List of practice Questions

A pump draws water (density \(=1000\ \mathrm{kg\,m^{-3}}\)) at a steady rate of \(10\ \mathrm{kg\,s^{-1}}\). The pressures at the suction and discharge sides of the pump are \(-20\ \mathrm{kPa}\) (gauge) and \(350\ \mathrm{kPa}\) (gauge), respectively. The pipe diameters at the suction and discharge side are \(70\ \mathrm{mm}\) and \(50\ \mathrm{mm}\), respectively. The suction and discharge lines are at the same elevation, and the pump operates at an efficiency of \(80%\). Neglecting frictional losses in the system, the power (in kW) required to drive the pump is __________ (rounded off to two decimal places).

A cylindrical tank with a diameter of \(500\ \text{mm}\) contains water (density \(=1\ \text{g}\cdot\text{cm}^{-3}\)) up to a height \(h\). A \(5\ \text{mm}\) diameter round nozzle, whose center is \(1\ \text{cm}\) above the base of the tank, has its exit open to the atmosphere. The pressure above the water level in the tank is maintained at \(2\ \text{bar (abs)\). Neglect all frictional and entry/exit losses. Take \(g=10\ \text{m}\,\text{s}^{-2}\) and atmospheric pressure \(=1\ \text{bar}\). The absolute value of initial \(\dfrac{dh}{dt}\) (in \(\text{mm}\,\text{s}^{-1}\)) when \(h=51\ \text{cm}\) is ____________ (rounded off to two decimal places).}

A large tank is filled with water (density \(=1\ \mathrm{g\,cm^{-3}}\)) up to a height of \(5\ \mathrm{m}\). A \(100\ \mu\mathrm{m}\) diameter solid spherical particle (density \(=0.8\ \mathrm{g\,cm^{-3}}\)) is released at the bottom of the tank. The particle attains its terminal velocity \((v_t)\) after traveling to a certain height in the tank. Use acceleration due to gravity as \(10\ \mathrm{m\,s^{-2}}\) and water viscosity as \(10^{-3}\ \mathrm{Pa\,s}\). Neglect wall effects on the particle. If Stokes’ law is applicable, the absolute value of \(v_t\) (in \(\mathrm{mm\,s^{-1}}\)) is ________________ (rounded off to two decimal places).

Which one of the following represents the CORRECT effects of concentration polarization in a reverse osmosis process?

CO and H\(_2\) participate in a catalytic reaction. The partial pressures (in atm) of the reacting species CO and H\(_2\) in the feed stream are \(p_{CO}\) and \(p_{H_2}\), respectively. While CO undergoes molecular adsorption, H\(_2\) adsorbs via dissociative adsorption (as H atoms). The equilibrium constants (in atm\(^{-1}\)) corresponding to adsorption of CO and H\(_2\) to the catalyst sites are \(K_{CO}\) and \(K_{H_2}\), respectively. Total molar concentration of active sites per unit mass of the catalyst is \(C_t\) (in mol\(\cdot\)(g cat)\(^{-1}\)). Both the adsorption steps are at equilibrium. Which one of the following expressions is the CORRECT ratio of the concentration of catalyst sites occupied by CO to that by hydrogen atoms?

Level (\(h\)) in a steam boiler is controlled by manipulating the flow rate (\(F\)) of the make-up water using a proportional (P) controller. The transfer function is \[ \frac{h(s)}{F(s)} = \frac{0.25(1-s)}{s(2s+1)}. \] The measurement and valve transfer functions are both 1. A process engineer wants the closed-loop response to give decaying oscillations under servo mode. Which one of the following is the CORRECT value of the controller gain?

Which of the following statements is/are CORRECT?

An exhibition was held in a hall on 15 August 2022 between 3 PM and 4 PM during which any person was allowed to enter only once. Visitors who entered before 3:40 PM exited the hall exactly after 20 minutes from their time of entry. Visitors who entered at or after 3:40 PM, exited exactly at 4 PM. The probability distribution of the arrival time of any visitor is uniform between 3 PM and 4 PM. Two persons \(X\) and \(Y\) entered the exhibition hall independent of each other. Which one of the following values is the probability that their visits to the exhibition overlapped with each other?

Simpson’s one-third rule is used to estimate the definite integral \(I=\displaystyle\int_{-1}^{1}\sqrt{1-x^{2}}\,dx\) with an interval length of \(0.5\). Which one of the following is the CORRECT estimate of \(I\) obtained using this rule?

Water in a container at 290 K is exposed to air containing \(3\ %\) \(\mathrm{CO_2}\) by volume. Air behaves like an ideal gas and is maintained at \(100\ \text{kPa}\) pressure. The liquid phase comprising of dissolved \(\mathrm{CO_2}\) in water behaves like an ideal solution. Use Henry’s constant of \(\mathrm{CO_2}\) dissolved in water at 290 K as \(12\ \text{MPa}\). Under equilibrium conditions, which one of the following is the CORRECT value of the mole fraction of \(\mathrm{CO_2}\) dissolved in water?

