Recent questions tagged numerical-answers

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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...
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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 $s$ ...
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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 :$$C_{T...
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A proposed chemical plant is estimated to have a fixed capital $(FC)$ of $Rs$. $24$ crores. Assuming other costs to be small, the total investment may be taken to be same...
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A foundry has a fixed daily cost of Rs $50,000$ whenever it operates and a variable cost of Rs $800Q,$ where $Q$ is the daily production in tonnes. What is the cost of pr...
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The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is $3:4:5:6.$ The larg...
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Consider the following block diagram for a closed-loop feedback control system A proportional controller is being used with $K_{c}=-4$. If a step change in distrubance of...
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In a steady and incompressible flow of a fluid (density = $1.25\: kg\: m^{-3}$), the difference between stagnation and static pressures at the same location in the flow i...
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Consider a binary liquid mixture at equilibrium with its vapour at $25^{\circ}C$.Antoine equation for this system is given as $log_{10}\:p_{t}^{sat}=A-\frac{B}{t+C}$ wher...
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In a steady incompressible flow, the velocity distribution is given by $\bar{V}=3x\hat{i}-Py\hat{j}+5z\hat{k}$, where, $V$ is in $m/s$ and $x,y$ and $z$ are in $m$. In or...
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The bottom face of a horizontal slab of thickness $6 \:mm$ is maintained at $300^{\circ}C$. The top face is exposed to a flowing gas at $30^{\circ}C$. The thermal conduct...
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A step change of magnitude $2$ is introduced into a system having the following transfer function$$G\left ( s \right )=\frac{2}{s^{2}+2s+4}$$The percent overshoot is ____...
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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...
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A cash flow of Rs. $12,000$ per year is received at the end year (uniform periodic payment) for $7$ consecutive years. The rate of interest is $9\%$ per year compounded a...
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Carbon monoxide $(CO)$ is burnt in pressure of $200\%$ excess pure oxygen and the flame temperature achieved is $2298\:K$. The inlet streams are at $25^{\circ}$. The stan...
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Two elemental gases ($A$ and $B$) are reacting to form a liquid ($C$) in a steady state process as per the reaction $A+B{\rightarrow}C$. The single-pass conversion of the...
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An incompressible fluid is flowing through a contraction section of length $L$ and has a $1-D$ ($x$- direction steady state velocity distribution, $u=u_{0}\left ( 1+\frac...
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A binary distillation column is operating with a mixed feed containing $20$ mol$\%$ vapour. If the feed quality is changed to $80$ mol$\%$ vapour, the change is the slope...
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In rolling of two fair dice, the outcome of an experiments is considered to be the sum of the numbers appearing on the dice. The probability is highest for the outcome of...
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An oil with a flow rate of $1000\:kg/h$ is to be cooled using water in a double-pipe counter-flow heat exchanger from a temperature of $70^{\circ}C$ to $40^{\circ}C$. Wat...
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A brick wall of $20\:cm$ thickness has thermal conductivity of $0.7\:W\:m^{-1}\:K^{-1}$. An insulation of thermal conductivity $0.2\:W\:m^{-1}\:K^{-1}$ is to be applied o...
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A wet solid of $100\:kg$ is dried from a moisture content of $40\:wt\%$ to $10\:wt\%$. The critical moisture content is $15\:wt\%$ and the equilibrium moisture content is...
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Consider the following differential equation$\frac{dy}{dx}=x+In\:\left ( y \right ); y=2 \: at \: x=0$The solution of this equation at $x=0.4$ using Euler method with a s...
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Liquid reactant A decomposes as follows A $\rightarrow$ R r${_R} $= k${_1}$C$^{2}$${_A}$ k${_1}$ = 0.5m$^{3}$/mol-s...
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Liquid reactant A decomposes as follows A $\rightarrow$ R r${_R} $= k${_1}$C$^{2}$${_A}$ k${_1}$ = 0.5m$^{3}$/mol-s...
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A fraction $f$ of the feed is bypassed and mixed with the permeate to obtain treated water having a fluoride concentration of 1 mg/L. Here also the flow rate of the rejec...
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A reverse osmosis unit treats feed water (F) containing fluoride and its output consists of a permeate stream (P) and a reject stream (R). Let C${_F}$, C${_p}$, and C${_R...
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A plant manufactures compressors at the rate of N units/day. The daily fixed charges are Rs. 20000 and the variable cost per compressor is Rs. 500 + 0.2 N$^{1.3}$. The se...
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The purchase cost of a heat exchanger of 20 m$^{2}$ area was Rs 500000 in 2006. What will be the estimated cost (in Rs to the nearest integer) of a similar heat exchanger...
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A control value, with a turndown ratio of 50, follows equal percentage characteristics. The flow rate of a liquid through the value at 40% stem positions is 1 m$^{3}$/h. ...
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A first order liquid phase reaction is carried out isothermally at a steady state in a CSTR and 90% conversion is attained. With the same inlet conditions and for the sam...
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The gas phase decomposition of azomethane to give ethane and nitrogen takes place according to the following sequence of elementary reactions.(CH${_3}){_2}$N${_2}$ + (CH$...
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A study was conducted in which water was pumped through cylindrical pipes made of a sparingly soluble solid. For a given pipe and certain flow conditions, the mass transf...
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The vapor-liquid equilibrium curve of a binary mixture A-B,may be approximated by a linear equation over a narrow range of liquid mole fractions (0.2 < x${_A}$ < 0.3) as...
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Calculate the heat required (in kJ, up to 1 digit after the decimal point) to raise the temperature of 1 mole of a solid material from 100 $^{o}$C to 1000 $^{o}$C. The sp...
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100 ton/h of a rock feed, of which 80% passed through a mesh size of 2.54 mm, were reduced in size such that 80% of the crushed product passed through a mesh size of 1.27...
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The value of the integral${\scriptstyle \int^{0.5} _{0.1}}$ e$^{-x^3}$dxevaluated by Simpson’s rule using 4 subintervals (up to 3 digits after the decimal point) is $\_...
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For the functionf(z) = $\frac{1}{(2-z)(z+2)}$the residue at z = 2 is $\_\_\_\_\_$
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Water (density 1000 kg/m$^{3}$) is flowing through a nozzle, as shown below and exiting to the atmosphere. The relationship the diameters of the nozzle at location 1 and ...
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A binary liquid mixture is in equilibrium with its vapor at a temperature T = 300 K. The liquid mole fraction x${_1}$ of species 1 is 0.4 and the molar excess Gibbs free ...