List of top Questions asked in GATE CH

The velocity profile for a fully developed laminar flow of an incompressible Newtonian fluid, at steady state, through a horizontal infinitely wide and long slit of gap 0.01 m is given by the following equation.
\[ u(y) = 7.5 - 3\times10^{5}y^2 \]
where \(y\) is the vertical distance measured from the center of the slit. The average velocity of the fluid (in m s-1) is ______ (rounded off to the nearest integer).
The flooding velocity curves for two different structured packings are shown in the figure. The ratio of mass velocities of liquid (\(G_x\)) to that of the gas (\(G_y\)) is 1.27. The density of the liquid (\(\rho_x\)) is 1200 kg m-3 and that of the gas (\(\rho_y\)) is 1.2 kg m-3. For both the packings, the allowable superficial vapor velocity is 60% of the flooding velocity (\(u_{0,F}\)). The ratio of the allowable mass velocity of the vapor in packing P to that in packing Q is ______ (rounded off to one decimal place).
Consider a differential equation:
\[ x^2 \frac{d^2y}{dx^2} + 3x\frac{dy}{dx} - 3y = 0 \]
with \(y = 3\) and \(\dfrac{dy}{dx} = -5\) at \(x = 1\).
The value of \(y\) at \(x = 2\) is ______ (rounded off to two decimal places).
Cyclohexane (C6H12) is produced from benzene (C6H6) and hydrogen (H2) according to the following reaction.
\[ C_6H_6 + 3H_2 \rightarrow C_6H_{12} \]
Consider the process flow diagram shown in the figure.

In this process, the overall and single-pass conversions are 90% and 25%, respectively. The recycle stream contains 25 mol% C6H6 and 75 mol% H2. If the fresh feed contains 25% excess H2, at steady state, the ratio of the molar flow rate of the recycle stream to that of the fresh feed is ______ (rounded off to one decimal place).
The data given in the table are fitted to the equation \(y = mx\) using the method of least squares. The value of \(m\) is ______ (rounded off to one decimal place).
x1234
y26710
For the equipment sizing problem described under the given operating and design conditions, the required diameter of the equipment is ______ mm (rounded off to one decimal place).
For the given heat exchange/power process operating under the stated conditions, the net power requirement of the process is ______ kW (rounded off to one decimal place).
A flooding velocity curves for two different structured packings are considered. Under the design operating conditions given for the packed absorption column, the process temperature at which the operation reaches its target condition is ______ K (rounded off to one decimal place).
For the given separation process operating under the stated conditions, the percentage recovery of the target component is ______ % (rounded off to one decimal place).
For the particle settling/separation system described under the given operating conditions, the cut size of the separation is ______ \(\mu\)m (rounded off to nearest integer).
For the reactor system described under the given feed and kinetic conditions, the mole percent of the limiting reactant remaining unconverted in the exit stream is ______ mol% (rounded off to two decimal places).

A thermometer initially at a steady temperature of \(30^\circ\mathrm{C}\) is inserted in a water bath maintained at \(90^\circ\mathrm{C}\). The initial rate of temperature rise of the thermometer is \(2\ ^\circ\mathrm{C\,s^{-1}}\). Assuming first order behavior, the thermometer reading (in \(^\circ\mathrm{C}\)) after one minute is ______ (rounded off to one decimal place).

In a double pipe cocurrent heat exchanger, operating at steady state, oil (specific heat capacity = \(2100\ \mathrm{J\,kg^{-1}\,^\circ C^{-1}}\)) entering at \(7\ \mathrm{kg\,s^{-1}}\) at \(100^\circ\mathrm{C}\) is used to heat water (specific heat capacity = \(4200\ \mathrm{J\,kg^{-1}\,^\circ C^{-1}}\)) flowing at \(3.5\ \mathrm{kg\,s^{-1}}\) from \(20^\circ\mathrm{C}\) to \(50^\circ\mathrm{C}\). If the overall heat transfer coefficient is \(291\ \mathrm{W\,m^{-2}\,^\circ C^{-1}}\), the required heat transfer area (in \(\mathrm{m^2}\)) is ______ (rounded off to one decimal place).

Consider three identical non-interacting first order processes in series, each having unit gain and a time constant of 2 min. Tuning of a proportional controller using the closed loop Ziegler-Nichols technique is considered. Which one of the following is the ultimate period of sustained cycling (in min per cycle)?

Methanol is formed by the following gas phase homogeneous reaction:

\[ \mathrm{CO(g) + 2H_2(g) \rightleftharpoons CH_3OH(g)} \]

The standard Gibbs free energies of formation at \(298\ \mathrm{K}\) for CO and \(\mathrm{CH_3OH}\) are \(-137\ \mathrm{kJ\,mol^{-1}}\) and \(-162\ \mathrm{kJ\,mol^{-1}}\), respectively. The value of the universal gas constant is \(8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}\). The equilibrium constant for the given reaction at \(298\ \mathrm{K}\) is ______ \(\times 10^4\) (rounded off to one decimal place).

