Solve a steady-state material balance for a two-stream mixer. Enter the mass flow and component-A mass fraction of each inlet stream, and the calculator returns the combined outlet flow, its composition, and the component-A flow rate using the overall and component balances.
The material balance is the first calculation in nearly every process design: what comes in must equal what goes out, plus whatever accumulates inside. This calculator solves the simplest but most common case — a steady-state mixer that combines two streams into one — by applying the overall mass balance and a component balance on species A. The same conservation logic scales up to entire flowsheets with reactors, separators, and recycles.
For any defined system boundary, the conservation of mass over a chosen time period is:
Input + Generation = Output + Consumption + Accumulation
Mass itself is neither generated nor consumed, so for total mass the generation and consumption terms are zero. At steady state nothing accumulates, which reduces the statement to the familiar "in = out". For an individual chemical species, generation and consumption can be nonzero if a reaction occurs — but in a non-reacting mixer they vanish too, so each component is also conserved.
For two inlet streams (mass flows m₁, m₂, A-fractions x₁, x₂) combining into outlet stream m₃ with fraction x₃:
Overall balance: m₃ = m₁ + m₂ Component-A balance: m₃·x₃ = m₁·x₁ + m₂·x₂
Solving the component balance for the outlet composition gives x₃ = (m₁x₁ + m₂x₂)/m₃. The component-A mass flow rate is simply m₁x₁ + m₂x₂, and the remaining component (B) flow follows from m₃ − (component-A flow). This calculator evaluates all three.
A material-balance problem is solvable only when the number of independent balance equations equals the number of unknowns — a zero degrees-of-freedom analysis. For this two-stream mixer there are two independent balances (overall plus one component, since the second component balance is not independent). With all four inlet quantities specified, the two outlet unknowns (m₃ and x₃) are exactly determined. If you instead knew an outlet quantity and were missing an inlet, the same two equations would back-solve for it. Counting variables, specifications, and independent equations before calculating is the key discipline for larger flowsheets.
Many balance problems give only compositions or ratios, not absolute flows. The standard technique is to choose a convenient basis — 100 kg of feed, 1 hour of operation, or 100 mol of a key stream — carry the calculation through on that basis, and scale the answer to actual conditions at the end. A well-chosen basis (often the stream with the most information) turns a fractional problem into simple arithmetic. Because this calculator works in mass flow rates (kg/h), the basis is one hour of steady operation.
Steady state means the amount of material inside the system is constant in time — nothing accumulates or depletes. The general balance Input + Generation = Output + Consumption + Accumulation then loses the accumulation term, and for non-reacting systems the generation and consumption terms vanish too, leaving the simple statement that total mass in equals total mass out, which this mixer calculator applies.
The overall balance accounts for total mass: m₃ = m₁ + m₂. A component balance tracks one species, e.g. component A: m₃x₃ = m₁x₁ + m₂x₂. For a mixture you can write one overall balance plus one balance per component, but they are not all independent — the overall balance equals the sum of the component balances, so for two components you have only two independent equations.
Perform a degrees-of-freedom analysis: count the unknown stream variables, subtract the number of independent balance equations and any extra specifications (given compositions, ratios, conversions). Zero degrees of freedom means the problem is exactly solvable; a positive number means you need more information, and a negative number means it is over-specified or inconsistent.
A mass fraction is the mass of one component divided by the total mass, so by definition all the component fractions in a stream must add up to exactly 1 (or 100%). Each fraction must also lie between 0 and 1. This calculator warns if a fraction falls outside that range, since a value below 0 or above 1 is physically impossible and points to a data-entry error.
This tool is a non-reacting, two-stream mixer, so it uses pure conservation with no generation or consumption. For reactors you add generation/consumption terms tied to the reaction stoichiometry and conversion. For multi-stream units, separators, or flowsheets with recycle, you write a balance around each unit (or the overall system) and solve the resulting set of equations simultaneously.