Each downcomer has a cross-sectional area of $575 \mathrm{~cm}^{2}$. For a tray, the percentage column cross-sectio...
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The vector $\overrightarrow{\boldsymbol{v}}$ is defined as$$\overrightarrow{\boldsymbol{v}}=z x \hat{\imath}+2 x y \hat{\jmath}+3 y z \hat{k} .$$Which one of the followin...
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Given that$$F=\frac{\left|z_1+z_2\right|}{\left|z_1\right|+\left|z_2\right|},$$where $z_1=2+3 i$ and $z_2=-2+3 i$ with $i=\sqrt{-1}$, which one of the following options i...
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For a two-dimensional plane, the unit vectors, $\left(\hat{e}_r, \hat{e}_\theta\right)$ of the polar coordinate system and $(\hat{\imath}, \hat{\jmath})$ of the cartesian...
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Which one of the following statements related to octane number is NOT correct?Linear alkanes with higher carbon number have higher octane number.Branching in linear alkan...
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Which one of the following options represents the major components of oleum?Sulfuric acid and nitric acidConcentrated sulfuric acid and petroleum jellySulfuric acid and h...
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For a reversible endothermic chemical reaction with constant heat of reaction over the operating temperature range, $K$ is the thermodynamic equilibrium constant. Which o...
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Nitrile rubber is manufactured via polymerization process. Which one of the following options is the $\text{CORRECT}$ pair of monomers used in this process?Acrylonitrile ...
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John and Jane independently performed a thermodynamic experiment, in which $\mathbf{X}$ and $\mathbf{Y}$ represent the initial and final thermodynamic states of the syste...
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For a packed-bed comprising of uniform-sized spherical particles of diameter $D_{\mathrm{p}}$, the pressure drop across the bed is given by the Kozeny-Carman equation whe...
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Match the quantities in Group $1$ with their units in Group $2$ listed in the table below.$$\begin{array}{|l|l|} \hline \qquad \qquad \qquad \textbf{Group 1} & \textbf{Gr...