ANS:C - Both (a) & (b)

In atomization of fuel oil through a pressure jet burner, both the output (or flow rate) and the velocity of the fuel oil vary as the square root of oil pressure. Here's the explanation for both (a) and (b): (a) Output & fineness: The output or flow rate of fuel oil through the pressure jet burner nozzle is directly related to the oil pressure. As the oil pressure increases, the flow rate of fuel oil also increases. Additionally, the fineness of atomization, which refers to the degree to which the fuel oil is broken up into small droplets, is influenced by the oil pressure. Higher oil pressure typically results in finer atomization, leading to smaller fuel droplets being formed. Both the output (flow rate) and fineness of atomization are crucial factors in achieving efficient combustion in the burner. (b) Velocity: The velocity of the fuel oil exiting the nozzle of the pressure jet burner also varies as the square root of oil pressure. As the oil pressure increases, the velocity of the fuel oil exiting the nozzle also increases. This relationship is governed by the Bernoulli's principle, which states that an increase in fluid pressure results in a decrease in fluid velocity, and vice versa. Since the velocity varies as the square root of pressure, doubling the oil pressure would result in a √2 (or approximately 1.41) times increase in velocity. Therefore, both the output (flow rate) and fineness of atomization, as well as the velocity of the fuel oil, vary as the square root of oil pressure during atomization through a pressure jet burner.