Recent questions tagged numerical-answers

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For a non-catalytic homogeneous reaction $A\rightarrow B$, the rate expression at $300\:K$ is $-r_{A}$$\left (mol\; m^{-3} s^{-1}\right )=\frac{10C_{A}}{1+5C_{A}}$...
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Hydrogen iodide decomposes through the reaction $2HI\leftrightharpoons H_{_{2}}+I_{2}$. The value of the universal gas constant $R$ is $8.314 \:J\:mol^{-1}K^{-1}$. The ac...
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A set of simultaneous linear algebraic equations is represented in a matrix form as shown below.$\begin{bmatrix} 0 &0 &0 &4 &13 \\ 2& 5& 5& 2& 10\\ 0&0 &2 &5 &3 \\ 0&0 &0...
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The model $y=mx^{2}$ is to be fit to the data given below.$$\begin{array}{|cl|cI|}\hline&{x} & {1} & {\sqrt{2}} & {\sqrt{3}} \\ \hline &{y} & {2} & {5} & {8} \\ \hline \e...
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The Lagrange mean-value theorem is satisfied for $f\left ( x \right )=x^{3}+5$, in the interval $\left ( 1,4 \right )$ at a value (rounded off to the second decimal place...
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Values of $f\left ( x \right )$ in the interval $\left [ 0,4 \right ]$ are given below.$\begin{array}{|cl|cI|cI|cI|cI|cI|}\hline&{x} & \text{0} & \text{1} & \text{2} & \t...
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An ideal gas is adiabatically and irreversibly compressed from $3$ bar and $300\:K$ to $6$ bar in a closed system. The work required for the irreversible compression is $...
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A gas obeying the Clausius equation of state is isothermally compressed from $5\:Mpa$ to $15\:MPa$ in a closed system at $400\:K$. The Clausius equation of state is $P=\f...
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A binary system at a constant pressure with species $’1’$ and $’2’$ is described by the two-suffix Margules equation, $\frac{g^{E}}{RT}=3x_{1}x_{2}$, where $g^{E}...
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Consider a rigid solid sphere falling with a constant velocity in a fluid. The following data are known at the conditions of interest: viscosity of the fluid = $0.1\:Pa\;...
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The characteristics curve (Head-Capacity relationship) of a centrifugal pimp is represented by the equation $\Delta H_{pump}=43.8-0.19Q$, where $\Delta H_{pump}$ is the h...
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Water flows through a smooth circular pipe under turbulent conditions. In the viscous sub-layer, the velocity varies linearly with the distance from the wall. The Fanning...
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The space between two hollow concentric spheres of radii $0.1\:m$ and $0.2\:m$ is under vacuum. Exchange of radiation (uniform in all directions) occurs only between the ...
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A binary distillation column is to be designed using McCabe Thiele method. The distillate contains $90$ mol$\%$ of the more volatile component. The point of intersection ...
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The liquid phase reversible reaction $A\rightleftharpoons B$ is carried out in an isothermal $CSTR$ operating under steady state conditions. The inlet stream does not con...
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A liquid phase irreversible reaction$A{\rightarrow}B$ is carried out in an adiabatic $CSTR$ operating under steady state conditions. The reaction is elementary and follow...
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A $CSTR$ has a long inlet pipe. A tracer is injected at the entrance of the pipe. The $E$-curve obtained at the exit of the $CSTR$ is shown in the figure below.Assuming p...
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A liquid flows through an “equal percentage” valve at a rate of $2\:m^{3}/h$ when the valve is $10\%$ open. When the valve opens to $20\%$ the flowrate increases to $...
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A $PI$ controller with integral time constant of $0.1$ min is to be designed to control a process with transfer function$$G_{P}\left ( s \right )=\frac{10}{s^{2}+2s+100}$...
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For the matrix $\begin{pmatrix} 4 & 3\\ 3& 4 \end{pmatrix}$, if $\begin{pmatrix} 1\\ 1 \end{pmatrix}$ is an eigenvector, the corresponding eigenvalue is __________ .
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For a pure liquid, the rate of change of vapour pressure with temperature is $0.1$ bar/$K$ in the temperature range of $300$ to $350\:K$. If the boiling point of the liqu...
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Two different liquids are flowing through different pipes of the same diameter. In the first pipe, the flow is laminar with centerline velocity, $V_{max,1}$, whereas in t...
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A cylindrical packed bed of height $1\:m$ is filled with equal sized spherical particles. The particles are nonporous and have a density of $1500$ kg/$m^{3}$. The void fr...
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Benzene is removed from air by absorbing it n a non-volatile wash-oil at $100$ $kPa$ in a counter- current gas absorber. Gas flow rate is $100$ mol/min , which includes $...
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A spherical naphthalene ball of $2\:mm$ diameter is subliming very slowly in stagnant air at $25^{\circ}C$. The change in the size of the ball during the sublimation can ...
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The diameters of sand particles in a sample range from $50$ to $150$ microns. The number of particles of diameter x in the sample is proportional to $\frac{1}{50+x}$. The...
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A vector $u=-2y\hat{i}+2x\hat{j}$, where $\hat{i}$ and $\hat{j}$ are unit vectors in $x$ and $y$ directions, respectively. Evaluate the line integral$$I=\oint _{C}u.dr$$w...
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For complex variable $z$, the value of the contour integral $\frac{1}{2\pi i} \underset{C}{\int }\frac{e^{-2z}}{z(z-3)}dz$ along the clockwise contour $C:\left | z \right...
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The schematic diagram of a steady state process is shown below. The fresh feed $(F)$ to the reactor consists ot $96$ mol$\%$ reactant $A$ and $4$ mol$\%$ inert $I$. The s...
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An ideal gas is initially at a pressure of $0.1\:MPa$ and a total volume of $2\:m^{3}$. It is first compressed to $1\:MPa$ by a reversible adiabatic process and then cool...
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A binary mixture of components $(1)$ and $(2)$ forms an azeotrope at $130^{\circ}C$ and $X_{1}=0.3$. The liquid phase non-ideality is described by In $\gamma _{1}=Ax{_{2}...
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A centrifugal pump delivers water at the rate of $0.22 m^{3}/s$ from a reservoir at ground level to another reservoir at a height $H$,through a vertical pipe ot $0.2\:m$ ...
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A typical batch filtration cycle consists of filtration followed by washing. One such filtration unit operating at constant pressure difference first filters a slurry dur...
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A spherical solid particle of $1\: mm$ diameter is falling with a downward velocity of $1.7\:mm/s$ through a liquid (viscosity $0.04\: Pa.s$) at a low Reynolds number Sto...
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Air is flowing at a velocity of $3\:m/s$ perpendicular to a long pipe as shown in the figure below. The outer diameter of the pipe is $d=6\:cm$ and temperature at the out...
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A binary feed consisting of $25$ mol$\%$ liquid and $75$ mol$\%$ vapour is separated in a staged distillation column. The mole fraction of the more volatile component in ...
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Consider a steady state mass transfer process between well-mixed liquid and vapour phases of a binary mixture comprising of components $A$ and $B$. The mole fractions of ...
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Adsorption on activated carbon is to be used for reducing phenol concentration in wastewater from $0.04$ mol/$1$ to $0.008$ mol/$1$. The adsorption isotherm at the operat...
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A catalyst slab of half-thickness $L$ (the width and length of the slab $>>\:L$) is used to conduct thefirst order reaction $A{\rightarrow} B$. At $450\: K$, the Thiele m...