Recent questions tagged numerical-answers

A vertical cylindrical tank with a flat roof and bottom is to be constructed for storing $150\:m^{3}$ of ethylene glycol. The cost of material and fabrication for the tan...

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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...

For a gas phase cracking reaction $A{\rightarrow}B+C$ at $300^{\circ}$, the Gibbs free energy of the reaction at this temperature is $\Delta G^{\circ}=-2750$ $J$/mol. The...

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...

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...

Two infinitely large parallel plates ($I$ and $II$) are held at temperatures $T_{I}$ and $T_{II}$ $(T_{I}>T_{II})$ respectively, and placed at a distance $2d$ apart in va...

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 $...

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 ...

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...

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...

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...

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...

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...

Given that molar residual Gibbs free energy, $g^{R}$, and molar residual volume, $v^{R}$, are related as $\frac{g^{R}}{RT}=\int _{0}^{P}\left ( \frac{v^{R}}{RT} \right )d...

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}...

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 $0.2\:m$ ...

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...

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...

A heated solid copper sphere (of surface area $A$ and volume $V$) is immersed in a large body of cold fluid. Assume the resistance to heat transfer inside the sphere to b...

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...

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 ...

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 ...

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...

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...

An isothermal steady state mixed flow reactor $(CSTR)$ of $1\:m^{3}$ volume is used to carry out the first order liquid-phase reaction $A{\rightarrow}$ products. Fresh fe...

The block diagram for a process with feedback control for output deviation $h$ is shown in the figure below. All transfer functions are given with pre-factor of $s$ in mi...

Consider a control system with the open loop transfer function given by :$G_{OL}\left ( s \right )=\frac{K_{c}e^{-0.3z}}{1.5s+1}$In the above function, pre-factor of $s$ ...

The cost of two independent process variables $f_{1}$ and $f_{2}$ affects the total cost $C_{T}$ (in lakhs of rupees) of the process as per the following function :$$C_{T...

A proposed chemical plant is estimated to have a fixed capital $(FC)$ of $Rs$. $24$ crores. Assuming other costs to be small, the total investment may be taken to be same...

A foundry has a fixed daily cost of Rs $50,000$ whenever it operates and a variable cost of Rs $800Q,$ where $Q$ is the daily production in tonnes. What is the cost of pr...

The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is $3:4:5:6.$ The larg...

Consider the following block diagram for a closed-loop feedback control system A proportional controller is being used with $K_{c}=-4$. If a step change in distrubance of...

In a steady and incompressible flow of a fluid (density = $1.25\: kg\: m^{-3}$), the difference between stagnation and static pressures at the same location in the flow i...

Consider a binary liquid mixture at equilibrium with its vapour at $25^{\circ}C$.Antoine equation for this system is given as $log_{10}\:p_{t}^{sat}=A-\frac{B}{t+C}$ wher...

In a steady incompressible flow, the velocity distribution is given by $\bar{V}=3x\hat{i}-Py\hat{j}+5z\hat{k}$, where, $V$ is in $m/s$ and $x,y$ and $z$ are in $m$. In or...

The bottom face of a horizontal slab of thickness $6 \:mm$ is maintained at $300^{\circ}C$. The top face is exposed to a flowing gas at $30^{\circ}C$. The thermal conduct...

A step change of magnitude $2$ is introduced into a system having the following transfer function$$G\left ( s \right )=\frac{2}{s^{2}+2s+4}$$The percent overshoot is ____...

A polymer plant with a production capacity of $10,000$ tons per year has an overall yield of $70\%$, on mass basis ($kg$ of product per $kg$ of raw material), The raw mat...