List of top Questions asked in GATE CH

Schmidt number is defined as
Choose the CORRECT option for pathlines, streaklines and streamlines for a STEADY flow field.
The sum of the components of the force due to pressure and shear at the solid-fluid boundary of a solid body in the direction normal to the flow is:
In industrial heat exchanger design, the overall heat transfer coefficient \( U \) is estimated from the equation: \[ \frac{1}{U} = \frac{1}{h_i} + \frac{1}{h_o} \] where \( h_i \) and \( h_o \) are the convective heat transfer coefficients on the inner and outer side of the tube, respectively. This is valid for (i) tube of (ii) thermal conductivity.
Which one of the following is the CORRECT option to fill in the gaps (i) and (ii)?
The boundary of a system does not allow exchange of either mass or energy (in the form of heat and/or work) with the surroundings. The system is termed
The number of independent intensive variables that need to be specified to determine the thermodynamic state of a ternary mixture at vapor-liquid-liquid equilibrium is:
A box contains 3 identical green balls and 7 identical blue balls. Two balls are randomly drawn without replacement from the box. The probability of drawing 1 green and 1 blue ball is
Consider a Cartesian coordinate system defined over a 3-dimensional vector space with orthogonal unit basis vectors \(\hat{i}, \hat{j}\), and \(\hat{k}\). Let vector \(\mathbf{a} = \sqrt{2}\hat{i} + \frac{1}{\sqrt{2}}\hat{k}\), and vector \(\mathbf{b} = \frac{1}{\sqrt{2}}\hat{i} + \sqrt{2}\hat{j} - \hat{k}\). The inner product of these vectors (\(\mathbf{a} \cdot \mathbf{b}\)) is:

To manufacture paper from ______(i) _______, the ________ (ii) _______ must be freed from the binding matrix of ________(iii) ________ in the pulping step. Which one of the following is the CORRECT option to fill in the gaps (i), (ii) and (iii)?

The block diagram of a series cascade control system (with time in minutes) is shown in the figure. For \( \tau_1 = 8 \) min and \( K_s^c = 1 \), the maximum value of \( K_m^c \), below which the cascade control system is stable, is \_\_\_\_ (rounded off to the nearest integer).
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An adiabatic pump of efficiency 40% is used to increase the water pressure from 200 kPa to 600 kPa. The flow rate of water is 600 L/min. The specific heat of water is 4.2 kJ/(kg°C). Assuming water is incompressible with a density of 1000 kg/m³, the maximum temperature rise of water across the pump is \_\_\_\_°C (rounded off to 3 decimal places).
A zero-order gas phase reaction \(A \to B\) with rate \((-r_A) = k = 100\) mol/(L min) is carried out in a mixed flow reactor of volume 1 L. Pure \(A\) is fed to the reactor at a rate of 1 mol/min. At time \(t = 0\), the outlet flow is stopped while the inlet flow rate and reactor temperature remain unchanged. Assume that the reactor was operating under steady state before the flow was stopped (\(t<0\)). The rate of consumption of \(A\), \(-\frac{dC_A}{dt}\), in mol/(L min), at \(t = 1\) min is:
Consider a Cartesian coordinate system with orthogonal unit basis vectors \( \hat{i}, \hat{j} \) defined over a domain: \( x, y \in [0,1] \). Choose the condition for which the divergence of the vector field \( \mathbf{v} = ax\hat{i} - by\hat{j} \) is zero.
Choose the CORRECT ordering of the diameter \( d \) of the different types of pores in a solid catalyst.
Consider two complex numbers \( z_1 = 1 - i \) and \( z_2 = i \). The argument of \( z_1z_2 \) is:
Given the random variable \( X \) which takes the values 0, 1, 2, 7, 11, and 12 with the following probabilities: \[ P(X = 0) = 0.4, \quad P(X = 1) = 0.3, \quad P(X = 2) = 0.1, \quad P(X = 7) = 0.1, \quad P(X = 11) = ? \]
Find the sum of the series: \[ 1 + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \cdots \]
Given that \( \lambda \) is an eigenvalue of matrix \( A \) with the corresponding eigenvector \( x \), and \( x \) is also an eigenvector of \( B = A - 2I \), find the relationship between \( \lambda \) and the eigenvalue of \( B \).
Sequence of Reactions of Ethylene and Chlorine to form PVC:
Find the maximum value of the function \( f(x) = -x^3 + 2x^2 \) in the interval \( [-1, 1.5] \).
Which of the following are characteristics of steady flow?
What is the first stage of production of paper from wood?
Mean Residence Time Calculation for a given system: \[ t_m = \int_0^{\infty} t E(t) \, dt \] Where \( E(t) \) is the distribution function. For the given system, the distribution function is: \[ E(t) = 1 - 2t, \quad t \leq 0.5 \] \[ E(t) = 0, \quad t > 0.5 \]
Classify the following diameters into the corresponding categories:
Given the following parameters for a fluid flow, calculate the appropriate quantities: \[ V_0 = 1 \, \text{m/s}, \quad P_r = 7.01, \quad \nu = 10^{-6} \, \text{m}^2/\text{s} \] \[ S_{hn} = \frac{4.91}{\sqrt{Re_x}}, \quad \Delta x = 0.01 \, \text{m} \]