A hair dryer is a duct of constant diameter in which a few layers of electrical resistors are placed. A small fan draws air in and forces it past the resistors, where it heats up. If the density of the air is 1.2 kg/m3 at the inlet and 0.98 kg/m3 at the outlet, determine the percentage increase in air velocity as it flows through the dryer.

To determine the percentage increase in air velocity as it flows through the hair dryer, you can use the principle of conservation of mass, which states that the mass entering a system must equal the mass exiting the system. In this case, we can assume that the mass of air entering the hair dryer is equal to the mass of air exiting the hair dryer. Since density (ρ) is defined as mass (m) per unit volume (V), we can express this as: ρ_inlet * V_inlet = ρ_outlet * V_outlet Where: ρ_inlet = density of air at the inlet (1.2 kg/m³) ρ_outlet = density of air at the outlet (0.98 kg/m³) V_inlet = velocity of air at the inlet (initial velocity) V_outlet = velocity of air at the outlet (final velocity) We want to find the percentage increase in air velocity, which can be expressed as: Percentage Increase = [(V_outlet - V_inlet) / V_inlet] * 100 Rearrange the conservation of mass equation to solve for V_outlet: V_outlet = (ρ_inlet / ρ_outlet) * V_inlet Now, plug in the given values: V_outlet = (1.2 kg/m³ / 0.98 kg/m³) * V_inlet V_outlet = 1.2245 * V_inlet Now, calculate the percentage increase in velocity: Percentage Increase = [(V_outlet - V_inlet)/v-inlet]*100% =(1.2254V_inlet-v_inlet)/v_inlet* 100 =22.54%