OpenSpecEngineering

Finds the flow and temperature of the stream you get when two streams mix, from a steady-state mass and energy balance. Pick a fluid for each stream to fill in its specific heat, or type your own. Use it to blend hot and cold water to a target temperature, to estimate a mixing-tee or tank outlet, or to check a process-flow diagram.

Equations

m_out = m₁ + m₂

T_out = (m₁·c_p1·T₁ + m₂·c_p2·T₂) / (m₁·c_p1 + m₂·c_p2)

m₁ and m₂ are the mass flows of the two inlet streams, T₁ and T₂ their temperatures, and c_p1 and c_p2 their specific heats. Mass is conserved, and the heat one stream gives up is the heat the other takes in [1], [2]. The flow fields take a mass, so enter the mass per second, per hour or per batch: the outlet comes out on the same basis, and the temperature doesn’t depend on which one you use. The fluid presets give c_p for water [3], glycol, oils and mercury [4], and alcohols and air [5], at the temperature named in each preset.

Limits and common mistakes

• The mixer is adiabatic: no heat lost to the surroundings, no work done, and no reaction.
• c_p is taken as constant over each stream’s temperature range. Choose the preset nearest the mean temperature.
• There is no phase change. Steam condensing into water, or a liquid flashing, needs enthalpies and latent heat, not c_p·T.
• Mixing two different liquids can release or absorb heat (acid into water is the usual case). The page ignores heat of mixing.
• Use mass flow, not volume flow. Convert liters per minute with the density first.

Worked example

A wash station blends 2 kg/s of hot water at 90 °C with 3 kg/s of mains water at 10 °C. What temperature reaches the spray header?

1. Enter Stream 1 Mass Flow (m₁) 2 kg and Stream 1 Temperature (T₁) 90 °C.
2. Choose Stream 1 Fluid Water, 90°C. The specific heat fills in as 4205 J/(kg·K).
3. Enter Stream 2 Mass Flow (m₂) 3 kg and Stream 2 Temperature (T₂) 10 °C.
4. Choose Stream 2 Fluid Water, 10°C, which fills in 4196 J/(kg·K).
5. Press Solve. The Solution shows: Outlet Mass Flow: 5 kg
   Outlet Temperature: 42.0411 °C
   Outlet Temperature: 315.191 K

The outlet flow is 5 kg/s. Check by hand: with equal specific heats the outlet would be the mass-weighted mean, (2 × 90 + 3 × 10)/5 = 42 °C. The hot water’s slightly higher c_p lifts that by 0.04 °C.