List of top Fluid Mechanics Questions on Fluid Dynamics asked in GATE CH

A gas stream containing 95 mol\% CO\(_2\) and 5 mol\% ethanol is to be scrubbed with pure water in a counter-current, isothermal absorption column to remove ethanol. The desired composition of ethanol in the exit gas stream is 0.5 mol\%. The equilibrium mole fraction of ethanol in the gas phase, \( y^* \), is related to that in the liquid phase, \( x \), as \( y^* = 2x \). Assume CO\(_2\) is insoluble in water and neglect evaporation of water. If the water flow rate is twice the minimum, the mole fraction of ethanol in the spent water is:
Consider a tray-column of diameter \( 120 \, \text{cm} \). Each downcomer has a cross-sectional area of \( 575 \, \text{cm}^2 \). For a tray, the percentage column cross-sectional area not available for vapour flow due to the downcomers, rounded off to 1 decimal place, is:
Water of density \( 1000 \, \text{kg/m}^3 \) is pumped at a volumetric flow rate of \( 3.14 \times 10^{-2} \, \text{m}^3/\text{s} \), through a pipe of inner diameter \( 10 \, \text{cm} \) and length \( 100 \, \text{m} \), from a large Reservoir 1 to another large Reservoir 2 at a height \( 50 \, \text{m} \) above Reservoir 1, as shown in the figure. The flow in the pipe is in the turbulent regime with a Darcy friction factor \( f = 0.06 \), and a kinetic energy correction factor \( \alpha = 1 \). Take \( g = 9.8 \, \text{m/s}^2 \). If all minor losses are negligible, and the pump efficiency is \( 100\% \), the pump power, in \( \text{kW} \), rounded off to 2 decimal places, is: \includegraphics[width=0.5\linewidth]{q59 CE.PNG}
A Venturi meter with a throat diameter \( d = 2 \, \text{cm} \) measures the flow rate in a pipe of diameter \( D = 6 \, \text{cm} \), as shown in the figure. A U-tube manometer is connected to measure the pressure drop. Assume the discharge coefficient is independent of the Reynolds number and geometric ratios. If the volumetric flow rate through the pipe is doubled \( Q_2 = 2Q_1 \), the corresponding ratio of the manometer readings \( \Delta h_2 / \Delta h_1 \), rounded off to the nearest integer, is: \includegraphics[width=0.5\linewidth]{q60 CE.PNG}
A chemostat with cell recycle is shown in the figure. The feed flow rate and culture volume are \( F = 75 \, \text{L h}^{-1} \) and \( V = 200 \, \text{L} \), respectively. The glucose concentration in the feed \( C_{S0} = 15 \, \text{g L}^{-1} \). Assume Monod kinetics with specific cell growth rate: \[ \mu_g = \mu_m \frac{C_S}{K_S + C_S}, \] where \( \mu_m = 0.25 \, \text{h}^{-1} \) and \( K_S = 1 \, \text{g L}^{-1} \). Assume maintenance and death rates to be zero, input feed to be sterile (\( C_{S0} = 0 \)) and steady-state operation. The glucose concentration in the recycle stream, \( C_{S1} \), in \( \text{g L}^{-1} \), rounded off to 1 decimal place, is: \includegraphics[width=0.5\linewidth]{q62 CE.PNG}
Consider the surge drum in the figure. Initially, the system is at steady state with a hold-up \( \bar{V} = 5 \, \text{m}^3 \), which is \( 50\% \) of full tank capacity, \( V_{\text{full}} \), and volumetric flow rates \( F_{\text{in}} = F_{\text{out}} = 1 \, \text{m}^3/\text{h} \). The high hold-up alarm limit \( V_{\text{high}} = 0.8 V_{\text{full}} \) while the low hold-up alarm limit \( V_{\text{low}} = 0.2 V_{\text{full}} \). A proportional (P-only) controller manipulates the outflow to regulate the hold-up as \( F_{\text{out}} = K_c (V - \bar{V}) + F_{\text{out} \). At \( t = 0 \), \( F_{\text{in}} \) increases as a step from \( 1 \, \text{m}^3/\text{h} \) to \( 2 \, \text{m}^3/\text{h} \). Assume linear control valves and instantaneous valve dynamics. Let \( K_c^{\text{min}} \) be the minimum controller gain that ensures \( V \) never exceeds \( V_{\text{high}} \). The value of \( K_c^{\text{min}} \), in \( \text{h}^{-1} \), rounded off to 2 decimal places, is:} \includegraphics[width=0.5\linewidth]{q63 CE.PNG}
Consider the process in the figure for manufacturing \( B \). The feed to the process is 90 mol\% \( A \) and a close-boiling inert component \( I \). At a particular steady-state: - \( B \) product rate is \( 100 \, \text{kmol/h} \), - Single-pass conversion of \( A \) in the reactor is \( 50\% \), - Recycle-to-purge stream flow ratio is \( 10 \). The flow rate of \( A \) in the purge stream, in \( \text{kmol/h} \), rounded off to 1 decimal place, is: \includegraphics[width=0.5\linewidth]{q54 CE.PNG}
A simple distillation column separates a binary mixture of A and B. The relative volatility of A with respect to B is \( 2 \). The steady-state composition of A in the vapor leaving the 1\textsuperscript{st, 2\textsuperscript{nd}, and 3\textsuperscript{rd} trays in the rectifying section are \( 94\% \), \( 90\% \), and \( 85\% \) (mol\%), respectively. For ideal trays and constant molal overflow, the reflux-to-distillate ratio is:}
