Consider the psychrometric process denoted by the straight line from state 1 to 2 in the figure. The specific humidity, Dry Bulb Temperature (DBT), and Wet Bulb Temperature (WBT) at the two states are shown in the table. The latent heat of vaporization of water \( h_{fg} = 2440 \, {kJ/kg} \). If the flow rate of air is 1 kg/s, the rate of heat transfer from the air is_________kW (rounded off to two decimal places).
Water of density \( \rho = 1000 \, {kg/m}^3 \) flows with a velocity \( V = 50 \, {m/s} \) through a 180° curved tube of uniform cross-section as shown in the figure. If the flow rate is \( 0.06 \, {m}^3/{s} \), the magnitude of the reaction force \( F_x \) required to keep it stationary is ________ kN (rounded off to one decimal place).
A tank with a constant water level of 4 m above the centreline of an opening of diameter 100 mm is shown in the figure. Neglect all losses and assume \( g = 9.81 \, {m/s}^2 \). The discharge through the opening is ________ litres/s (answer in integer).
While doing Bayesian inference, consider estimating the posterior distribution of the model parameter (m), given data (d). Assume that Prior and Likelihood are proportional to Gaussian functions given by \[ {Prior} \propto \exp(-0.5(m - 1)^2) \] \[ {Likelihood} \propto \exp(-0.5(m - 3)^2) \] 
The mean of the posterior distribution is (Answer in integer)
Consider a medium of uniform resistivity with a pair of source and sink electrodes separated by a distance \( L \), as shown in the figure. The fraction of the input current \( (I) \) that flows horizontally \( (I_x) \) across the median plane between depths \( z_1 = \frac{L}{2} \) and \( z_2 = \frac{L\sqrt{3}}{2} \), is given by \( \frac{I_x}{I} = \frac{L}{\pi} \int_{z_1}^{z_2} \frac{dz}{(L^2/4 + z^2)} \). The value of \( \frac{I_x}{I} \) is equal to 
Suppose a mountain at location A is in isostatic equilibrium with a column at location B, which is at sea-level, as shown in the figure. The height of the mountain is 4 km and the thickness of the crust at B is 1 km. Given that the densities of crust and mantle are 2700 kg/m\(^3\) and 3300 kg/m\(^3\), respectively, the thickness of the mountain root (r1) is km. (Answer in integer)