Question

In engineering applications, the steady-flow mixing of two streams of the same fluid is another common process. The section where the mixing process takes place is referred to as a mixing chamber, as shown in Figure Q4. The mass flow rate and the energy of the flowing fluid for the inlets, are shown in the figure. Knowing that the amount of heat loss to the surrounding is 5.5 kW. Determine the energy carried from this rigid mixing chamber by the fluid mixture per unit mass of fluid, in kJ/kg. Cold stream 15 kg/s 50 kJ/kg 1 Hot stream 5 kg/s 150 kJ/kg

Answer 1

Given Mass flow rate of the hot fluid, m= 5 kg/s Energy carried per unit mass by the hot fluid, e; = 150 kJ/kg Mass flow rate of the cold fluid, m, = 15 kg/s Energy carried per unit mass by the cold fluid, ez = 50 kJ/kg Rate of Heat loss, Q = 5.5 kW Taking the mixing chamber as our control volume and applying the principle of conservation of mass to the steady state mixing process Rate at which mass entering the mixing chamber = Rate at which mass leaving the mixing chamber Or m + m2 = m3 Where, mz is the mass flow rate of the fluid mixture leaving the mixing chamber Substituting the known values m3 = 15 + 5 = 20 kg/s Applying energy balance to the steady state mixing process Rate at which energy enters the mixing chamber = Rate at which energy leaves the mixing chamber + Energy lost Mathematically, me + mzez = m3e3 + Q Where, ez is the rate at which energy is carried by the fluid mixture. Or mzeg = me+ m,ez -

Or me + mze - Q тз Substituting the known values (5 x 150) + (15 x 50) – 5.5 ez = 74.725 kJ/kg 20 Energy carried by the fluid mixture per unit mass of the fluid = 74.725 kJ/kg