The enthalpy (\(H\), in J\(\cdot\)mol\(^{-1}\)) of a binary liquid system at constant temperature and pressure is given as \[ H=40x_1+60x_2+x_1x_2(4x_1+2x_2), \] where \(x_1\) and \(x_2\) represent the mole fractions of species 1 and 2 in the liquid, respectively. Which one of the following is the CORRECT value of the partial molar enthalpy of species 1 at infinite dilution, \(\overline{H}_1^{\infty}\) (in J\(\cdot\)mol\(^{-1}\))?

For a fully developed turbulent flow of an incompressible Newtonian fluid through a pipe of constant diameter, which of the following statements is/are CORRECT?

Given that \(E\) (in W\(\cdot\)m\(^{-2}\)) is the total hemispherical emissive power of a surface maintained at a certain temperature, which of the following statements is/are CORRECT?

Burning of methane in a combustor yields carbon monoxide, carbon dioxide, and water vapor. Methane is fed to the combustor at 100 mol·hr\(^{-1}\), of which 50% reacts. The theoretical oxygen requirement (in mol·hr\(^{-1}\)) is ____________ (rounded off to one decimal place).

The viscosity of an incompressible Newtonian fluid is measured using a capillary tube of diameter \(0.5\ \text{mm}\) and length \(1.5\ \text{m}\). The fluid flow is laminar, steady and fully developed. For a flow rate of \(1\ \text{cm}^3\text{s}^{-1}\), the pressure drop across the length of the tube is \(1\ \text{MPa}\). If the viscosity of the fluid is \(k \times 10^{-3}\ \text{Pa}\cdot\text{s}\), the value of \(k\) is ____________________ (rounded off to two decimal places).

A liquid \(L\) containing a dissolved gas \(S\) is stripped in a countercurrent operation using a pure carrier gas \(V\). The liquid phase inlet and outlet mole fractions of \(S\) are \(0.1\) and \(0.01\), respectively. The equilibrium distribution of \(S\) between \(V\) and \(L\) is governed by \(y_e = x_e\), where \(y_e\) and \(x_e\) are the mole fractions of \(S\) in \(V\) and \(L\), respectively. The molar feed rate of the carrier gas stream is twice that of the liquid stream. Under dilute solution conditions, the minimum number of ideal stages required is \(\underline{\hspace{2cm}}\) (in integer).

In a binary gas-liquid system, \(N_{A,EMD}\) is the molar flux of a gas \(A\) for equimolar counter diffusion with a liquid \(B\). \(N_{A,UMD}\) is the molar flux of \(A\) for steady one-component diffusion through stagnant \(B\). Using the mole fraction of \(A\) in the bulk of the gas phase as 0.2 and that at the gas-liquid interface as 0.1 for both the modes of diffusion, the ratio of \(N_{A,UMD}\) to \(N_{A,EMD}\) is equal to __________ (rounded off to two decimal places).

Spray dryers have many advantages. Which one of the following is NOT an advantage of a typical spray dryer?

Which one of the following quantities of a flowing fluid is measured using a rotameter?

A liquid surge tank has \(F_{in}\) and \(F_{out}\) as the inlet and outlet flow rates respectively, as shown in the figure. \(F_{out}\) is proportional to the square root of the liquid level \(h\). The cross-sectional area of the tank is \(20~\text{cm}^2\). Density of the liquid is constant everywhere in the system. At steady state, \(F_{in}=F_{out}=10~\text{cm}^3\text{s}^{-1}\) and \(h=16~\text{cm}\). The variation of \(h\) with \(F_{in}\) is approximated as a first-order transfer function. Which one of the following is the CORRECT value of the time constant (in seconds) of this system?

A packed distillation column, with vapor having an average molecular weight of \(45~\text{kg}\cdot\text{kmol}^{-1}\), density of \(2~\text{kg}\cdot\text{m}^{-3}\) and a molar flow rate of \(0.1~\text{kmol}\cdot\text{s}^{-1}\), has a flooding velocity of \(0.15~\text{m}\cdot\text{s}^{-1}\). The column is designed to operate at \(60%\) of the flooding velocity. Which one of the following is the CORRECT value for the column diameter (in m)?

An isothermal jacketed continuous stirred tank reactor (CSTR) operating at \(150^{\circ}\mathrm{C}\) is shown. The cold feed at \(30^{\circ}\mathrm{C}\) is first preheated to \(T\) (\(T<150^{\circ}\mathrm{C}\)) in heat exchanger \(HX_1\) (using process-to-process heat recovery) and then heated to \(150^{\circ}\mathrm{C}\) in a utility heater \(HX_2\). Mass flow rate and heat capacity are the same for all process streams and the overall 64ac0493b52af67589bd410c coefficient is independent of temperature. Which action will increase the value of \(T\)?

Consider a system where a Carnot engine is operating between a source and a sink. Which of the following statements about this system is/are NOT correct?

For a reversible endothermic chemical reaction with constant heat of reaction over the operating temperature range, \(K\) is the thermodynamic equilibrium constant. Which one of the following figures shows the CORRECT dependence of \(K\) on temperature \(T\)?

Nitrile rubber is manufactured via polymerization process. Which one of the following options is the CORRECT pair of monomers used in this process?