Recent questions tagged numerical-answers

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The elementary irreversible gas-phase reaction $A\rightarrow B+C$ is carried out adiabatically in an ideal $CSTR$ (Continuous-Stirred Tank Reactor) operating at 10 $atm$....
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For the closed loop system shown in figure, the phase margin (in degrees) is ____________ (rounded off to one decimal place).
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A countercurrent absorption tower is designed to remove $95\%$ of component $A$ from an incoming binary gas mixture using pure solvent $B$. The mole ratio of $A$ in the i...
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A binary mixture with components $A$ and $B$ is to be separated in a distillation column to obtain $95$ mol$\%$ $A$ as the top product. The binary mixture has a constant ...
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Consider the reactor-separator-recycle process operating under steady state conditions as shown in the figure. The reactor is an ideal Continuous-Stirred Tank Reactor ($C...
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Consider two competing equipment $A$ and $B$. For a compound interest rate of $10\%$ per annum, in order for equipment $B$ to be the economically cheaper option, its mini...
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A taxi-car is bought for $Rs\: 10$ lakhs. Its salvage value is zero. The expected yearly income after paying all expenses and applicable taxes is $Rs$ $3$ lakhs. The comp...
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The value of $\underset{x\rightarrow 0}{\lim}\:\frac{\tan\left ( x \right )}{x}$ is ________________.
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The real part of $6e^{i\pi /3}$ is _______________.
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The number of positive roots of the function $f(x)$ shown below in the range $0<x<6$ is ___________________.
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A gas bubble (gas density $\rho_{g} =2\:kg/m^{3}$ ; bubble diameter $D=10^{-4}\:m$ is rising vertically through water (density $\rho =1000\:kg/m^{3}$; viscosity $\mu =0.0...
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In a heat exchanger, the inner diameter of a tube is $25\:mm$ and its outer diameter is $30\:mm$. The overall heat transfer coefficient based on the inner area is $360\:W...
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The composition of vapour entering a tray in a distillation column is $0.47$. The average composition of the vapour leaving the tray is $0.53$. The equilibrium compositio...
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The cost of a new pump (including installation) is $24,000$ Rupees. The pump has a useful life of $10$ years. Its salvage value is $4000$ Rupees. Assuming straight line d...
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For the initial value problem$$\frac{dx}{dt}=\sin\left ( t \right ),\:\:\:\:x\left ( 0 \right )=0$$the value of $x$ at $t=\pi /3$ , is _____________.
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A box has $6$ red balls and $4$ white balls. A ball is picked at random and replaced in the box, after which a second ball is picked.The probability of both the balls bei...
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An aqueous salt-solution enters a crystallizer operating at steady state at $25^{\circ}C$. The feed temperature is $90^{\circ}C$ and the salt concentration in the feet is...
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Reaction $A{\rightarrow}B$ is carried out in a reactor operating at steady state and $1$ mol/$s$ of pure $A$ at $425^{\circ}C$ enters the reactor. The outlet stream leave...
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The pressure of a liquid is increased isothermally. The molar volume of the liquid decreases from $50.45\times 10^{-6}$ $m^{3}$/mol to $48\times 10^{-6}$ $m^{3}$/mol duri...
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A sparingly soluble gas (solute) is in equilibrium with a solvent at $10$ bar. The mole fraction of the solvent in the gas phase is $0.01$. At the operating temperature a...
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The vapour pressure of a pure substance at a temperature $T$ is $30$ bar. The actual and ideal gas values of $g/RT$ for the saturated vapour at this temperature $T$ and $...
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Oil is being delivered at a steady flowrate through a circular pipe of radius $1.25\times10^{-2}\:m$ and $10\:m$. The pressure drop across the pipe is $500\:Pa$.The shear...
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A propeller (diameter $D=15\:m$) rotates at $N=1$ revolution per second $(rps)$. To understand the flow around the propeller, a lab-scale model is made. Important paramet...
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Size analysis was carried out on a sample of gravel. The data for mass fraction $(x_{i})$ and average particle diameter $(D_{pi})$ of the fraction is given in the table b...
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The vapour phase composition and relative volatilities (with respect to $n$-propane) on an ideal tray of a distillation column are$$\begin{array}{clcIcIcI|cI|c}\hline&\te...
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In a countercurrent stripping operation using pure steam, the mole ratio of a solute in the liquid stream is reduced from $0.25$ to $0.05$. The liquid feed flowrate, on a...
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In a batch absorption process, $5\:g$ of fresh absorbent is used to treat $1$ liter of an aqueous phenol solution. The initial phenol concentration is $100\:mg$/liter. Th...
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The $C$-curve measured during a pulse tracer experiment is shown below. In the figure, $C(t)$ is the concentration of the tracer measured at the reactor exit in mol/liter...
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The following liquid phase second-order reaction is carried out in an isothermal $CSTR$ steady steady$$A{\rightarrow}R\:\:\:\:\:(-r_{A})=0.005C_{A}^{2}\:mol/m^{3}.hr$$whe...
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The reversible reaction of $t$-butyl alcohol $(TBA)$ and ethanol $(EtOH)$ to ethyl $t$-butyl ether $(ETBE)$ is$$TBA+Et0H\rightleftharpoons ETBE+water$$The equilibrium con...
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The following gas-phase reaction is carried out in a constant-volume isothermal batch reactor$$A+B{\rightarrow}R+S$$The reactants $A$ and $B$ as well as the product $S$ a...
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The transfer function of a system is$$\frac{1}{4s^{2}+1.2s+1}$$For a unit step increase in the input, the fractional overshoot, rounded to $2$ decimal place, is _________...
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The open loop transfer function of a process with a proportional controller (gain $K_{C}$) is$$G_{OL}=K_{C}\frac{e^{-2s}}{s}$$Based on the Bode criterion for closed-loop ...
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The characteristics equation of a closed-loop system is$$6s^{3}+11s^{2}+6s+\left ( 1+K \right )=0,\:\:\:\:\:\: where \:K>0$$The value of $K$ beyond which the system just ...
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A bond has a maturity value of $20,000$ Rupees at the end of $4$ years. The interest is compounded at the rate of $5\%$ per year.The initial investment to be made, rounde...
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The total cost $(C_{T})$ of an equipment in terms of the operating variables $x$ and $y$ is$$C_{T}=2x+\frac{12000}{xy}+y+5$$The optimal value of $C_{T}$, rounded to $1$ d...
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The partial molar enthalpy (in $kJ$/mol) of species $1$ in a binary mixture is given by $\bar{h}_{1}=2 -60x_{2}^{2}+100x^{1}x_{2}^{2},$ where $x_{1}$ and $x_{2}$ are the ...
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A vertical cylindrical vessel has a layer of kerosene (of density $800\: kg/m^{3}$) over a layer of water (of density $1000 \:kg/m^{3}$). $L$ – shaped glass tubes are c...
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A composite wall is made of four different materials of construction in the fashion shown below. The resistance (in $K/W$) of each sections of the wall is indicated in th...
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A binary liquid mixture of benzene and toluene contains $20$ mol$\%$ of benzene. At $350 \:K$ the vapour pressures of pure benzene and pure toluene are $92\: kPa$ and $35...