A pipe with an outer diameter of \(0.02\ \mathrm{m}\) carries hot water. The temperature at the outer surface of the pipe is \(70^\circ\mathrm{C}\). This pipe is covered with two concentric layers of insulation, each having a thickness of \(0.01\ \mathrm{m}\). The first layer (adjacent to the pipe) is made up of felt material (thermal conductivity \(k_f = 0.12\ \mathrm{W\,m^{-1}\,^\circ C^{-1}}\)), and the next layer is made up of asbestos (thermal conductivity \(k_{as} = 0.15\ \mathrm{W\,m^{-1}\,^\circ C^{-1}}\)). The insulated pipe is exposed to ambient air at \(20^\circ\mathrm{C}\). The convection heat transfer coefficient at the outer insulation layer is \(3\ \mathrm{W\,m^{-2}\,^\circ C^{-1}}\). At steady state, neglecting heat transfer due to radiation, the heat loss at the outer insulation layer (in \(\mathrm{W\,m^{-1}}\)) is ______ (rounded off to two decimal places).

A gas stream with 2.01 mol% ammonia is to be scrubbed in a counter-current isothermal packed bed absorber using pure water to reduce its concentration to 0.01 mol%. Assume dilute conditions apply, the operating line is linear and the mass transfer coefficients are constant throughout the column. The liquid and the gas flows inside the absorber (in \(\text{kmol}\,\text{m}^{-2}\,\text{h}^{-1}\)) are 1000 and 200, respectively. The equilibrium relationship is \(y^* = 0.9x\), where y is the mole fraction of ammonia in the gas phase and x is that in the liquid. Under these conditions, the height of an overall gas transfer unit (\(H_{tOG}\)) is 0.8 m and the number of overall gas transfer units (\(N_{tOG}\)) is given by the following integral.
\[ N_{tOG} = \int_{y_2}^{y_1} \frac{dy}{y - y^*} \]
The integration is performed between the two ends of the column, and y* is the equilibrium mole fraction in the gas phase corresponding to the composition of the liquid at the corresponding location. Which one of the following is the minimum length of the packing (in m) necessary to achieve the desired scrubbing?
A continuous distillation column is used to separate an equimolar mixture of diethylamine (DEA) and methanol. The feed enters the column as saturated liquid at a flow rate of 30 mol \(\text{s}^{-1}\). It is desired to obtain 92 mol% DEA as distillate. The rate of withdrawal of the distillate from the column is 10 mol \(\text{s}^{-1}\). The equilibrium curve for the conditions in the column is given below. The latent heat of vaporization of the reboiler contents is 35 kJ \(\text{mol}^{-1}\). Neglect heat loss to the surroundings and assume constant molal overflow. Which one of the following is the minimum reboiler heat duty (in kW)?

Laboratory filtration is conducted at a constant pressure drop of 200 kPa on a slurry of \(\mathrm{CaCO_3}\) in water at room temperature. The time taken to collect filtrate is shown in the table.

Filtrate volume collected (in \(\mathrm{m^3}\))Time (in s)
\(1 \times 10^{-3}\)40
\(2 \times 10^{-3}\)100

The filter area is \(0.05\ \mathrm{m^2}\) and the viscosity of the filtrate is \(10^{-3}\ \mathrm{Pa\,s}\). Which one of the following is the filter medium resistance (in \(\mathrm{m^{-1}}\))?

The gross energy requirement, to reduce a very large feed of coal to such a size that 80% of the product passes through a 100 \(\mu\text{m}\) screen, is 13 kWh per ton of feed. In a process, 250 tons \(\text{h}^{-1}\) of coal is crushed. The range of feed sizes is such that 80% of the feed passes through an opening of 100 mm. The product size range is to be such that 80% of the product passes through an opening of 25 mm. According to Bond's law, which one of the following is the power consumption (in kW)?
A control valve with hyperbolic characteristics has a turndown ratio (ratio of maximum flow to minimum controllable flow) of 50. The flow rate through the valve at 70% open is 5 \(\text{m}^3\,\text{s}^{-1}\). Assuming constant fluid density and pressure drop across the valve, which one of the following is the flow rate (in \(\text{m}^3\,\text{s}^{-1}\)) through the valve at 30% open?
In a certain project, 15% of the total investment is the working capital. The minimum acceptable rate of return is 4.95% and the period of evaluation is 15 years. Which one of the following is the maximum acceptable project payback period (in years)?
The reaction rate constants of two reactions follow Arrhenius' law. The activation energies of Reaction 1 and Reaction 2 are \(E_1\) and \(E_2\), respectively, and \(E_1 < E_2\). Assuming the same value of the frequency factor for both reactions, which one of the following statements is CORRECT?
Consider the following curve in polar coordinates.
\[ r = 2 - 2\sin\theta \]
Which one of the following is the area enclosed by the curve for \(0 \le \theta \le 2\pi\)?
Consider the following homogeneous isothermal liquid-phase parallel reactions carried out in three reactor configurations (having identical volumes and same operating temperatures), as shown in the figure.
\[ A + B \rightarrow D \qquad \text{Rate of formation of D: } r_D = k_1 C_A C_B \]\[ A + B \rightarrow U \qquad \text{Rate of formation of U: } r_U = k_2 C_A^2 C_B \]
where D is the desired product and U is the undesired product. The inlet concentrations of A and B are the same in all three configurations (\(C_{A0}=C_{B0}=1\ \text{mol L}^{-1}\)). The total molar feed flow rate of A (\(F_{A0}\)) and that of B (\(F_{B0}\)) are the same in all three configurations (\(F_{A0}=F_{B0}=10\ \text{mol min}^{-1}\)). In configuration I, \(F_{A0}\) is equally distributed among all the inlets. Similarly, in configuration III, \(F_{B0}\) is equally distributed among all the inlets. Assuming plug flow behavior, at steady state, which one of the following statements is CORRECT?