A first-order liquid phase reaction \( \text{A} \rightarrow \text{B} \) is carried out in two isothermal plug flow reactors (PFRs) of volume \( 1 \, \text{m}^3 \) each, connected in series. The feed flow rate and concentration of \( \text{A} \) to the first reactor are \( 10 \, \text{m}^3/\text{h} \) and \( 1 \, \text{kmol}/\text{m}^3 \), respectively. At steady-state, the concentration of \( \text{A} \) at the exit of the second reactor is \( 0.2 \, \text{kmol}/\text{m}^3 \). If the two PFRs are replaced by two equal-volume continuously stirred tank reactors (CSTRs) to achieve the same overall steady-state conversion, the volume of each CSTR, in \( \text{m}^3 \), is:
The residence time distribution, \( E \), for a non-ideal flow reactor is given in the figure. A first-order liquid phase reaction with a rate constant \( 0.2 \, \text{min}^{-1} \) is carried out in the reactor. For an inlet reactant concentration of \( 2 \, \text{mol/L} \), the reactant concentration (in \( \text{mol/L} \)) in the exit stream is: \includegraphics[width=0.5\linewidth]{q46 CE.PNG}
Consider a steady, fully-developed, uni-directional laminar flow of an incompressible Newtonian fluid (viscosity \( \mu \)) between two infinitely long horizontal plates separated by a distance \( 2H \) as shown in the figure. The flow is driven by the combined action of a pressure gradient and the motion of the bottom plate at \( y = -H \) in the negative \( x \)-direction. Given that \( \frac{\Delta P}{L} = \frac{P_1 - P_2}{L}>0 \), where \( P_1 \) and \( P_2 \) are the pressures at two \( x \)-locations separated by a distance \( L \). The bottom plate has a velocity of magnitude \( V \) with respect to the stationary top plate at \( y = H \). Which one of the following represents the \( x \)-component of the fluid velocity vector?
Hot oil at \( 110^\circ\text{C} \) heats water from \( 30^\circ\text{C} \) to \( 70^\circ\text{C} \) in a counter-current double-pipe heat exchanger. The flow rates of water and oil are \( 50 \, \text{kg/min} \) and \( 100 \, \text{kg/min} \), respectively, and their specific heat capacities are \( 4.2 \, \text{kJ/kg}^\circ\text{C} \) and \( 2.0 \, \text{kJ/kg}^\circ\text{C} \), respectively. Assume the heat exchanger is at steady state. If the overall heat transfer coefficient is \( 200 \, \text{W/m}^2{}^\circ\text{C} \), the heat transfer area in \( \text{m}^2 \) is:
Consider the reaction \( \text{N}_2(g) + 3\text{H_2(g) \rightarrow 2\text{NH}_3(g) \) in a continuous flow reactor under steady-state conditions. The component flow rates at the reactor inlet are: \[ F_{\text{N}_2}^0 = 100 \, \text{mol/s}, \quad F_{\text{H}_2}^0 = 300 \, \text{mol/s}, \quad F_{\text{inert}}^0 = 1 \, \text{mol/s}. \] If the fractional conversion of \( \text{H}_2 \) is \( 0.60 \), the outlet flow rate of \( \text{N}_2 \), in mol/s, rounded off to the nearest integer, is \_\_\_\_\_\_\_.}
Consider the steady, uni-directional, fully-developed, pressure-driven laminar flow of an incompressible Newtonian fluid through a circular pipe of inner radius \( 5.0 \, \text{cm} \). The magnitude of shear stress at the inner wall of the pipe is \( 0.1 \, \text{N} \, \text{m}^{-2} \). At a radial distance of \( 1.0 \, \text{cm} \) from the pipe axis, the magnitude of the shear stress, in \( \text{N} \, \text{m}^{-2} \), rounded off to 3 decimal places, is \_\_\_\_\_\_\_.
Consider the control structure for the overhead section of a distillation column shown in the figure. The composition controller (CC) controls the heavy key impurity in the distillate by adjusting the setpoint of the reflux flow controller in a cascade arrangement. The sign of the controller gain for the pressure controller (PC) and that for the composition controller (CC) are, respectively: \includegraphics[width=0.5\linewidth]{q23 CE.PNG}
The velocity field in an incompressible flow is \( \mathbf{v} = axy \, \mathbf{i} + v_y \, \mathbf{j} + \beta \, \mathbf{k} \), where \( \mathbf{i}, \mathbf{j}, \mathbf{k} \) are unit-vectors in the \( (x, y, z) \) Cartesian coordinate system. Given that \( a \) and \( \beta \) are constants, and \( v_y = 0 \) at \( y = 0 \), the correct expression for \( v_y \) is:
Consider the steady, uni-directional diffusion of a binary mixture of \( A \) and \( B \) across a vertical slab of dimensions \( 0.2 \, \text{m} \times 0.1 \, \text{m} \times 0.02 \, \text{m} \) as shown in the figure. The total molar concentration of \( A \) and \( B \) is constant at \( 100 \, \text{mol} \, \text{m}^{-3} \). The mole fraction of \( A \) on the left and right faces of the slab are maintained at \( 0.8 \) and \( 0.2 \), respectively. If the binary diffusion coefficient \( D_{AB} = 1 \times 10^{-5} \, \text{m}^2 \, \text{s}^{-1} \), the molar flow rate of \( A \) in \( \text{mol} \, \text{s}^{-1} \), along the horizontal \( x \)-direction is: \includegraphics[width=0.5\linewidth]{q17 ce ..PNG}